Size-dependent axisymmetric vibration of functionally graded circular plates in bifurcation/limit point instability

Science.gov (United States)

Ashoori, A. R.; Vanini, S. A. Sadough; Salari, E.

2017-04-01

In the present paper, vibration behavior of size-dependent functionally graded (FG) circular microplates subjected to thermal loading are carried out in pre/post-buckling of bifurcation/limit-load instability for the first time. Two kinds of frequently used thermal loading, i.e., uniform temperature rise and heat conduction across the thickness direction are considered. Thermo-mechanical material properties of FG plate are supposed to vary smoothly and continuously throughout the thickness based on power law model. Modified couple stress theory is exploited to describe the size dependency of microplate. The nonlinear governing equations of motion and associated boundary conditions are extracted through generalized form of Hamilton's principle and von-Karman geometric nonlinearity for the vibration analysis of circular FG plates including size effects. Ritz finite element method is then employed to construct the matrix representation of governing equations which are solved by two different strategies including Newton-Raphson scheme and cylindrical arc-length method. Moreover, in the following a parametric study is accompanied to examine the effects of the several parameters such as material length scale parameter, temperature distributions, type of buckling, thickness to radius ratio, boundary conditions and power law index on the dimensionless frequency of post-buckled/snapped size-dependent FG plates in detail. It is found that the material length scale parameter and thermal loading have a significant effect on vibration characteristics of size-dependent circular FG plates.

Closed solutions to a differential-difference equation and an associated plate solidification problem.

Science.gov (United States)

Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

2016-01-01

Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

Solution of the two- dimensional heat equation for a rectangular plate

Directory of Open Access Journals (Sweden)

Nurcan BAYKUŞ SAVAŞANERİL

2015-11-01

Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.

A form of MHD universal equations of unsteady incompressible fluid flow with variable elctroconductivity on heated moving plate

Directory of Open Access Journals (Sweden)

Boričić Zoran

2005-01-01

Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.

Pullback attractors for a singularly nonautonomous plate equation

Directory of Open Access Journals (Sweden)

Vera Lucia Carbone

2011-06-01

Full Text Available We consider the family of singularly nonautonomous plate equations with structural damping $$ u_{tt} + a(t,xu_t - Delta u_t + (-Delta^2 u + lambda u = f(u, $$ in a bounded domain $Omega subset mathbb{R}^n$, with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in $H^2_0(Omega imes L^2(Omega$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

Experimental study of the conventional equation to determine a plate's moment of inertia

International Nuclear Information System (INIS)

Pintao, Carlos A F; Filho, Moacir P de Souza; Grandini, Carlos R; Hessel, Roberto

2004-01-01

In this work, we describe an experimental setup in which an electric current is used to determine the angular velocity attained by a plate rotating around a shaft in response to a torque applied for a given period. Based on this information, we show how the moment of inertia of a plate can be determined using a procedure that differs considerably from the ones most commonly used, which generally involve time measurements. Some experimental results are also presented which allow one to determine parameters such as the exponents and constant of the conventional equation of a plate's moment of inertia

Investigating wake patterns and propulsive frequencies of a flat plate under pitching motion

Science.gov (United States)

Moubogha Moubogha, Joseph; Astolfi, Jacques Andre

Fundamental mechanisms of swimming are explored using a simple geometry device - flat plate - in pure-pitching motion in a hydrodynamic tunnel. The experiments are carried out at different Reynolds numbers based on the plate length c. Pitching motion is generated for reduced frequencies k between 0 and 2 and for an angular amplitude of 10 deg. Velocity fields are obtained in the wake of the plate using Particle Image Velocimetry and measurements of drag coefficients are estimated from mean velocity profiles. This study confirms the occurrence of a threshold oscillation frequency beyond which the plate enters a propulsive regime and the wake features organized structures. In this case an inversion of the typical Karman vortex street is observed. The evolution of mean transverse velocity profiles in the wake of the plate shows that the usual wake profile with velocity deficit - plate with drag - can be transformed into a jet - plate with thrust - above a certain reduced frequency. Phd Student Mechanical Engineering Departement.

Approaches for Reduced Order Modeling of Electrically Actuated von Karman Microplates

KAUST Repository

Saghir, Shahid; Younis, Mohammad I.

2016-01-01

and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate

Initially Imperfect MEMS Microplates Under Electrostatic Actuation: Theory and Experiment

KAUST Repository

Saghir, Shahid

2016-12-05

Microplates are building blocks of many Micro-Electro-Mechanical Systems (MEMS). It is common for them to undergo imperfections due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat plates and cannot be modeled using the governing equations of flat plates. In this article, we adopt the governing equations of imperfect plates employing the modified von-Karman strains. These equations then are used to develop a Reduced Order Model based on the Galerkin procedure to simulate the static and dynamic behavior of an electrostatically actuated microplate. Also, microplates made of silicon nitride are fabricated and tested. First, the static behaviour of the microplate is investigated when applying a static voltage Vdc. To study the dynamic behaviour we apply a harmonic voltage, Vac, superimposed to Vdc. Simulation results show good agreement with the experimentally measured responses.

The solutions of Navier-Stokes equations in squeezing flow between parallel plates

Czech Academy of Sciences Publication Activity Database

Petrov, A. G.; Kharlamova, Irina

2014-01-01

Roč. 48, November–December (2014), s. 40-48 ISSN 0997-7546 Grant - others:Russian Foundation for Basic Research(RU) 14-01- 00818; Russian Foundation for Basic Research(RU) 14-01-00892 Institutional support: RVO:67985874 Keywords : closed form solution * Navier-Stokes equations * squeezing flow between plates * counterflow Subject RIV: BK - Fluid Dynamics Impact factor: 1.656, year: 2014

Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions

International Nuclear Information System (INIS)

Di Cristo, M; Lin, C-L; Morassi, A; Rosset, E; Vessella, S; Wang, J-N

2013-01-01

We prove the upper and lower estimates of the area of an unknown elastic inclusion in a thin plate by one boundary measurement. The plate is made of non-homogeneous linearly elastic material belonging to a general class of anisotropy and the domain of the inclusion is a measurable subset of the plate. The size estimates are expressed in terms of the work exerted by a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate. The main new mathematical tool is a doubling inequality for solutions to fourth-order elliptic equations whose principal part P(x, D) is the product of two second-order elliptic operators P 1 (x, D), P 2 (x, D) such that P 1 (0, D) = P 2 (0, D). The proof of the doubling inequality is based on the Carleman method, a sharp three-spheres inequality and a bootstrapping argument. (paper)

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

Science.gov (United States)

Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Hydrodynamical and magnetohydrodynamic global bifurcations in a highly turbulent von Karman flow; Bifurcations globales hydrodynamiques et magnetohydrodynamiques dans un ecoulement de von Karman turbulent

Energy Technology Data Exchange (ETDEWEB)

Ravelet, F

2005-09-15

We report experimental studies of the turbulent von Karman flow, inertially stirred between counter-rotating impellers. We first study the flow and its transition from laminar to turbulent regime. We highlight the role of slowly varying large scales, due to the presence of an azimuthal mixing layer. The large scales of this flow can be unstable in turbulent regime. We study the statistics of the transitions between the different mean states. The second part is dedicated to an experiment in liquid sodium, called VKS2. We optimize the time-averaged flow in order to allow kinematic dynamo action. We report the very first results of the experiment, and discuss the role of the large scales temporal non-stationariness. (author)

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African Journals Online (AJOL)

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plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

A Powerful Friendship: Theodore von Karman and Hugh L. Dryden

Science.gov (United States)

Gorn, Michael

2003-01-01

During their long personal friendship and professional association, Theodore von Karman (1882-1963) and Hugh L. Dryden (1898-1965) exercised a pivotal if somewhat elusive influence over American aeronautics and spaceflight. Both decisive figures in organizing scientists and engineers at home and abroad, both men of undisputed eminence in their technical fields, their range of contacts in government, academia, the armed forces, industry, and professional societies spanned the globe to an extent unparalleled then as now. Moreover, because they coordinated their activities closely, their combined influence far exceeded the sum of each one s individual contributions. This paper illustrates their personal origins as well as the foundations of their friendship, how their relationship became a professional alliance, and their joint impact on the world of aeronautics and astronautics during the twentieth century.

Bending and stretching of plates

CERN Document Server

Mansfield, E H; Hemp, W S

1964-01-01

The Bending and Stretching of Plates deals with elastic plate theory, particularly on small- and large-deflexion theory. Small-deflexion theory concerns derivation of basic equations, rectangular plates, plates of various shapes, plates whose boundaries are amenable to conformal transformation, plates with variable rigidity, and approximate methods. Large-deflexion theory includes general equations and some exact solutions, approximate methods in large-deflexion theory, asymptotic large-deflexion theories for very thin plates. Asymptotic theories covers membrane theory, tension field theory, a

Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations

Energy Technology Data Exchange (ETDEWEB)

Singhatanadgid, Pairod; Jommalai, Panupan [Chulalongkorn University, Bangkok (Thailand)

2016-05-15

The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.

Hydrodynamical and magnetohydrodynamic global bifurcations in a highly turbulent von Karman flow

International Nuclear Information System (INIS)

Ravelet, F.

2005-09-01

We report experimental studies of the turbulent von Karman flow, inertially stirred between counter-rotating impellers. We first study the flow and its transition from laminar to turbulent regime. We highlight the role of slowly varying large scales, due to the presence of an azimuthal mixing layer. The large scales of this flow can be unstable in turbulent regime. We study the statistics of the transitions between the different mean states. The second part is dedicated to an experiment in liquid sodium, called VKS2. We optimize the time-averaged flow in order to allow kinematic dynamo action. We report the very first results of the experiment, and discuss the role of the large scales temporal non-stationariness. (author)

Cálculo numérico y analítico de las ecuaciones de Karman-Prandtl para la estimación de coeficiente de fricción

OpenAIRE

Escobar Zamora, Iván

2014-01-01

El objetivo de este PFC es el desarollo, adaptación y aplicación de diferentes métodos numéricos para la resolución de las ecuaciones de Karman-Prandtl. Se realizará un estudio de los diferentes métodos numéricos para la resolución de ecuaciones y sistemas de ecuaciones diferenciales ordinarias, así como para la resolución de sistemas de ecuaciones no lineales. Se aplicarán dentro del campo de la Ingeniería Naval, en particular se buscará aproximar las ecuaciones de Karman-P...

Initially curved microplates under electrostatic actuation: theory and experiment

KAUST Repository

Saghir, Shahid

2016-07-01

Microplates are the building blocks of many micro-electro-mechanical systems. It is common for them to experience initial curvature imperfection due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat ones and cannot be modeled using flat plate models. In this paper, we adopt a dynamic analog of the von Karman governing equations of imperfect plates. These equations are then used to develop a reduced order model based on the Galerkin procedure, to simulate the static and dynamic behavior of the microplate under electrostatic actuation. To validate the simulation results, an initially curved imperfect microplate made of silicon nitride is fabricated and tested. The static behaviour of the microplate is investigated when applying a DC voltage Vdc. Then, the dynamic behaviour of the microplate is examined under the application of a harmonic AC voltage, Vac, superimposed to Vdc. The simulation results show good agreement with the experimentally measured responses. © 2016 IOP Publishing Ltd.

PIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches

Science.gov (United States)

Guissart, A.; Bernal, L. P.; Dimitriadis, G.; Terrapon, V. E.

2017-05-01

This work presents, compares and discusses results obtained with two indirect methods for the calculation of aerodynamic forces and pitching moment from 2D Particle Image Velocimetry (PIV) measurements. Both methodologies are based on the formulations of the momentum balance: the integral Navier-Stokes equations and the "flux equation" proposed by Noca et al. (J Fluids Struct 13(5):551-578, 1999), which has been extended to the computation of moments. The indirect methods are applied to spatio-temporal data for different separated flows around a plate with a 16:1 chord-to-thickness ratio. Experimental data are obtained in a water channel for both a plate undergoing a large amplitude imposed pitching motion and a static plate at high angle of attack. In addition to PIV data, direct measurements of aerodynamic loads are carried out to assess the quality of the indirect calculations. It is found that indirect methods are able to compute the mean and the temporal evolution of the loads for two-dimensional flows with a reasonable accuracy. Nonetheless, both methodologies are noise sensitive, and the parameters impacting the computation should thus be chosen carefully. It is also shown that results can be improved through the use of dynamic mode decomposition (DMD) as a pre-processing step.

The baffle influence on sound radiation characteristics of a plate

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Bao Liu

2017-01-01

Full Text Available The acoustic radiation characteristics of the baffle plates and unbaffle plates are calculated and compared by single-layer potential and double-layer potential. Based on the boundary integral equation, the sound pressure integral equation of the baffle and the baffle are deduced respectively. According to the boundary compatibility condition, the sound pressure and the vibration velocity of the plates are obtained. Further, the dynamic equation of the structure is substituted into the vibration equation in the form of the baffle plate and the baffle plate. The sound pressure difference and the displacement of a plate surface are in the form of the vibration mode superposition and the acoustic radiation impedance of the double integral form is obtained, which determines vibration mode coefficient and sound radiation parameters. The effect of the baffle on the acoustic radiation characteristics of the thin plate is analyzed by comparing the acoustic radiation parameters with the simple and simple rectangular plate in water.

Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

International Nuclear Information System (INIS)

Bucci, Francesca; Toundykov, Daniel

2010-01-01

The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

Analysis of hydraulic instability of ANS involute fuel plates

International Nuclear Information System (INIS)

Sartory, W.K.

1991-11-01

Curved shell equations for the involute Advanced Neutron Source (ANS) fuel plates are coupled to two-dimensional hydraulic channel flow equations that include fluid friction. A complete set of fluid and plate boundary conditions is applied at the entrance and exit and along the sides of the plate and the channel. The coupled system is linearized and solved to assess the hydraulic instability of the plates

Strain resolving method of composite plane plates

Directory of Open Access Journals (Sweden)

Ion FUIOREA

2011-06-01

Full Text Available The paper deals with the extension of isotropic plates problem to the case of composite plates. In order to perform it, the Kirchhoff-Love hypotheses were “softened” by some additional ones. Considering the constitutive laws for composite materials the stress functions were eliminated by using Cauchy equations. As a result a partial derivative equation in displacements was obtained. Finally the boundary condition formulation was extended for the case of complex composite plates.

Stochastic analysis of laminated composite plates on elastic foundation: The cases of post-buckling behavior and nonlinear free vibration

International Nuclear Information System (INIS)

Singh, B.N.; Lal, Achchhe

2010-01-01

This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C 0 nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.

Modeling particulate removal in plate-plate and wire-plate electrostatic precipitators

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S Ramechecandane

2016-09-01

Full Text Available The present study is concerned with the modeling of electrically charged particles in a model plate-plate and a single wire-plate electrostatic precipitator (ESP. The particle concentration distributions for both a plate-plate and a wire-plate ESP are calculated using a modified drift flux model. Numerical investigations are performed using the modified drift flux model for particle number concentration, in addition to the RNG k - ε model for the mean turbulent flow field and the Poisson equation for the electric field. The proposed model and the outlined methodology for coupling the flow field, electric field, charging kinetics and particle concentration is applied to two model precipitators that are truly representative of a wide class of commercialized ESPs. The present investigation is quite different from the earlier studies as it does not make assumptions like a homogeneous electric field or an infinite turbulent diffusivity. The electric field calculated is a strong function of position and controls the migration velocity of particles. Hence, the proposed model can be implemented in a flow solver to obtain a full-fledged solution for any kind of ESP with no limitations on the particle number concentration, as encountered in a Lagrangian approach. The effect of turbulent diffusivity on particle number concentration in a plate-plate ESP is investigated in detail and the results obtained are compared with available experimental data. Similarly, the effect of particle size/diameter and applied electric potential on the accumulative collection performance in the case of a wire-plate ESP is studied and the results obtained are compared with available numerical data. The numerical results obtained using the modified drift flux model for both the plate-plate and wire-plate ESP are in close agreement with available experimental and numerical data.

Vibration analysis of partially cracked plate submerged in fluid

Science.gov (United States)

Soni, Shashank; Jain, N. K.; Joshi, P. V.

2018-01-01

The present work proposes an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium. The governing equation of motion for the isotropic plate based on the classical plate theory is modified to accommodate a part through continuous line crack according to simplified line spring model. The influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations. Both partially and totally submerged plate configurations are considered. The governing equation also considers the in-plane stretching due to lateral deflection in the form of in-plane forces which introduces geometric non-linearity into the system. The fundamental frequencies are evaluated by expressing the lateral deflection in terms of modal functions. The assessment of the present results is carried out for intact submerged plate as to the best of the author's knowledge the literature lacks in analytical results for submerged cracked plates. New results for fundamental frequencies are presented as affected by crack length, fluid level, fluid density and immersed depth of plate. By employing the method of multiple scales, the frequency response and peak amplitude of the cracked structure is analyzed. The non-linear frequency response curves show the phenomenon of bending hardening or softening and the effect of fluid dynamic pressure on the response of the cracked plate.

Finite element modeling of penetration of rigid cylindrical bar impacting on a clamped circular plate, employing a strain rate dependent flow rate and a Gruneisen equation of state

International Nuclear Information System (INIS)

Tariq, M.; Khan, I.A.

2003-01-01

A time dependent Finite Element simulation of penetration of a rigid cylindrical bar impacting on a copper plate is conducted, to demonstrate how material behavior appears to change when Johnson-Cook plasticity rule is employed along with a Gruneisen, equation of state with cubic shock velocity-particle relationship, and defining pressure both for compressed and expanded materials, as compared to the behavior when only isotropic strain-hardening model is employed. The bar impacts the plate with a velocity of 1000 m/s, and penetrates the plate, a portion of it coming out of the other side. Results are obtained and compared taking both an isotropic strain-hardening model, and a model incorporating Johnson-Cook flow rule along with Gruneisen equation of state. (author)

Vibration modes of a single plate with general boundary conditions

Directory of Open Access Journals (Sweden)

Phamová L.

2016-06-01

Full Text Available This paper deals with free flexural vibration modes and natural frequencies of a thin plate with general boundary conditions — a simply supported plate connected to its surroundings with torsional springs. Vibration modes were derived on the basis of the Rajalingham, Bhat and Xistris approach. This approach was originally used for a clamped thin plate, so its adaptation was needed. The plate vibration function was usually expressed as a single partial differential equation. This partial differential equation was transformed into two ordinary differential equations that can be solved in the simpler way. Theoretical background of the computations is briefly described. Vibration modes of the supported plate with torsional springs are presented graphically and numerically for three different values of stiffness of torsional springs.

Dynamic coupled piezothermoelasticity of pyroelectric composite plate

International Nuclear Information System (INIS)

Heidary, F.; Reza Eslami, M.

2005-01-01

The equations governing the linear response of coupled piezothermolelastic composite plate, considering the pyroelectric effect, are outlined in this paper. The finite element method with linear shape functions for a first-order shear deformation theory of laminated plates is used to obtain the defections and temperature. The finite element equations are developed for piezothermoelectric sensor and actuator. The governing equations are solved using the time marching method. Numerical results are presented for the conventional active direct proportional control of the plate. Controlled and uncontrolled displacements and temperature responses are graphically illustrated. the corresponding temperature response with consideration of the pyroelectric effects is also presented. Dynamic case studies are carried out to observe the pyroelectric effects in the piezothermoelastic control systems. (authors)

Modelling of CMUTs with Anisotropic Plates

DEFF Research Database (Denmark)

la Cour, Mette Funding; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt

2012-01-01

Traditionally, CMUTs are modelled using the isotropic plate equation and this leads to deviations between analytical calculations and FEM simulations. In this paper, the deflection profile and material parameters are calculated using the anisotropic plate equation. It is shown that the anisotropic...... calculations match perfectly with FEM while an isotropic approach causes up to 10% deviations in deflection profile. Furthermore, we show how commonly used analytic modelling methods such as static calculations of the pull-in voltage and dynamic modelling through an equivalent circuit representation can...

Application of generalized function to dynamic analysis of thick plates

International Nuclear Information System (INIS)

Zheng, D.; Weng, Z.

1987-01-01

The structures with thick plates have been used extensively in national defence, mechanical engineering, chemical engineering, nuclear engineering, civil engineering, etc.. Various theories have been established to deal with the problems of elastic plates, which include the classical theory of thin plates, the improved theory of thick plates, three-dimensional elastical theory. In this paper, the derivative of δ-function is handled by using the generalized function. The dynamic analysis of thick plates subjected the concentrated load is presented. The improved Donnell's equation of thick plates is deduced and employed as the basic equation. The generalized coordinates are solved by using the method of MWR. The general expressions for the dynamic response of elastic thick plates subjected the concentrated load are given. The numerical results for rectangular plates are given herein. The results are compared with those obtained from the improved theory and the classical theory of plates. (orig./GL)

Theories for Elastic Plates via Orthogonal Polynomials

DEFF Research Database (Denmark)

Krenk, Steen

1981-01-01

A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori......, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending...... of transversely isotropic plates. This theory has three boundary conditions, like Reissner's, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations...

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

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Vladimir P. Gerdt

2006-05-01

Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

NATURAL TRANSVERSE VIBRATIONS OF A PRESTRESSED ORTHOTROPIC PLATE-STRIPE

Directory of Open Access Journals (Sweden)

Egorychev Oleg Aleksandrovich

2012-10-01

Full Text Available The article represents a new outlook at the boundary-value problem of natural vibrations of a homogeneous pre-stressed orthotropic plate-stripe. In the paper, the motion equation represents a new approximate hyperbolic equation (rather than a parabolic equation used in the majority of papers covering the same problem describing the vibration of a homogeneous orthotropic plate-stripe. The proposed research is based on newly derived boundary conditions describing the pin-edge, rigid, and elastic (vertical types of fixing, as well as the boundary conditions applicable to the unfixed edge of the plate. The paper contemplates the application of the Laplace transformation and a non-standard representation of a homogeneous differential equation with fixed factors. The article proposes a detailed representation of the problem of natural vibrations of a homogeneous orthotropic plate-stripe if rigidly fixed at opposite sides; besides, the article also provides frequency equations (no conclusions describing the plate characterized by the following boundary conditions: rigid fixing at one side and pin-edge fixing at the opposite side; pin-edge fixing at one side and free (unfixed other side; rigid fixing at one side and elastic fixing at the other side. The results described in the article may be helpful if applied in the construction sector whenever flat structural elements are considered. Moreover, specialists in solid mechanics and theory of elasticity may benefit from the ideas proposed in the article.

Investigation of acoustic field near to elastic thin plate using integral method

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В.І. Токарев

2004-01-01

Full Text Available  Investigation of acoustic field near to elastic thin plate using  integral method The influence of boundary conditions on sound wave propagation, radiation and transmission through thin elastic plate is investigated. Necessary for that numerical model was found using the Helmholtz equation and equation of oscilated plate by means of integral formulation of the solution for acoustic fields near to elastic thin plate and for bending waves of small amplitudes.

Capacity of the circular plate condenser: analytical solutions for large gaps between the plates

International Nuclear Information System (INIS)

Rao, T V

2005-01-01

A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to O(τ -(2N+1) ) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to O(τ -9 ). Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the O(τ -9 ) approximation predicts the capacity extremely well for any τ ≥ 2 and an O(τ -3 ) approximation gives, for all practical purposes, results of adequate accuracy for τ ≥ 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to O(τ -6 ) for τ ≥ 2

Natural Convective Heat Transfer from Narrow Plates

CERN Document Server

Oosthuizen, Patrick H

2013-01-01

Natural Convective Heat Transfer from Narrow Plates deals with a heat transfer situation that is of significant practical importance but which is not adequately dealt with in any existing textbooks or in any widely available review papers. The aim of the book is to introduce the reader to recent studies of natural convection from narrow plates including the effects of plate edge conditions, plate inclination, thermal conditions at the plate surface and interaction of the flows over adjacent plates. Both numerical and experimental studies are discussed and correlation equations based on the results of these studies are reviewed.

Global collapse and J integral analysis for inner-diameter defected curved plates in tension

International Nuclear Information System (INIS)

Hertelé, Stijn; Verstraete, Matthias; Denys, Rudi; De Waele, Wim

2013-01-01

Reference stress equations are widely used to predict both the limit load and the J integral response of defected structures. Their validity is key to performing a safe assessment of structural integrity (plastic collapse and fracture). An analytical reference stress equation based upon global collapse has recently been developed for curved plates with a part-through defect located at the inner diameter surface. This equation predicts decreasing reference stress values as plate curvature increases. To qualify the predictions, the authors have performed a series of finite element analyses covering a wide range of possible geometries. This paper compares the numerically obtained limit loads and J integral responses with the analytical predictions of the reference stress equation. The finite element results generally confirm the decrease of reference stress with increasing plate curvature. Highly pronounced differences may occur between flat plates and slightly curved plates. Overall, the analytically predicted decrease in reference stress is overestimated for small defects but is representative for larger defects. -- Highlights: • A reference stress equation for inner-diameter defected curved plates in tension was developed earlier. • The equation predicts a lower reference stress as plate curvature increases. • The analytical predictions are validated through finite element analysis. • Collapse and J integral are insensitive to curvature for small defects. • For large defects, the analytically predicted trend is confirmed

Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...

Bifurcation of cubic nonlinear parallel plate-type structure in axial flow

International Nuclear Information System (INIS)

Lu Li; Yang Yiren

2005-01-01

The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of plate-type beam in axial flow was established. The partial differential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to in our analysis. The results show that there's no Hopf bifurcation for simply supported plate-type beams while the cantilevered plate-type beams has. At last, the analytic expression of critical flow velocity of cantilevered plate-type beams in axial flow and the purely imaginary eigenvalues of the corresponding linear system were gotten. (authors)

Modeling of plates with multiple anisotropic layers and residual stress

DEFF Research Database (Denmark)

Engholm, Mathias; Pedersen, Thomas; Thomsen, Erik Vilain

2016-01-01

Usually the analytical approach for modeling of plates uses the single layer plate equation to obtain the deflection and does not take anisotropy and residual stress into account. Based on the stress–strain relation of each layer and balancing stress resultants and bending moments, a general...... multilayered anisotropic plate equation is developed for plates with an arbitrary number of layers. The exact deflection profile is calculated for a circular clamped plate of anisotropic materials with residual bi-axial stress.From the deflection shape the critical stress for buckling is calculated......, and an excellent agreement between the two models is seen with a relative difference of less than 2% for all calculations. The model was also used to extract the cell capacitance, the parasitic capacitance and the residual stress of a pressure sensor composed of a multilayered plate of silicon and silicon oxide...

The Interaction between the Plane Wave and the Plate with Limited Height in Soil

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N.A. Lokteva

2017-03-01

Full Text Available A solution of the two-dimensional task on interaction between the harmonic wave and the plate with the limited height in soil has been provided. The plate surrounded on both sides with the half-spaces filled with soil medium has been used as a vibro-absorbing obstacle. The mechanical behavior of the plate has been described by S.P. Timoshenko's shift model and the mechanical behavior of soil by a linear elasticity theory equation. The main purpose of the paper is to determine the total acceleration vector field inducted by the penetrated and radiated waves in the second half-space. The mathematical formulation of the task includes a model of upcoming wave, soil medium and plate movement equation, infinity conditions, and conditions of soil contact with obstacle. Conditions of free slip have been taken as the contact conditions between the soil and the obstacle. We have considered a closed system of equations, which includes wave equations for scalar and vector potentials, elasticity theory equations for soil mediums, Koshi's relations, physical law, and plate movement equation. The boundary conditions for the plate correspond to a hinged support. To solve this task, all functions have been expanded in trigonometric series that allowed to obtain potential values in the coefficients of the series. To define the integrations constants, the contact conditions between the obstacle and soil have been used. On the basis of the revealed potentials, we have defined displacements on the boundary between the plate and soil and in other points of the second half-space. The vibro-absorbing properties of the plate have been investigated depending on the frequency of the harmonic wave falling on the plate. From the practical point of view, this task is related to protection of buildings from vibrations formed at a distance from underground railways.

Theory of the propagation dynamics of spiral edges of diffusion flames in von Karman swirling flows

Energy Technology Data Exchange (ETDEWEB)

Urzay, Javier; Williams, Forman A. [Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093-0411 (United States); Nayagam, Vedha [National Center for Space Exploration Research, NASA Glenn Research Center, Cleveland, OH 44135 (United States)

2011-02-15

This analysis addresses the propagation of spiral edge flames found in von Karman swirling flows induced in rotating porous-disk burners. In this configuration, a porous disk is spun at a constant angular velocity in an otherwise quiescent oxidizing atmosphere. Gaseous methane is injected through the disk pores and burns in a flat diffusion flame adjacent to the disk. Among other flame patterns experimentally found, a stable, rotating spiral flame is observed for sufficiently large rotation velocities and small fuel flow rates as a result of partial extinction of the underlying diffusion flame. The tip of the spiral can undergo a steady rotation for sufficiently large rotational velocities or small fuel flow rates, whereas a meandering tip in an epicycloidal trajectory is observed for smaller rotational velocities and larger fuel flow rates. A formulation of this problem is presented in the equidiffusional and thermodiffusive limits within the framework of one-step chemistry with large activation energies. Edge-flame propagation regimes are obtained by scaling analyses of the conservation equations and exemplified by numerical simulations of straight two-dimensional edge flames near a cold porous wall, for which lateral heat losses to the disk and large strains induce extinction of the trailing diffusion flame but are relatively unimportant in the front region, consistent with the existence of the cooling tail found in the experiments. The propagation dynamics of a steadily rotating spiral edge is studied in the large-core limit, for which the characteristic Markstein length is much smaller than the distance from the center at which the spiral tip is anchored. An asymptotic description of the edge tangential structure is obtained, spiral edge shapes are calculated, and an expression is found that relates the spiral rotational velocity to the rest of the parameters. A quasiestatic stability analysis of the edge shows that the edge curvature at extinction in the tip

Modelling conjugation with stochastic differential equations

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

2010-01-01

Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

Non-linear analysis of skew thin plate by finite difference method

International Nuclear Information System (INIS)

Kim, Chi Kyung; Hwang, Myung Hwan

2012-01-01

This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed

Free Vibration of Rectangular Plates with Attached Discrete Sprung Masses

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Ding Zhou

2012-01-01

Full Text Available A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

Science.gov (United States)

Newman, J. C., Jr.; Raju, I. S.

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Autonomous Sensors Powered by Energy Harvesting from von Karman Vortices in Airflow.

Science.gov (United States)

Demori, Marco; Ferrari, Marco; Bonzanini, Arianna; Poesio, Pietro; Ferrari, Vittorio

2017-09-13

In this paper an energy harvesting system based on a piezoelectric converter to extract energy from airflow and use it to power battery-less sensors is presented. The converter is embedded as a part of a flexure beam that is put into vibrations by von Karman vortices detached from a bluff body placed upstream. The vortex street has been investigated by Computational Fluid Dynamics (CFD) simulations, aiming at assessing the vortex shedding frequency as a function of the flow velocity. From the simulation results the preferred positioning of the beam behind the bluff body has been derived. In the experimental characterization the electrical output from the converter has been measured for different flow velocities and beam orientations. Highest conversion effectiveness is obtained by an optimal orientation of the beam, to exploit the maximum forcing, and for flow velocities where the repetition frequency of the vortices allows to excite the beam resonant frequency at its first flexural mode. The possibility to power battery-less sensors and make them autonomous has been shown by developing an energy management and signal conditioning electronic circuit plus two sensors for measuring temperature and flow velocity and transmitting their values over a RF signal. A harvested power of about 650 μW with retransmission intervals below 2 min have been obtained for the optimal flow velocity of 4 m/s.

Autonomous Sensors Powered by Energy Harvesting from von Karman Vortices in Airflow

Directory of Open Access Journals (Sweden)

Marco Demori

2017-09-01

Full Text Available In this paper an energy harvesting system based on a piezoelectric converter to extract energy from airflow and use it to power battery-less sensors is presented. The converter is embedded as a part of a flexure beam that is put into vibrations by von Karman vortices detached from a bluff body placed upstream. The vortex street has been investigated by Computational Fluid Dynamics (CFD simulations, aiming at assessing the vortex shedding frequency as a function of the flow velocity. From the simulation results the preferred positioning of the beam behind the bluff body has been derived. In the experimental characterization the electrical output from the converter has been measured for different flow velocities and beam orientations. Highest conversion effectiveness is obtained by an optimal orientation of the beam, to exploit the maximum forcing, and for flow velocities where the repetition frequency of the vortices allows to excite the beam resonant frequency at its first flexural mode. The possibility to power battery-less sensors and make them autonomous has been shown by developing an energy management and signal conditioning electronic circuit plus two sensors for measuring temperature and flow velocity and transmitting their values over a RF signal. A harvested power of about 650 μW with retransmission intervals below 2 min have been obtained for the optimal flow velocity of 4 m/s.

Theroretical modelling of the plate-tubes coupling in the hydroelasticity of the perforated plates

International Nuclear Information System (INIS)

Dzhupanov, V.A.; Manoach, E.S.

1983-01-01

In the previous investigations on the perforated plate hydroelasticity the problem of the plates-tubes-liquid interaction in the process of the general structural vibration is stated. But the interaction of the vibrating plates with the tubes, passing through them, is taken into account considering the tubes only as absolutely rigid supports. This is one of the possible technical realizations. In the present article the case when the tubes are taking part in the plate motion (vibration) is studied. Two circular perforated plates are supported by the absolutely rigid wall of the modelled roundcircular reactor barrel. The distance between the plates is given. They are connected by tubes, passing through, and clamped into the perforation holes. The plates and the tubes are made by any elastic HOOKIAN material. The volume between the two plates and outwardly to the tubes, but intrinsically of the barrel is filled by ideal, compressible and heavy liquid. Evidently the liquid volume is multiconnected one. The free vibration of the whole system is considered with the purposes: i) to give a theoretical model of the plates-tubes-liquid interaction including governing equations and boundary conditions; ii) to trace the solution of the eigen-value problem for the modelled structure; iii) to underline the engineering sides of the modelling process. (orig./GL)

Thermoelastic wave propagation in laminated composites plates

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Verma K. L.

2012-12-01

Full Text Available The dispersion of thermoelastic waves propagation in an arbitrary direction in laminated composites plates is studied in the framework of generalized thermoelasticity in this article. Three dimensional field equations of thermoelasticity with relaxation times are considered. Characteristic equation is obtained on employing the continuity of displacements, temperature, stresses and thermal gradient at the layers’ interfaces. Some important particular cases such as of free waves on reducing plates to single layer and the surface waves when thickness tends to infinity are also discussed. Uncoupled and coupled thermoelasticity are the particular cases of the obtained results. Numerical results are also obtained and represented graphically.

Acoustic impact on the laminated plates placed between barriers

Science.gov (United States)

Paimushin, V. N.; Gazizullin, R. K.; Fedotenkov, G. V.

2016-11-01

On the basis of previously derived equations, analytical solutions are established on the forced vibrations of two-layer and three-layers rectangular plates hinged in an opening of absolutely rigid walls during the transmission of monoharmonic sound waves. It is assumed that the partition wall is situated between two absolutely rigid barriers, one of them by harmonic oscillation with a given displacements amplitude on the plate forms the incident sound wave, and the other is stationary and has a coating of deformable energy absorbing material with high damping properties. The behavior of acoustic environments in the spaces between the deformable plate and the barriers described by classical wave equation based on the ideal compressible fluid model. To describe the process of dynamic deformation of the energy absorbing coating of fixed barrier, two-dimensional equations of motion based on the use of models transversely soft layer are derived with a linear approximation of the displacement field in the thickness direction of the coating and taking into account the damping properties of the material and the hysteresis model for it. The influence of the physical and mechanical properties of the concerned mechanical system and the frequency of the incident sound wave on the parameters of its insulation properties of the plate, as well as on the parameters of the stress-strain state of the plate has been analyzed.

Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates

International Nuclear Information System (INIS)

Rafiee, M; He, X Q; Liew, K M

2014-01-01

This paper investigates the nonlinear analysis of energy harvesting from piezoelectric functionally graded carbon nanotube reinforced composite plates under combined thermal and mechanical loadings. The excitation, which derives from harmonically varying mechanical in-plane loading, results in parametric excitation. The governing equations of the piezoelectric functionally graded carbon nanotube reinforced composite plates are derived based on classical plate theory and von Kármán geometric nonlinearity. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned, straight and have a uniform layout. The linear buckling and vibration behavior of the nanocomposite plates is obtained in the first step. Then, Galerkin’s method is employed to derive the nonlinear governing equations of the problem with cubic nonlinearities associated with mid-plane stretching. Periodic solutions are determined by using the Poincaré–Lindstedt perturbation scheme with movable simply supported boundary conditions. The effects of temperature change, the volume fraction and the distribution pattern of the SWCNTs on the parametric resonance, in particular the amplitude of vibration and the average harvested power of the smart functionally graded carbon nanotube reinforced composite plates, are investigated through a detailed parametric study. (paper)

Auto-ignition of methane-air mixtures flowing along an array of thin catalytic plates

Science.gov (United States)

Treviño, C.

2010-12-01

In this paper, the heterogeneous ignition of a methane-air mixture flowing along an infinite array of catalytic parallel plates has been studied by inclusion of gas expansion effects and the finite heat conduction on the plates. The system of equations considers the full compressible Navier-Stokes equations coupled with the energy equations of the plates. The gas expansion effects which arise from temperature changes have been considered. The heterogeneous kinetics considers the adsorption and desorption reactions for both reactants. The limits of large and small longitudinal thermal conductance of the plate material are analyzed and the critical conditions for ignition are obtained in closed form. The governing equations are solved numerically using finite differences. The results show that ignition is more easily produced as the longitudinal wall thermal conductance increases, and the effects of the gas expansion on the catalytic ignition process are rather small due to the large value of the activation energy of the desorption reaction of adsorbed oxygen atoms.

Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory

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Alireza Shooshtari

Full Text Available Abstract Free vibration of a magnetoelectroelastic rectangular plate is investigated based on the Reddy's third-order shear deformation theory. The plate rests on an elastic foundation and it is considered to have different boundary conditions. Gauss's laws for electrostatics and magnetostatics are used to model the electric and magnetic behavior. The partial differential equations of motion are reduced to a single partial differential equation and then by using the Galerkin method, the ordinary differential equation of motion as well as an analytical relation for the natural frequency of the plate is obtained. Some numerical examples are presented to validate the proposed model and to investigate the effects of several parameters on the vibration frequency of the considered smart plate.

The centre of mass of a triangular plate

International Nuclear Information System (INIS)

Sluesarenko, Viktor; Rojas, Roberto; Fuster, Gonzalo

2008-01-01

We present a derivation for the coordinates of the centre of mass-or centre of gravity-of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the midpoint of the line joining their centres of mass. By relating the centres of mass of the original to those of the scaled plates, we find the coordinates of the centre of mass as the solution of an algebraic equation

Static and Monoharmonic Acoustic Impact on a Laminated Plate

Science.gov (United States)

Paimushin, V. N.; Gazizullin, R. K.

2017-07-01

A discrete layered damping model of a multilayer plate at small displacements and deformations, with account of the internal damping of layers according to the Thompson-Kelvin-Voight model, is presented. Based on the equations derived, an analytical solution to the static deformation problem for single-layer rectangular plate hinge-supported along its contour and subjected of a uniformly distributed pressure applied to one of its boundary planes is obtained. Its convergence to the three-dimensional solution is analyzed in relation to the dimension of mesh in the thickness direction of the plate. It is found that, for thin plates, the dimension of the problem formulated can be reduced on the basis of simplified hypotheses applied to each layer. An analytical solutions is also constructed for the forced vibrations of two- and three-layer rectangular plates hinged in the opening of an absolutely stiff dividing wall upon transmission of a monoharmonic sound wave through them. It was assumed that the dividing wall is situated between two absolutely stiff barriers; one of them, owing to the harmonic vibration with a given displacement amplitude of the plate, forms an incident sound wave, and the other is stationary and is coated by a energy-absorbing material with high damping properties. Behavior of the acoustic media in spaces between the deformable plate and the barriers is described by the classical wave equations based on the model of an ideal compressible fluid. To describe the process of dynamic deformation of the energy-absorbing coating of the fixed barrier, two-dimensional equations of motion are derived based on the model of a transversely soft layer, a linear approximation of displacement fields in the thickness direction of the coating, and the account of damping properties of its material by using the hysteresis model. The effect of physical and mechanical parameters of the mechanical system considered and of frequency of the incident sound wave on the

Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation

KAUST Repository

Saghir, Shahid

2016-01-01

The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear

Resonant frequency function of thickness-shear vibrations of rectangular crystal plates.

Science.gov (United States)

Wang, Ji; Yang, Lijun; Pan, Qiaoqiao; Chao, Min-Chiang; Du, Jianke

2011-05-01

The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers. By satisfying the major boundary conditions of the dominant thickness-shear mode, three wavenumber solutions are obtained and the frequency equation is constructed. It is shown the resonant frequency of thickness-shear mode is a second-order polynomial of aspect ratios. This conforms to known results in the simplest form and is applicable to further analytical and experimental studies of the frequency equation of quartz crystal resonators.

Polar plate theory for orthogonal anisotropy

Science.gov (United States)

Bailey, Michelle D.

1998-11-01

The following paper discusses the derivation and evaluation of the plate equations for a circular composite disk with orthogonal anisotropy. The work will be on a macromechanical level and include buckling, static and dynamic load applications. Necessary to a complete examination of the circular disk is the conversion of the stiffness matrix to cylindrical coordinates. In the transformed state, these coefficients are no longer constant, adding to the complexity of the proposed differential equations. Laminated fiber-reinforced (or filamentary) composites are used today for their high strength-to weight and stiffness-to-weight ratios. However, because of the typical anisotropic behavior of composites, determining the material properties on a microscopic level and the mechanics on a macroscopic level is much more difficult. This difficulty manifests itself particularly well in the evaluation of material properties and governing differential equations of a circular disk with the fibers of the lamina oriented orthogonally. One could encounter such a situation in space structures that require a circular geometry. For example, determining fastener pull through in a circular composite plate would best be performed in a polar coordinate system. In order to calculate the strain (which is a function of the angle, θ) from the displacements, the stiffness matrix and boundary conditions would need to be expressed in cylindrical coordinates. Naturally the composite would be constructed with fibers in orthogonal directions, then the necessary geometry would be cut out, thus the required lengthy transformation of coordinate systems. To bypass this derivation, numerical methods have been used and finite element models have been attempted. FEM over predicts plate stiffness by 20% and underpredicts failure by 70%. Obviously there is a need to transform classical plate theory to a cylindrical coordinate system.

Octanol reduces end-plate channel lifetime

Science.gov (United States)

Gage, Peter W.; McBurney, Robert N.; Van Helden, Dirk

1978-01-01

1. Post-synaptic effects of n-octanol at concentrations of 0·1-1 mM were examined in toad sartorius muscles by use of extracellular and voltage-clamp techniques. 2. Octanol depressed the amplitude and duration of miniature end-plate currents and hence depressed neuromuscular transmission. 3. The decay of miniature end-plate currents remained exponential in octanol solutions even when the time constant of decay (τD) was decreased by 80-90%. 4. The lifetime of end-plate channels, obtained by analysis of acetylcholine noise, was also decreased by octanol. The average lifetime measured from noise spectra agreed reasonably well with the time constant of decay of miniature end-plate currents, both in control solution and in octanol solutions. 5. Octanol caused a reduction in the conductance of end-plate channels. Single channel conductance was on average about 25 pS in control solution and 20 pS in octanol. 6. In most cells the normal voltage sensitivity of the decay of miniature end-plate currents was retained in octanol solutions. The lifetime of end-plate channels measured from acetylcholine noise also remained voltage-sensitive in octanol solutions. In some experiments in which channel lifetime was exceptionally reduced the voltage sensitivity was less than normal. 7. In octanol solutions, τD was still very sensitive to temperature changes in most cells although in some the temperature sensitivity of τD was clearly reduced. Changes in τD with temperature could generally be fitted by the Arrhenius equation suggesting that a single step reaction controlled the decay of currents both in control and in octanol solutions. In some cells in which τD became less than 0·3 ms, the relationship between τD and temperature became inconsistent with the Arrhenius equation. 8. As the decay of end-plate currents in octanol solutions remains exponential, and the voltage and temperature sensitivity can be unchanged even when τD is significantly reduced, it seems likely that

Size-Dependent Dynamic Behavior of a Microcantilever Plate

Directory of Open Access Journals (Sweden)

Xiaoming Wang

2012-01-01

Full Text Available Material length scale considerably affects the mechanical properties of microcantilever components. Recently, cantilever-plate-like structures have been commonly used, whereas the lack of studies on their size effects constrains the design, testing, and application of these structures. We have studied the size-dependent dynamic behavior of a cantilever plate based on a modified couple stress theory and the differential quadrature method in this note. The numerical solutions of microcantilever plate equation involving the size effect have been presented. We have also analyzed the bending and vibration of the microcantilever plates considering the size effect and discussed the dependence of the size effect on their geometric dimensions. The results have shown that (1 the mechanical characteristics of the cantilever plate show obvious size effects; as a result, the bending deflection of a microcantilever plate reduces whereas the natural frequency increases effectively and (2 for the plates with the same material, the size effect becomes more obvious when the plates are thinner.

Mathematical methods for elastic plates

CERN Document Server

Constanda, Christian

2014-01-01

Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one.   The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions.   The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex ana...

Magneto-elastic dynamics and bifurcation of rotating annular plate*

International Nuclear Information System (INIS)

Hu Yu-Da; Piao Jiang-Min; Li Wen-Qiang

2017-01-01

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton’s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos. (paper)

Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

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Mohammad Mehdi Rashidi

2008-01-01

Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

Dynamic temperature field in the ferromagnetic plate induced by moving high frequency inductor

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Milošević-Mitić Vesna

2014-01-01

Full Text Available The subject of the paper is the temperature distribution in the thin metallic ferromagnetic plate influenced by moving linear high frequency induction heater. As a result of high frequency electromagnetic field, conducting currents appear in the part of the plate. Distribution of the eddy-current power across the plate thickness is obtained by use of complex analysis. The influences of the heater frequency, magnetic field intensity and plate thickness on the heat power density were discussed. By treating this power as a moving heat source, differential equations governing distribution of the temperature field are formulated. Temperature across the plate thickness is assumed to be in linear form. Differential equations are analytically solved by using integral-transform technique, Fourier finite-sine and finite-cosine transform and Laplace transform. The influence of the heater velocity to the plate temperature is presented on numerical examples based on theoretically obtained results. [Projekat Ministarstva nauke Republike Srbije, br. TR 35040 i br. TR 35011

Postbuckling Investigations of Piezoelectric Microdevices Considering Damage Effects

Science.gov (United States)

Sun, Zhigang; Wang, Xianqiao

2014-01-01

Piezoelectric material has been emerging as a popular building block in MEMS devices owing to its unique mechanical and electrical material properties. However, the reliability of MEMS devices under buckling deformation environments remains elusive and needs to be further explored. Based on the Talreja's tensor valued internal state damage variables as well as the Helmhotlz free energy of piezoelectric material, a constitutive model of piezoelectric materials with damage is presented. The Kachanvo damage evolution law under in-plane compressive loads is employed. The model is applied to the specific case of the postbuckling analysis of the piezoelectric plate with damage. Then, adopting von Karman's plate theory, the nonlinear governing equations of the piezoelectric plates with initial geometric deflection including damage effects under in-plane compressive loads are established. By using the finite difference method and the Newmark scheme, the damage evolution for damage accumulation is developed and the finite difference procedure for postbuckling equilibrium path is simultaneously employed. Numerical results show the postbuckling behaviors of initial flat and deflected piezoelectric plates with damage or no damage under different sets of electrical loading conditions. The effects of applied voltage, aspect ratio of plate, thick-span ratio of plate, damage as well as initial geometric deflections on the postbuckling behaviors of the piezoelectric plate are discussed. PMID:24618774

Computation of the homogeneous and forced solutions of a finite length, line-driven, submerged plate.

Science.gov (United States)

DiPerna, Daniel T; Blake, William K; DiPerna, Xingguang Z

2006-12-01

A formulation is developed to predict the vibration response of a finite length, submerged plate due to a line drive. The formulation starts by describing the fluid in terms of elliptic cylinder coordinates, which allows the fluid loading term to be expressed in terms of Mathieu functions. By moving the fluid loading term to the right-hand side of the equation, it is considered to be a force. The operator that remains on the left-hand side is the same as that of the in vacuo plate: a fourth-order, constant coefficient, ordinary differential equation. Therefore, the problem appears to be an inhomogeneous ordinary differential equation. The solution that results has the same form as that of the in vacuo plate: the sum of a forced solution, and four homogeneous solutions, each of which is multiplied by an arbitrary constant. These constants are then chosen to satisfy the structural boundary conditions on the two ends of the plate. Results for the finite plate are compared to the infinite plate in both the wave number and spatial domains. The theoretical predictions of the plate velocity response are also compared to results from finite element analysis and show reasonable agreement over a large frequency range.

Damage of plates due to impact, dynamic pressure and explosive loads

Directory of Open Access Journals (Sweden)

Norman Jones

Full Text Available It is the purpose of this article to present design equations which can be used to predict the damage of ductile plating when subjected to mass impact, dynamic pressure or impulsive loadings. The external loadings are sufficiently severe to produce inelastic material behaviour and produce finite transverse displacement, or geometry change, effects. The damage is characterised as the final or permanent transverse displacement of a plate. The theoretical method predicts values for the maximum permanent transverse displacements which agree reasonably well with the corresponding experimental results generated on aluminium alloy circular, square and rectangular plates. Thus, the equations presented in this article are valuable for preliminary design purposes and for forensic studies, while the experimental data can be used for validating numerical schemes.

Natural Frequency of F.G. Rectangular Plate by Shear Deformation Theory

International Nuclear Information System (INIS)

Shahrjerdi, Ali; Sapuan, S M; Shahzamanian, M M; Mustapha, F; Zahari, R; Bayat, M

2011-01-01

Natural frequency of functionally graded (F.G.) rectangular plate is carried out by using second-order shear deformation theory (SSDT). The material properties of functionally graded rectangular plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution. The equations of motion are obtained by energy method. Numerical results for functionally graded plates are given in dimensionless graphical forms and the effects of material properties on natural frequency are determined.

The solution of certain loss of contact between a plate and unilateral supports

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Sompornjaroensuk Yos

2007-01-01

Full Text Available This paper examines the loss of contact between a square plate and the unilateral supports under uniformly distributed load. Since the plate is rested on the unilateral supports, it will have the regions of lost contact between a plate and the supports due to the absence of restraining corner force at the plate corners. This leads to the mixed boundary conditions and these conditions are then written in the form of dual-series equations which can further be reduced to a Fredholm integral equation by taking advantage of finite Hankel transform technique. Numerical results are given for the deflections of free edge and deflections along the middle line of the plate with deferent values of the Poisson’s ratio. In addition, the deflection surface is also presented. From the investigation, it can be indicated that the loss of contact is decreased upon the increasing Poisson’s ratio.

Frequency dependence of magnetic shielding performance of HTS plates in mixed states

International Nuclear Information System (INIS)

Kamitani, Atsushi; Yokono, Takafumi; Yokono, Takafumi

2000-01-01

The magnetic shielding performance of the high-Tc superconducting (HTS) plate is investigated numerically. The behavior of the shielding current density in the HTS plate is expressed as the integral-differential equation with a normal component of the current vector potential as a dependent variable. The numerical code for solving the equation has been developed by using the combination of the Newton-Raphson method and the successive substitution method and, by use of the code, damping coefficients and shielding factors are evaluated for the various values of the frequency ω. The results of computations show that the HTS plate has a possibility of shielding the high-frequency magnetic field with ω > or approx. 1 kHz. (author)

Frequency dependence of magnetic shielding performance of HTS plates in mixed states

Energy Technology Data Exchange (ETDEWEB)

Kamitani, Atsushi; Yokono, Takafumi [Yamagata Univ., Yonezawa (Japan). Faculty of Engineering; Yokono, Takafumi [Tsukuba Univ., Ibaraki (Japan). Inst. of Information Sciences and Electronics

2000-06-01

The magnetic shielding performance of the high-Tc superconducting (HTS) plate is investigated numerically. The behavior of the shielding current density in the HTS plate is expressed as the integral-differential equation with a normal component of the current vector potential as a dependent variable. The numerical code for solving the equation has been developed by using the combination of the Newton-Raphson method and the successive substitution method and, by use of the code, damping coefficients and shielding factors are evaluated for the various values of the frequency {omega}. The results of computations show that the HTS plate has a possibility of shielding the high-frequency magnetic field with {omega} > or approx. 1 kHz. (author)

Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

Science.gov (United States)

Wang, Yan Qing

2018-02-01

To provide reference for aerospace structural design, electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state are investigated. A modified power law formulation is employed to depict the material properties of the plates in the thickness direction. Three terms of inertial forces are taken into account due to the translation of plates. The geometrical nonlinearity is considered by adopting the von Kármán non-linear relations. Using the d'Alembert's principle, the nonlinear governing equation of the out-of-plane motion of the plates is derived. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method. Then, the approximate analytical results are validated by utilizing the adaptive step-size fourth-order Runge-Kutta technique. Additionally, the stability of the steady state responses is examined by means of the perturbation technique. Linear and nonlinear vibration analyses are both carried out and results display some interesting dynamic phenomenon for translational porous FGPM plates. Parametric study shows that the vibration characteristics of the present inhomogeneous structure depend on several key physical parameters.

Application of mixture length turbulence models in the domain of condensation; Application des modeles de turbulence de longueur de melange dans le domaine de la condensation

Energy Technology Data Exchange (ETDEWEB)

Louahlia, H.; Panday, P.K. [Institut de Genie Energetique, 90 - Belfort (France)

1997-12-31

This paper presents a comparison between turbulence models based on Prandtl theory and applied to the problem of pure fluids condensation. A theoretical model is defined which allows to determine the physical characteristics of condensation between two vertical or horizontal flat plates. The total heat flux exchanged at the wall and the mean Nusselt number are calculated using several closure models in the liquid and vapor phases. Calculation results obtained for the R123 condensation between two vertical plates show that the Pletcher`s model or the Groenwald and Kroeger`s one applied to the vapor flow and the Von Karman`s model used for the liquid film predict thermal fluxes close to the measured ones. It has been noticed also that the condensation heat transfer is underestimated in the laminar model. In the case of the R113 condensation on an horizontal flat plate, the mean Nusselt numbers estimated in the Pletcher`s model applied to both phases are close to the measurements performed by Lu and Suryanarayana. (J.S.) 12 refs.

Semiclassical theory of plate vibrations

International Nuclear Information System (INIS)

Bogomolny, E.; Hugues, E.

1996-11-01

The bi-harmonic equation of flexural vibrations of elastic plates is studied by a semiclassical method which can easily be generalized for other models of wave propagation. The surface and perimeter terms of the asymptotic number of levels are derived exactly. The next constant term is also derived. A semiclassical approximation of the quantization condition is obtained. A Berry-Tabor formula and a Gutzwiller trace formula are deduced for the integrable and chaotic cases respectively. From 600 eigenvalues of a clamped stadium plate obtained by a specially developed numerical algorithm, the trace formula is assessed, looking at its Fourier transform compared with the membrane case. (author)

computational study of Couette flow between parallel plates for steady and unsteady cases

International Nuclear Information System (INIS)

Rihan, Y.

2008-01-01

Couette flow between parallel plates is a classical problem that has important applications in various industrial processing. In this investigation an analytical solution was obtained to predict the steady and unsteady Couette flow between parallel plates. One of the plates was stationary and the other plate moved with constant velocity. The governing partial differential equations were solved numerically using Crank-Nicolson implicit method to represent the flow behavior of the fluid

Flexural-torsional buckling analysis of angle-bar stiffened plates

Energy Technology Data Exchange (ETDEWEB)

Ahmad, Rahbar Ranji [Amirkabir University of Technology, Tehran (Iran, Islamic Republic of)

2015-09-15

The interaction of flexural-torsional buckling modes is critical for stiffened plates with asymmetric stiffeners. However, this interaction is ignored in all design rules because it is complex to characterize. In the literature, the presence of an attached plate is ignored, and stiffened plate is treated as an ordinary asymmetric beam. In the flexural buckling mode, stiffener and the attached plate buckle together; in the torsional buckling mode, the attached plate cannot freely rotate with stiffener. Basic equations of the flexural-torsional buckling modes are deduced based on hybrid beam concept and a new strain distribution assumption for sideway bending of stiffeners. Elastic buckling stresses of different angle-bar stiffened plates are calculated and compared with those generated by the Finite element method (FEM) and those available in the literature. The present method has better agreements with FEM.

an elasticity solution for simply suported rectangular plates

African Journals Online (AJOL)

MIS

1983-09-01

Sep 1, 1983 ... σx, σy, σz. = direct stresses ξxy, ξxz, ξyz. = shear stresses εy, εy, εz. = direct strains rxy, rxz ryz. = shear strains μ. = Poisson's ratio α = rm /Pb. = nπ/2b. R = 2 ... based on Donnell's5 thick plate theory are examined. 2. BASIC EQUATIONS. The general solution of the equations of elasticity can be expressed in.

Dynamics of a Circular Mindlin Plate under Mechanical Loading and Elevated Temperature

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Warminska Anna

2016-01-01

Full Text Available Dynamics of a nonlinear circular Midlin plate is studied in the paper. The mathematical model represented by partial differential equations includes nonlinear geometrical terms resulted from large displacements. The plate is subjected to mechanical and thermal loadings. The dynamics of a coupled thermo-mechanical problem is reduced from partial to ordinary differential equations. Considering the first mode reduction and uniformly distributed temperature just a single nonlinear differential equation is obtained. The bifurcation analysis shows that elevated temperature shifts the rezonanse curve and new solutions arise. Depending on initial conditions this may lead to buckling phenomenon and then relatively small oscillations around this state, symmetric periodic oscillations of large amplitude, or irregular oscillations.

Fluid dynamics

CERN Document Server

Ruban, Anatoly I

This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. The present Part 1 consists of four chapters. Chapter 1 begins with a discussion of Continuum Hypothesis, which is followed by an introduction to macroscopic functions, the velocity vector, pressure, density, and enthalpy. We then analyse the forces acting inside a fluid, and deduce the Navier-Stokes equations for incompressible and compressible fluids in Cartesian and curvilinear coordinates. In Chapter 2 we study the properties of a number of flows that are presented by the so-called exact solutions of the Navier-Stokes equations, including the Couette flow between two parallel plates, Hagen-Poiseuille flow through a pipe, and Karman flow above an infinite rotating disk. Chapter 3 is d...

Modelling and solution of contact problem for infinite plate and cross-shaped embedment

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O.B. Kozin

2016-09-01

Full Text Available Development of efficient methods of determination of an intense-strained state of thin-walled constructional designs with inclusions, reinforcements and other stress raisers is an important problem both with theoretical, and from the practical point of view, considering their wide practical application. Aim: The aim of this research is to develop the analytical mathematical method of studying of an intense-strained state of infinite plate with cross-shaped embedment at a bend. Materials and Methods: The method of boundary elements is an efficient way of the boundary value problems solution for systems of differential equations. The methods based on boundary integral equations get wide application in many branches of science and technique, calculation of plates and shells. One of methods of solution of a numerous class of the integral equations and systems arising on the basis of a method of boundary integral equations is the analytical method of construction of these equations and systems to Riemann problems with their forthcoming decision. Results: The integral equation for the analysis of deflections and the analysis of an intense-strained state of a thin rigid plate with rigid cross-shaped embedment is received. The precise solution of this boundary value problem is received by reduction to a Riemann problem and its forthcoming solution. An asymptotical behavior of contact efforts at the ends of embedment is investigated.

Equivalent properties for perforated plates. An analytical approach

International Nuclear Information System (INIS)

Cepkauskas, M.M.; Yang Jianfeng

2005-01-01

Structures that contain perforated plates have been a subject of interest in the Nuclear Industry. Steam generators, condensers and reactor internals utilize plates containing holes which act as flow holes or separate structures from flow by using a 'tube bank' design. The equivalent plate method has been beneficial in analyzing perforate plates. Details are found in various papers found in the bibliography. In addition the ASME code addresses perforated plates in Appendix A-8000, but is limited to a triangular hole pattern. This early work performed in this field utilized test data and analytical approaches. This paper is an examination of an analytical approach for determining equivalent plate mechanical and thermal properties. First a patch of the real plate is identified that provides a model for the necessary physical behavior of the plate. The average strain of this patch is obtained by first applying simplified one dimensional mechanical load to the patch, determining stress as a function of position, converting the stress to strain and then integrating the strain over the patch length. This average strain is then equated to the average strain of an equivalent fictitious rectangular patch. This results in obtaining equivalent Young's Modulus and Poison's Ratio for the equivalent plate in all three orthogonal directions. The corresponding equivalent shear modulus in all three directions is then determined. An orthotropic material stress strain matrix relationship is provided for the fictitious properties. By equating the real average strain with the fictitious average strain in matrix form, a stress multiplier is found to convert average fictitious stress to average real stress. This same type of process is repeated for heat conduction coefficients and coefficients of thermal expansion. Results are provided for both a square and triangular hole pattern. Reasonable results are obtained when comparing the effective Young's Modulus and Poison's Ratio with ASME

A Geometrically—Nonlinear Plate Theory 12

Institute of Scientific and Technical Information of China (English)

AlbertC.J.LUO

1999-01-01

An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

Science.gov (United States)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

Sound insulation performance of plates with interconnected distributed piezoelectric patches

Directory of Open Access Journals (Sweden)

Yi Kaijun

2017-02-01

Full Text Available This paper deals with the sound insulation performance of a thin plate with interconnected distributed piezoelectric patches. Piezoelectric patches are periodically bonded on the surfaces of the plate in a collocated fashion, and are interconnected via an inductive circuit network. This piezoelectric system is termed as piezo-electromechanical (PEM plate in the paper. Homogenization methods are involved under a sub-wavelength assumption to analytically develop the dynamical equations for the PEM plate. The dispersion relationships and energy densities of the wave modes propagating in the PEM plate are studied; the sub-wavelength assumption is verified for the simulations in this paper. The coincidence frequency of the PEM plate is researched, and results show that the coincidence frequency of the PEM plate will disappear at certain circumstances; mathematical and physical explanations are made for this phenomenon. The disappearance of the coincidence frequency is used to optimize the value of inductance, for the purpose of improving the sound transmission loss of the PEM plate.

Forced convection on a heated horizontal flat plate with finite thermal conductivity in a non-Darcian porous medium

Energy Technology Data Exchange (ETDEWEB)

Luna, N. [Direccion de Operacion Petrolera, Direccion General de Exploracion y Explotacion de Hidrocarburos, Secretaria de Energia, 03100 Mexico DF (Mexico); Mendez, F. [Facultad de Ingenieria, UNAM, 04510 Mexico DF (Mexico)

2005-07-01

The steady-state analysis of conjugated heat transfer process for the hydrodynamically developed forced convection flow on a heated flat plate embedded in a porous medium is studied. The governing equations for the fluid-saturated porous medium are solved analytically using the integral boundary layer approximation. This integral solution is coupled to the energy equation for the flat plate, where the longitudinal heat conduction effects are taken into account. The resulting equations are then reduced to an integro-differential equation which is solved by regular perturbation techniques and numerical methods. The analytical and numerical predictions for the temperature profile of the plate and appropriate local and average Nusselt numbers are plotted for finite values of the conduction parameter, {alpha}, which represents the presence of the longitudinal heat conduction effects. (authors)

Equilibrium approach in the derivation of differential equations for ...

African Journals Online (AJOL)

In this paper, the differential equations of Mindlin plates are derived from basic principles by simultaneous satisfaction of the differential equations of equilibrium, the stress-strain laws and the strain-displacement relations for isotropic, homogenous linear elastic materials. Equilibrium method was adopted in the derivation.

Axisymmetric buckling analysis of laterally restrained thick annular plates using a hybrid numerical method

Energy Technology Data Exchange (ETDEWEB)

Malekzadeh, P. [Department of Mechanical Engineering, Persian Gulf University, Bushehr 75168 (Iran, Islamic Republic of); Center of Excellence for Computational Mechanics, Shiraz University, Shiraz (Iran, Islamic Republic of)], E-mail: malekzadeh@pgu.ac.ir; Ouji, A. [Department of Civil Engineering, Persian Gulf University, Bushehr 75168 (Iran, Islamic Republic of); Islamic Azad University, Larestan Branch, Larestan (Iran, Islamic Republic of)

2008-11-15

The buckling analysis of annular thick plates with lateral supports such as two-parameter elastic foundations or ring supports is investigated using an elasticity based hybrid numerical method. For this purpose, firstly, the displacement components are perturbed around the pre-buckling state, which is located using the elasticity theory. Then, by decomposing the plate into a set of sub-domain in the form of co-axial annular plates, the buckling equations are discretized through the radial direction using global interpolation functions in conjunction with the principle of virtual work. The resulting differential equations are solved using the differential quadrature method. The method has the capability of modeling the arbitrary boundary conditions either at the inner and outer edges of thin-to-thick plates and with different types of lateral restraints. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its accuracy and versatility for thin-to-thick plates.

Vibration analysis of a trimorph plate as a precursor model for smart automotive bodywork

International Nuclear Information System (INIS)

Big-Alabo, A; Cartmell, M P

2012-01-01

This study investigates the vibration characteristics of a proposed candidate structure for smarter car bodies. The material is conceived as a three-layer laminated structure in the form of a trimorph plate. The vibration response of the plate is investigated for large deflections by considering the effects of geometric nonlinearity. First, the governing equation for the mid-point deflection of the plate is developed based on classical laminate plate theory (CLPT). The governing equation is solved, and a simulation is run for different possible layer-stacking sequences. Comparisons are made between the nonlinear vibration response of this trimorph plate both with and without the effects of the von Kármán geometric nonlinearity. The results show that for the same material properties the different layer-stacking sequences produce different vibration responses, and from there it is concluded that layer-stacking sequencing is a basis for the definition of a suitable material configuration for high performance automotive applications.

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Science.gov (United States)

Newman, J. C., Jr.; Raju, I. S.

1984-01-01

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

Rotation and Radiation Effects on MHD Flow through Porous Medium Past a Vertical Plate with Heat and Mass Transfer

Directory of Open Access Journals (Sweden)

Uday Singh Rajput

2017-11-01

Full Text Available Effects of rotation and radiation on unsteady MHD flow past a vertical plate with variable wall temperature and mass diffusion in the presence of Hall current is studied here. Earlier we studied chemical reaction effect on unsteady MHD flow past an exponentially accelerated inclined plate with variable temperature and mass diffusion in the presence of Hall current. We had obtained the results which were in agreement with the desired flow phenomenon. To study further, we are changing the model by considering radiation effect on fluid, and changing the geometry of the model. Here in this paper we are taking the plate positioned vertically upward and rotating with velocity Ω . Further, medium of the flow is taken as porous. The plate temperature and the concentration level near the plate increase linearly with time. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations under consideration have been solved by Laplace transform technique. The model contains equations of motion, diffusion equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have been considered. The governing equations involved in the flow model are solved by the Laplace-transform technique. The results obtained have been analyzed with the help of graphs drawn for different parameters. The numerical values obtained for the drag at boundary and Nusselt number have been tabulated. We found that the values obtained for velocity, concentration and temperature are in concurrence with the actual flow of the fluid

Flutter and Thermal Buckling Analysis for Composite Laminated Panel Embedded with Shape Memory Alloy Wires in Supersonic Flow

Directory of Open Access Journals (Sweden)

Chonghui Shao

2016-01-01

Full Text Available The flutter and thermal buckling behavior of laminated composite panels embedded with shape memory alloy (SMA wires are studied in this research. The classical plate theory and nonlinear von-Karman strain-displacement relation are employed to investigate the aeroelastic behavior of the smart laminated panel. The thermodynamic behaviors of SMA wires are simulated based on one-dimensional Brinson SMA model. The aerodynamic pressure on the panel is described by the nonlinear piston theory. Nonlinear governing partial differential equations of motion are derived for the panel via the Hamilton principle. The effects of ply angle of the composite panel, SMA layer location and orientation, SMA wires temperature, volume fraction and prestrain on the buckling, flutter boundary, and amplitude of limit cycle oscillation of the panel are analyzed in detail.

New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

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Dan Xie

2017-01-01

Full Text Available A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs into a set of ordinary differential equations (ODEs in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.

Model to Analyze Micro Circular Plate Subjected to Electrostatic Force

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Cao Tian-Jie

2013-06-01

Full Text Available In this paper a distributed model with three possible static modes was presented to investigate the behavior of the plate subjected to electrostatic force and uniform hydrostatic pressure both before pull in and beyond pull in. The differential governing equation of the micro circular plate specifically used for numerical solution of the three modes, in which the singularity at the center of the micro plate did not occur, was presented based on the classical thin plate theory, Taylor's series expansion and Saint-Venant's principle. The numerical solution to the differential governing equation for the different mode was mainly attributed to solve for one unknown boundary condition and the applied voltage, which could be obtained by using a two-fold method of bisection based on the shooting method. The voltage ranges over which the three modes could exist and the points where transitions occurred between the modes were computed. Incorporating the above numerical solution to the applied voltage at the normal mode with some constrained optimization method, pull-in voltage and the corresponding pull-in position can automatically be obtained. In examples, the entire mechanical behavior of the circular plate over the operational voltage ranges was investigated and the effects of different parameters on pull-in voltage were studied. The obtained results were compared with the existing results and good agreement has been achieved.

Modeling and analysis of waves in a heat conducting thermo-elastic plate of elliptical shape

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R. Selvamani

Full Text Available Wave propagation in heat conducting thermo elastic plate of elliptical cross-section is studied using the Fourier expansion collocation method based on Suhubi's generalized theory. The equations of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermo elastic plate of elliptical cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by using the boundary conditions along outer and inner surface of elliptical cross-sectional plate using Fourier expansion collocation method. The computed non-dimensional frequency, velocity and quality factor are plotted in dispersion curves for longitudinal and flexural (symmetric and antisymmetric modes of vibrations.

MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate

International Nuclear Information System (INIS)

Bhattacharyya, Krishnendu; Mukhopadhyay, Swati; Layek, G. C.

2011-01-01

An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate. (fundamental areas of phenomenology(including applications))

equilibrium approach in thederivation of differential equations

African Journals Online (AJOL)

user

DEPT OF CIVIL ENGINEERING, ENUGU STATE UNIVERSITY OF SCIENCE & TECHNOLOGY ... In this paper, the differential equations of Mindlin plates are derived from basic principles by ..... Journal of Applied Mechanics, pages 31-38.

Vortex distribution in small star-shaped Mo{sub 80}Ge{sub 20} plate

Energy Technology Data Exchange (ETDEWEB)

Vu, The Dang, E-mail: vu-dang@pe.osakafu-u.ac.jp [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Department of Physics and Electronics, University of Sciences, Vietnam National University HCMC (Viet Nam); Matsumoto, Hitoshi; Miyoshi, Hiroki [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Huy, Ho Thanh [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Department of Physics and Electronics, University of Sciences, Vietnam National University HCMC (Viet Nam); Shishido, Hiroaki [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Institute for Nanofabrication Research, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Kato, Masaru [Institute for Nanofabrication Research, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Department of Mathematical Science, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Ishida, Takekazu [Department of Physics and Electronics, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan); Institute for Nanofabrication Research, Osaka Prefecture University, Sakai, Osaka 599-8531 (Japan)

2017-02-15

Highlights: • We found the general feature of vortex configuration in small star-shaped Mo{sub 80}Ge{sub 20} plates such as the appearance of symmetric line, the rule of shell filling and the existence of a magic number in both theoretical predictions and experimental results. • We found that the vortex distribution in a concave decagon tends to adapt to one of the five symmetric axes of the star-shaped plate expected in confining vortices in a restricted sample geometry. • The numerical results of Ginzburg–Landau equation confirmed that the filling rules for a vortex configuration and the existence of a magic number for small star-shaped plates are in good agreement with experiment results. - Abstract: We investigated vortex states in small star-shaped Mo{sub 80}Ge{sub 20} plates both theoretically and experimentally. The numerical calculations of the Ginzburg–Landau equation have been carried out with the aid of the finite element method, which is convenient to treat an arbitrarily shaped superconductor. The experimental results were observed by using a scanning SQUID microscope. Through systematic measurements, we figured out how vortices form symmetric configuration with increasing the magnetic field. The vortex distribution tends to adapt to one of five mirror symmetric lines when vortices were located at the five triangular horns of a star-shaped plate. The crystalline homogeneity of a sample was confirmed by the X-ray diffraction and the superconducting properties so that vortices are easily able to move for accommodating vortices in the geometric symmetry of the star-shaped plate. The experimental vortex configurations obtained for a star-shaped plate are in good agreement with theoretical predictions from the nonlinear Ginzburg–Landau equation.

A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

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Shi-Chao Yi

2017-01-01

Full Text Available Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs. Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

Dimensional analysis of detrimental ozone generation by positive wire-to-plate corona discharge in air

Science.gov (United States)

Bo, Z.; Chen, J. H.

2010-02-01

The dimensional analysis technique is used to formulate a correlation between ozone generation rate and various parameters that are important in the design and operation of positive wire-to-plate corona discharges in indoor air. The dimensionless relation is determined by linear regression analysis based on the results from 36 laboratory-scale experiments. The derived equation is validated by experimental data and a numerical model published in the literature. Applications of such derived equation are illustrated through an example selection of the appropriate set of operating conditions in the design/operation of a photocopier to follow the federal regulations of ozone emission. Finally, a new current-voltage characteristic equation is proposed for positive wire-to-plate corona discharges based on the derived dimensionless equation.

Dimensional analysis of detrimental ozone generation by positive wire-to-plate corona discharge in air

International Nuclear Information System (INIS)

Bo, Z; Chen, J H

2010-01-01

The dimensional analysis technique is used to formulate a correlation between ozone generation rate and various parameters that are important in the design and operation of positive wire-to-plate corona discharges in indoor air. The dimensionless relation is determined by linear regression analysis based on the results from 36 laboratory-scale experiments. The derived equation is validated by experimental data and a numerical model published in the literature. Applications of such derived equation are illustrated through an example selection of the appropriate set of operating conditions in the design/operation of a photocopier to follow the federal regulations of ozone emission. Finally, a new current-voltage characteristic equation is proposed for positive wire-to-plate corona discharges based on the derived dimensionless equation.

Study of the electric field inside microchannel plate multipliers

International Nuclear Information System (INIS)

Gatti, E.; Oba, K.; Rehak, P.

1982-01-01

Electric field inside high gain microchannel plate multipliers was studied. The calculations were based directly on the solution of the Maxwell equations applied to the microchannel plate (MCP) rather than on the conventional lumped RC model. The results are important to explain the performance of MCP's, (1) under a pulsed bias tension and, (2) at high rate conditions. The results were tested experimentally and a new method of MCP operation free from the positive ion feedback was demonstrated

Complex mapping of aerofoils - a different perspective

Science.gov (United States)

Matthews, Miccal T.

2012-01-01

In this article an application of conformal mapping to aerofoil theory is studied from a geometric and calculus point of view. The problem is suitable for undergraduate teaching in terms of a project or extended piece of work, and brings together the concepts of geometric mapping, parametric equations, complex numbers and calculus. The Joukowski and Karman-Trefftz aerofoils are studied, and it is shown that the Karman-Trefftz aerofoil is an improvement over the Joukowski aerofoil from a practical point of view. For the most part only a spreadsheet program and pen and paper is required, only for the last portion of the study of the Karman-Trefftz aerofoils a symbolic computer package is employed. Ignoring the concept of a conformal mapping and instead viewing the problem from a parametric point of view, some interesting mappings are obtained. By considering the derivative of the mapped mapping via the chain rule, some new and interesting analytical results are obtained for the Joukowski aerofoil, and numerical results for the Karman-Trefftz aerofoil.

Instability of a cantilevered flexible plate in viscous channel flow

Science.gov (United States)

Balint, T. S.; Lucey, A. D.

2005-10-01

The stability of a flexible cantilevered plate in viscous channel flow is studied as a representation of the dynamics of the human upper airway. The focus is on instability mechanisms of the soft palate (flexible plate) that cause airway blockage during sleep. We solve the Navier Stokes equations for flow with Reynolds numbers up to 1500 fully coupled with the dynamics of the plate motion solved using finite-differences. The study is 2-D and based upon linearized plate mechanics. When both upper and lower airways are open, the plate is found to lose its stability through a flutter mechanism and a critical Reynolds number exists. When one airway is closed, the plate principally loses its stability through a divergence mechanism and a critical flow speed exists. However, below the divergence-onset flow speed, flutter can exist for low levels of structural damping in the flexible plate. Our results serve to extend understanding of flow-induced instability of cantilevered flexible plates and will ultimately improve the diagnosis and treatment of upper-airway disorders.

Modeling and Measurements of CMUTs with Square Anisotropic Plates

DEFF Research Database (Denmark)

la Cour, Mette Funding; Christiansen, Thomas Lehrmann; Dahl-Petersen, Christian

2013-01-01

plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is white light interferometer. Fitting...

Far-Field Power Transmissions in Orthotropic Plates: A New Approach

Directory of Open Access Journals (Sweden)

Nirmal K. Mandal

2008-01-01

Full Text Available The structural intensity (SI technique is an essential tool for locating and ranking vibration sources and sinks on structures. It can quantify vibration fields by plotting a vector map of energy transmission on the structures. In this paper, a different strategy, changing coordinate systems of plate equations, is used to develop an intensity equation from shear force components in both x and y directions. The formulation is carried out in the frequency domain considering flexural waves. Orthotropic plate theory, far-field conditions, Fourier transform, and finite difference approximation are considered. The same intensity definition is obtained using this different strategy. A dual-channel FFT analyser is essential for data acquisition to get an intensity vector in a particular direction for far-field conditions.

Design, construction and evaluation of solar flat-plate collector simulator based on the thermohydraulic coefficient

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H Rahmati Aidinlou

2017-05-01

Full Text Available Introduction Increasing the area of absorber plate between the flowed air through the duct can be accomplished by corrugating the absorber plate or by using the artificial roughness underside of the absorber plate as the commercial methods for enhancing the thermohydraulic performance of the flat plate solar air heaters. Evaluation of this requires the construction of separated solar air heater which is costly and time consuming. The constructed solar flat-plate collector simulator can be a sufficient solution for obtaining the heat transfer and thermodynamic parameters for evaluating the absorber plate. The inclined broken roughness was chosen as the optimum roughness which is surrounded by three aluminum smooth walls. Materials and Methods The duct for both smooth and roughened plate have been constructed based on the ASHRAE 93-2010 standard. In order to achieve a fully thermal and hydraulic developed flow, the plenum is constructed. The centrifugal fan is considered by applying the required air volume at the pressure drop obtained by the duct, plenum and the orifice meter. The TSI velocity-meter 8355 is used to measure the velocity of air crossing through the pipe connected to the centrifugal fan. The micro manometer Kimo CPE310-s with the resolution of 0.1 Pa is used to measure the pressure drop across the test section of the smooth and roughened duct. The LM35 sensors are used to measure the absorber plate and air temperature through the test section. Obtained parameters are used to calculate the Nusselt number and friction factor across the test section for smooth and roughened absorber plate. The Nusselt number and friction factor parameters which is obtained for smooth absorber plate based on experimental set-up, is compared with Dittus-Bolter and Blasius equations, respectively, for validating the simulator. By calculating the Nusselt number and friction factor, Stanton number is obtained based on the equation (6, and thermohydraulic

Integral transform solution of bending problem of clamped orthotropic rectangular plates

International Nuclear Information System (INIS)

An, C.; Gu, J.-J.; Su, J.

2011-01-01

The generalized integral transform technique (GITT) is employed to obtain an exact solution for the bending problem of fully clamped orthotropic rectangular plates. The use of the GITT approach in the analysis of the transverse deflection equation leads to a coupled system of fourth order differential equations in the dimensionless longitudinal spatial variable. The resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from IMSL Library. Numerical results with automatic global accuracy control are produced for different values of aspect ratio. Critical comparisons with previously reported numerical results are performed with excellent agreement. Several sets of reference results for clamped orthotropic rectangular plates are also provided for future covalidation purposes. (author)

Using an equation based on flow stress to estimate structural integrity of annealed Type 304 stainless steel plate and pipes containing surface defects

International Nuclear Information System (INIS)

Reuter, W.G.; Place, T.A.

1981-01-01

An accurate assessment of the influence of defects on structural component integrity is needed. Generally accepted analytical techniques are not available for the very ductile materials used in many nuclear reactor components. Some results are presented from a test programme to obtain data by which to evaluate proposed models. Plate and pipe specimens containing surface flaws were fabricated from annealed Type 304 stainless steel and tested at room temperature. An evaluation of an empirical equation based on flow stress is presented. In essentially all instances the flow stress is not a constant but varies as a function of the size of the surface flaw. (author)

Mathematical modeling of impact of two metal plates using two-fluid approach

Science.gov (United States)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

Three dimensional mathematical modeling of violin plate surfaces: An approach based on an ensemble of contour lines.

Science.gov (United States)

Piantadosi, Steven

2017-01-01

This paper presents an approach to describing the three dimensional shape of a violin plate in mathematical form. The shape description begins with standard contour lines and ends with an equation for a surface in three dimensional space. The traditional specification of cross sectional arching is unnecessary. Advantages of this approach are that it employs simple and universal description of plate geometry and yields a complete, smoothed, precise mathematical equation of the plate that is suitable for modern three dimensional production. It is quite general and suitable for both exterior and interior plate surfaces, yielding the ability to control thicknesses along with shape. This method can produce mathematical descriptions with tolerances easily less than 0.001 millimeters suitable for modern computerized numerical control carving and hand finishing.

Quasi-estatic and dynamic elasto/viscoplastic analysis of plates and shells

International Nuclear Information System (INIS)

Dinis, L.M.S.

1981-01-01

The non-linear quasi-static and dynamic analysis of plates and shells is presented using the finite - element method for spatial discretization and the Central Finite Differences for the integration of the transient dynamic equation. The behaviour of the material is represented by the elasto/viscoplastic model of Perzyna together with approximations of the Von Mises yield surfaces for plates and shells. (Author) [pt

Numerical simulation of droplet evaporation between two circular plates

International Nuclear Information System (INIS)

Bam, Hang Jin; Son, Gi Hun

2015-01-01

Numerical simulation is performed for droplet evaporation between two circular plates. The flow and thermal characteristics of the droplet evaporation are numerically investigated by solving the conservation equations of mass, momentum, energy and mass fraction in the liquid and gas phases. The liquid-gas interface is tracked by a sharp-interface level-set method which is modified to include the effects of evaporation at the liquid-gas interface and contact angle hysteresis at the liquid-gas-solid contact line. An analytical model to predict the droplet evaporation is also developed by simplifying the mass and vapor fraction equations in the gas phase. The numerical results demonstrate that the 1-D analytical prediction is not applicable to the high rate evaporation process. The effects of plate gap and receding contact angle on the droplet evaporation are also quantified.

Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories

Science.gov (United States)

Ghodrati, Behnam; Yaghootian, Amin; Ghanbar Zadeh, Afshin; Mohammad-Sedighi, Hamid

2018-01-01

In this paper, Lamb wave propagation in a homogeneous and isotropic non-classical micro/nano-plates is investigated. To consider the effect of material microstructure on the wave propagation, three size-dependent models namely indeterminate-, modified- and consistent couple stress theories are used to extract the dispersion equations. In the mentioned theories, a parameter called 'characteristic length' is used to consider the size of material microstructure in the governing equations. To generalize the parametric studies and examine the effect of thickness, propagation wavelength, and characteristic length on the behavior of miniature plate structures, the governing equations are nondimensionalized by defining appropriate dimensionless parameters. Then the dispersion curves for phase and group velocities are plotted in terms of a wide frequency-thickness range to study the lamb waves propagation considering microstructure effects in very high frequencies. According to the illustrated results, it was observed that the couple stress theories in the Cosserat type material predict more rigidity than the classical theory; so that in a plate with constant thickness, by increasing the thickness to characteristic length ratio, the results approach to the classical theory, and by reducing this ratio, wave propagation speed in the plate is significantly increased. In addition, it is demonstrated that for high-frequency Lamb waves, it converges to dispersive Rayleigh wave velocity.

Development of stress correction formulae for heat formed steel plates

Directory of Open Access Journals (Sweden)

Hyung Kyun Lim

2018-03-01

Full Text Available The heating process such as line heating, triangular heating and so on is widely used in plate forming of shell plates found in bow and stern area of outer shell in a ship. Local shrinkage during heating process is main physical phenomenon used in plate forming process. As it is well appreciated, the heated plate undergoes the change in material and mechanical properties around heated area due to the harsh thermal process. It is, therefore, important to investigate the changes of physical and mechanical properties due to heating process in order to use them plate the design stage of shell plates. This study is concerned with the development of formula of plastic hardening constitutive equation for steel plate on which line heating is applied. In this study the stress correction formula for the heated plate has been developed based on the numerical simulation of tension test with varying plate thickness and heating speed through the regression analysis of multiple variable case. It has been seen the developed formula shows very good agreement with results of numerical simulation. This paper ends with usefulness of the present formula in examining the structural characteristic of ship's hull. Keywords: Heat input, Heat transfer analysis, Line heating, Shell plate, Stress correction, Thermo-elasto-plastic analysis

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

International Nuclear Information System (INIS)

Anjomshoa, Amin; Tahani, Masoud

2016-01-01

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded ortho tropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

Experimental and numerical study of the wave run-up along a vertical plate

DEFF Research Database (Denmark)

Molin, Bernard; Kimmoun, O.; Liu, Y.

2010-01-01

Results from experiments on wave interaction with a rigid vertical plate are reported. The 5m long plate is set against the wall of a 30m wide basin, at 100m from the wavemaker. This set-up is equivalent to a 10m plate in the middle of a 60m wide basin. Regular waves are produced, with wavelength...... on extended Boussinesq equations. In most of the experimental tests, despite the large distance from the wavemaker to the plate and the small amplitude of the incident wave, no steady state is attained by the end of the exploitable part of the records....

Parallel double-plate capacitive proximity sensor modelling based on effective theory

International Nuclear Information System (INIS)

Li, Nan; Zhu, Haiye; Wang, Wenyu; Gong, Yu

2014-01-01

A semi-analytical model for a double-plate capacitive proximity sensor is presented according to the effective theory. Three physical models are established to derive the final equation of the sensor. Measured data are used to determine the coefficients. The final equation is verified by using measured data. The average relative error of the calculated and the measured sensor capacitance is less than 7.5%. The equation can be used to provide guidance to engineering design of the proximity sensors

Hydromagnetic flow and radiative heat transfer of nanofluid past a vertical plate

Directory of Open Access Journals (Sweden)

B. Ganga

2017-11-01

Full Text Available Hydromagnetic flow of an incompressible viscous nanofluid past a vertical plate in the presence of thermal radiation is investigated both analytically and numerically. The radiative heat flux is described by the Rosseland diffusion approximation in the energy equation. The governing non-linear partial differential equations are converted into a set of ordinary differential equations by suitable similarity transformations. The resulting ordinary differential equations are successfully solved analytically with the help of homotopy analysis method and numerically by the fourth order Runge–Kutta method with shooting technique. The effects of various physical parameters are analyzed and discussed in graphical and tabular forms. The effects of some physical parameters such as Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, radiation parameter and magnetic parameter are analyzed on the velocity, temperature and solid volume fraction profiles as well as on the reduced Nusselt number and the local Sherwood number. An excellent agreement is observed between present analytical and numerical results. Keywords: Nanofluid, Hydromagnetic, Homotopy analysis method, Vertical plate and thermal radiation

A theoretical response of the electrostatic parallel plate to constant and low-frequency accelerations

International Nuclear Information System (INIS)

Lee, Ki Bang

2009-01-01

A theoretical response of an electrostatic gap-closing actuator based on parallel plates to constant and low-frequency accelerations has been derived as a function of the applied acceleration and voltage. The nonlinear equation of motion is obtained in a dimensionless form from the fact that the inertial and damping forces are neglected at a frequency much less than the resonant frequency of the parallel plate, and thereafter the nonlinear equation is solved for the stable inter-plate gap at the acceleration and voltage. From the derived solution, the pull-in acceleration is obtained as a function of the applied voltage, and the pull-in voltage is also expressed as a function of the acceleration. The closed-form solution is validated by comparison with a numerical solution. The theoretical solution is in excellent agreement with the numerical results when the actuator is exposed to a constant acceleration as well as a low-frequency acceleration. The theoretical solution and pull-in acceleration and voltage thus provide guidance to prescribe operational constraints for devices that use the parallel plate actuator and to predict the response of the electrostatic gap-closing parallel plates to constant and low-frequency acceleration

Finite thickness effect of a zone plate on focusing hard x-rays

International Nuclear Information System (INIS)

Yun, W.B.; Chrzas, J.; Viccaro, P.J.

1992-01-01

Spatial resolution and focusing efficiency are two important properties of a zone plate in x-ray focusing applications. A general expression of the zone plate equation describing its zone registration is derived from the interference of spherical waves emited from two mutually coherent point sources. An analytical expression of the focusing efficiency in terms of the zone plate thickness and x-ray refractive indices of the zones is also derived. Validity condition for using this expression is considered. Thickness required for obtaining adequate focusing efficiency is calculated as a function of x-ray energy for several representative materials. The spatial resolution of a finite thickness zone plate is worse than that of an infinetly thin zone plate. which is approximately equal to the smallest zone width of the zone plate. The effect of the finite thickness on the spatial resolution is considered

The Ritz - Sublaminate Generalized Unified Formulation approach for piezoelectric composite plates

Science.gov (United States)

D'Ottavio, Michele; Dozio, Lorenzo; Vescovini, Riccardo; Polit, Olivier

2018-01-01

This paper extends to composite plates including piezoelectric plies the variable kinematics plate modeling approach called Sublaminate Generalized Unified Formulation (SGUF). Two-dimensional plate equations are obtained upon defining a priori the through-thickness distribution of the displacement field and electric potential. According to SGUF, independent approximations can be adopted for the four components of these generalized displacements: an Equivalent Single Layer (ESL) or Layer-Wise (LW) description over an arbitrary group of plies constituting the composite plate (the sublaminate) and the polynomial order employed in each sublaminate. The solution of the two-dimensional equations is sought in weak form by means of a Ritz method. In this work, boundary functions are used in conjunction with the domain approximation expressed by an orthogonal basis spanned by Legendre polynomials. The proposed computational tool is capable to represent electroded surfaces with equipotentiality conditions. Free-vibration problems as well as static problems involving actuator and sensor configurations are addressed. Two case studies are presented, which demonstrate the high accuracy of the proposed Ritz-SGUF approach. A model assessment is proposed for showcasing to which extent the SGUF approach allows a reduction of the number of unknowns with a controlled impact on the accuracy of the result.

Lectures on nonlinear evolution equations initial value problems

CERN Document Server

Racke, Reinhard

2015-01-01

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

Simplified Procedure For The Free Vibration Analysis Of Rectangular Plate Structures With Holes And Stiffeners

Directory of Open Access Journals (Sweden)

Cho Dae Seung

2015-04-01

Full Text Available Thin and thick plates, plates with holes, stiffened panels and stiffened panels with holes are primary structural members in almost all fields of engineering: civil, mechanical, aerospace, naval, ocean etc. In this paper, a simple and efficient procedure for the free vibration analysis of such elements is presented. It is based on the assumed mode method and can handle different plate thickness, various shapes and sizes of holes, different framing sizes and types as well as different combinations of boundary conditions. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange’s equations. Mindlin theory is applied for a plate and Timoshenko beam theory for stiffeners. The applicability of the method in the design procedure is illustrated with several numerical examples obtained by the in-house developed code VAPS. Very good agreement with standard commercial finite element software is achieved.

Approximate method for solving the velocity dependent transport equation in a slab lattice

International Nuclear Information System (INIS)

Ferrari, A.

1966-01-01

A method is described that is intended to provide an approximate solution of the transport equation in a medium simulating a water-moderated plate filled reactor core. This medium is constituted by a periodic array of water channels and absorbing plates. The velocity dependent transport equation in slab geometry is included. The computation is performed in a water channel: the absorbing plates are accounted for by the boundary conditions. The scattering of neutrons in water is assumed isotropic, which allows the use of a double Pn approximation to deal with the angular dependence. This method is able to represent the discontinuity of the angular distribution at the channel boundary. The set of equations thus obtained is dependent only on x and v and the coefficients are independent on x. This solution suggests to try solutions involving Legendre polynomials. This scheme leads to a set of equations v dependent only. To obtain an explicit solution, a thermalization model must now be chosen. Using the secondary model of Cadilhac a solution of this set is easy to get. The numerical computations were performed with a particular secondary model, the well-known model of Wigner and Wilkins. (author) [fr

Heat transfer in plate heat exchanger channels: Experimental validation of selected correlation equations

Directory of Open Access Journals (Sweden)

Cieśliński Janusz T.

2016-09-01

Full Text Available This study is focused on experimental investigation of selected type of brazed plate heat exchanger (PHEx. The Wilson plot approach was applied in order to estimate heat transfer coefficients for the PHEx passages. The main aim of the paper was to experimentally check ability of several correlations published in the literature to predict heat transfer coefficients by comparison experimentally obtained data with appropriate predictions. The results obtained revealed that Hausen and Dittus-Boelter correlations underestimated heat transfer coefficient for the tested PHEx by an order of magnitude. The Aspen Plate code overestimated heat transfer coefficient by about 50%, while Muley-Manglik correlation overestimated it from 1% to 25%, dependent on the value of Reynolds number and hot or cold liquid side.

Vibroacoustic study of a point-constrained plate mounted in a duct

Science.gov (United States)

Sapkale, Swapnil L.; Sucheendran, Mahesh M.; Gupta, Shakti S.; Kanade, Shantanu V.

2018-04-01

The vibroacoustic study of the interaction of sound with a point-constrained, simply-supported square plate is considered in this paper. The plate is mounted flush on one of the walls of an infinite duct of rectangular cross section and is backed by a cavity. The plate response and the acoustic field is predicted by solving the coupled governing equations using modal expansion with the relevant eigenmodes of the plate dynamics and acoustic fields in the duct and cavity. By varying the location of the point constraint, the frequency characteristics of the transmission loss in the duct can be tuned. The point constraint can also alter the amplitude and spectral characteristics of the plate's response. Interestingly, some new peaks are observed in the response because of the excitation of unsymmetric modes which are otherwise dormant. Mode-localization phenomenon, which is the localization of vibration in specific regions of the plate, is observed for selected constrained points.

On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

NARCIS (Netherlands)

Zarubinskaya, M.A.; Van Horssen, W.T.

2003-01-01

In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is

Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

KAUST Repository

Said-Houari, Belkacem

2013-01-01

In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent

Calculation of similarity solutions of partial differential equations

International Nuclear Information System (INIS)

Dresner, L.

1980-08-01

When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/

Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

Directory of Open Access Journals (Sweden)

WANG Minhao

2017-08-01

Full Text Available Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

Vibration of functionally graded plate resting on viscoelastic elastic foundation subjected to moving loads

Science.gov (United States)

Duy Hien, Ta; Lam, Nguyen Ngoc

2018-04-01

The dynamics of plates subjected to a moving load must be considered by engineering mechanics and design structures. This paper deals with the dynamic responses of functionally graded (FG) rectangular plates resting on a viscoelastic foundation under moving loads. It is assumed that material properties of the plate vary continuously in the thickness direction according to the power-law. The governing equations are derived by using Hamilton’s principle, which considers the effect of the higher-order shear deformation in the plate. Transient responses of simply supported FG rectangular plates are employed by using state-space methods. Several examples are given for displacement and stresses in the plates with various structural parameters, and the effects of these parameters are discussed.

Modeling Open-Loop MEMS Tunneling Accelerometer Based on Circular Plate

Directory of Open Access Journals (Sweden)

Hossein Jodat Kordlar

2007-04-01

Full Text Available In this paper open-loop MEMS tunneling accelerometer was modeled based on a clamped micro circular plate with a tip tunneling at its centre. Mechanical behavior of the micro plate was studied deriving governing equation based on classic Kirchhoff thin plate theory and it was discretized using Galerkin method. Dynamic response of the proposed accelerometer due to step and harmonic external excitation was studied and the magnitude of the applied acceleration was identified by measuring of the changing of tunneling current. Obtained results show that the proposed tunneling accelerometer very sensitive and it can be measure acceleration with very high resolution but very small gap of tip tunneling limit the range of measurable acceleration.

Wettability measurements of irregular shapes with Wilhelmy plate method

Science.gov (United States)

Park, Jaehyung; Pasaogullari, Ugur; Bonville, Leonard

2018-01-01

One of the most accurate methods for measuring the dynamic contact angle of liquids on solid surfaces is the Wilhelmy plate method. This method generally requires the use of rectangular samples having a constant perimeter in the liquid during advancing and receding cycles. A new formulation based on the Wilhelmy force balance equation to determine the contact angle for plate samples with irregular shapes has been developed. This method employs a profile plot obtained from an optical image to determine the perimeter (i.e. wetted length) of the sample as a function of the immersion depth. The raw force data measured by the force tensiometer is manipulated using the profile plot and the Wilhelmy equation to determine the wetting force and consequently advancing and the receding contact angle. This method is verified with both triangular and irregular PTFE samples in water, and measured contact angles are in good agreement with results from conventional regular shaped samples with a constant perimeter.

Group analysis for natural convection from a vertical plate

Science.gov (United States)

Rashed, A. S.; Kassem, M. M.

2008-12-01

The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.

Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes

International Nuclear Information System (INIS)

Ortega J, R.; Valle G, E. del

2003-01-01

There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S 4 with expansions of the dispersion cross sections until P 3 order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

Magnetohydrodynamic unsteady flow of a Maxwell fluid past a flat plate

International Nuclear Information System (INIS)

Khandpur, S.L.; Ravi Kant

1979-01-01

A study of the equations describing the flow pattern set up in a linear electrically conducting viscoelastic fluid past an infinite flat plate in the presence of a transverse magnetic field has been made, when the plate is moving parallel to itself with an arbitrary time dependent velocity. The pressure is assumed to be uniform with initial velocity distribution in an exponential form. Operational methods are used to obtain the exact solutions for the velocity profiles. The effects of relaxation parameter of the fluid and magnetic field have been studied. Several particular cases are easily deduced of which two cases: (i) when the plate is moving in its own plane harmonically with time, and (ii) when the velocity of the plate is decaying exponentially with time, are discussed. (auth.)

Modelling of plate-out under gas-cooled reactor (GCR) accident conditions

International Nuclear Information System (INIS)

Taig, A.R.

1981-01-01

The importance of plate-out in mitigating consequences of gas-cooled reactor accidents, and its place in assessing these consequences, are discussed. The data requirements of a plate-out modelling program are discussed, and a brief description is given of parallel work programs on thermal/hydraulic reactor behaviour and fuel modelling, both of which will provide inputs to the plate-out program under development. The representation of a GCR system used in SRD studies is presented, and the equations governing iodine adsorption, desorption and transport round the circuit are derived. The status of SRD's plate-out program is described, and the type of sensitivity studies to be undertaken with the partially-developed computer program in order to identify the most useful lines for future research is discussed. (author)

Thin-plate spline quadrature of geodetic integrals

Science.gov (United States)

Vangysen, Herman

1989-01-01

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

An Irrotational Flow Field That Approximates Flat Plate Boundary Conditions

OpenAIRE

Ruffa, Anthony A.

2004-01-01

An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow, with severe numerical difficulties in some regions.

Numerical solution of the problems for plates on partial internal supports of complicated configurations

International Nuclear Information System (INIS)

Quang A, Dang; Hai, Truong Ha

2014-01-01

Very recently in the work S imple Iterative Method for Solving Problems for Plates with Partial Internal Supports, Journal of Engineering Mathematics, DOI: 10.1007/s10665-013-9652-7 (in press) , we proposed a numerical method for solving some problems of plates on one and two line partial internal supports (LPIS). In the essence they are problems with strongly mixed boundary conditions for biharmonic equation. Using this method we reduced the problems to a sequence of boundary value problems for the Poisson equation with weakly mixed boundary conditions, which are easily solved numerically. The advantages of the method over other ones were shown. In this paper we apply the method to plates on internal supports of more complicated configurations. Namely, we consider the case of three LPIS and the case of the cross support. The convergence of the method is established theoretically and its efficiency is confirmed on numerical experiments

Effect of magnetic field on Blasius and Sakiadis flow of nanofluids past an inclined plate

Directory of Open Access Journals (Sweden)

S.P. Anjali Devi

2017-11-01

Full Text Available A theoretical study on the effect of magnetic field on the classical Blasius and Sakiadis flow of nanofluids over an inclined plate is presented in this paper. The governing partial differential equations are converted into ordinary differential equations using suitable similarity transformations. The transformed boundary layer equations are solved numerically using MATLAB (bvp4c. Two types of nanoparticles are chosen namely copper and alumina in the base fluid of water with the Prandtl number (Pr = 6.2. The effects of the governing physical parameters over the velocity, temperature, skin friction coefficient and reduced Nusselt number for both the Blasius and Sakiadis flows are displayed graphically. The characteristics of physical and engineering interest are discussed in detail. Keywords: Nanofluid, Blasius flow, Sakiadis flow, MHD, Inclined plate, Mixed convection

Analysis of stress wave propagation in an elasto-viscoplastic plate

International Nuclear Information System (INIS)

Nakagawa, Noritoshi; Kawai, Ryoji; Urushi, Norio.

1986-01-01

Stress waves which propagate in the body are reflected at the boundary, and due to the interaction of the reflected stress waves, the focussing of stress waves will take place and a high stress level can be caused. The focussing of stress waves due to the reflection from the boundary may bring about fracture of the body, so that this is an important problem from a viewpoint of dynamic strength of structures. In this paper the process of stress wave focussing and the strain-rate dependence of constitutive equation in elastic and plastic regions are investigated. In the case where an in-plane step load uniformly acts on the straight edge of the plate with a semi-circular boundary, the propagation of stress waves in the plate was numerically analyzed by the finite element method, applying viscoelastic, elasto-plastic and elasto-viscoplastic constitutive equations. As the result, the process of focussing of stress waves due to reflection from the semi-circular boundary was observed and the difference in propagation behaviour of stress waves was discussed in materials represented by some kinds of constitutive equations. (author)

Static Analysis of Laminated Composite Plate using New Higher Order Shear Deformation Plate Theory

Directory of Open Access Journals (Sweden)

Ibtehal Abbas Sadiq

2017-02-01

Full Text Available In the present work a theoretical analysis depending on the new higher order . element in shear deformation theory for simply supported cross-ply laminated plate is developed. The new displacement field of the middle surface expanded as a combination of exponential and trigonometric function of thickness coordinate with the transverse displacement taken to be constant through the thickness. The governing equations are derived using Hamilton’s principle and solved using Navier solution method to obtain the deflection and stresses under uniform sinusoidal load. The effect of many design parameters such as number of laminates, aspect ratio and thickness ratio on static behavior of the laminated composite plate has been studied. The modal of the present work has been verified by comparing the results of shape functions with that were obtained by other workers. Result shows the good agreement with 3D elasticity solution and that published by other researchers.

Rigid-Plastic Post-Buckling Analysis of Columns and Quadratic Plates

DEFF Research Database (Denmark)

Jönsson, Jeppe

2008-01-01

the compressive load as a function of the transverse displacement. An estimate of the magnitude of the transverse displacement prior to the forming of the collapse mechanism is introduced into the compressive load function, determined by the virtual work equation, thereby revealing a qualified estimate...... yield lines accommodate differential rotations of rigid parts and the area “collapse” yield lines accommodate local area changes of the rigid parts thereby preserving compatibility of the rigid parts of a plate. The approach will be illustrated for rigid plastic column analysis and for a quadratic plate...

Conjugate heat transfer of laminar film condensation along a horizontal plate

Energy Technology Data Exchange (ETDEWEB)

Lee, Euk Soo [Pusan National Univesity, Busan (Korea, Republic of)

2006-03-15

This paper proposes appropriate conjugate parameters and dimensionless temperatures to analysis the conjugate problem of heat conduction in solid wall coupled with laminar film condensation flow adjacent to horizontal flat plate. An efficient methods for some fluids are proposed for its solution. The momentum and energy balance equations are reduced to a nonlinear system of ordinary differential equations with four parameters: the Prandtl number, Pr, Modified Jacob number, Ja{sup *}/Pr, defined by an overall temperature difference, a property ratio {radical}{rho}{sub {iota}}{mu}{sub {iota}} {radical}{rho}{sub {upsilon}}{mu}{sub {upsilon}} and the conjugate parameter {zeta}. The obtained similarity solution reveals the effect of the conjugate parameter, and the results are compared with the simplified solution. The variations of the heat transfer rates as well as the interface temperature and frictions along the plate are shown explicitly.

Compounded natural convection enhancement in a vertical parallel-plate channel

Energy Technology Data Exchange (ETDEWEB)

Andreozzi, Assunta [Dipartimento di Energetica, Termofluidodinamica Applicata e Condizionamenti Ambientali, Universita degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Campo, Antonio [Department of Mechanical Engineering, The University of Vermont, 33 Colchester Ave., Burlington, VT 05405 (United States); Manca, Oronzio [Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universita degli Studi di Napoli, via Roma 29, Aversa (CE) 81031 (Italy)

2008-06-15

This paper addresses the natural convection behavior of air when heated in single vertical, parallel-plate channels. To enhance the heat transfer two passive schemes are combined: (1) an equidistant short plate is inserted at the inlet and (2) two parallel, colinear insulated plates are appended at the exit. The channel plates are symmetrically heated with a uniform heat flux. The computational procedure is made by solving the full elliptic Navier-Stokes and energy equations with the finite-volume methodology in an I-type computational domain that is much larger than the physical domain. Within the framework of a ''proof-of-concept'' the controlling Grashof number based on the heated plate height ranges between 10{sup 3} and 10{sup 6}. The numerical velocity, pressure and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, the pressure at the channel mid-plane and the temperature along the plates. In addition, the Nusselt number and the average Nusselt number, both based on the heated plate height, are presented in graphical form. At the end, optimal channel configurations expressed in terms of the highest average Nusselt number are obtained for the pair of pre-assigned Grashof numbers. (author)

Reinforcement of a plate weakened by multiple holes with several patches for different types of plate-patch attachment

KAUST Repository

Zemlyanova, A.

2014-01-24

The most general situation of the reinforcement of a plate with multiple holes by several patches is considered. There is no restriction on the number and the location of the patches. Two types of patch attachment are considered: only along the boundary of the patch or both along the boundary of the patch and the boundaries of the holes which this patch covers. The unattached boundaries of the holes may be loaded with given in-plane stresses. The mechanical problem is reduced to a system of singular integral equations which can be further reduced to a system of Fredholm equations. A new numerical procedure for the solution of the system of singular integral equations is proposed in this paper. It is demonstrated on numerical examples that this procedure has advantages in the case of multiple patches and holes and allows achievement of better numerical convergence with less computational effort.

Parametric study on nonlinear vibration of composite truss core sandwich plate with internal resonance

Energy Technology Data Exchange (ETDEWEB)

Chen, Jia Nen; Liu, Jun [Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System, Tianjin University of Technology, Tianjin (China); Zhang, Wei; Yao, Ming Hui [College of Mechanical Engineering, Beijing University of Technology, Beijing (China); Sun, Min [School of Science, Tianjin Chengjian University, Tianjin (China)

2016-09-15

Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy's third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude.

Frequency response of rectangular plates with free-edge openings and carlings subjected to point excitation force and enforced displacement at boundaries

Directory of Open Access Journals (Sweden)

Dae Seung Cho

2016-03-01

Full Text Available In this paper, a numerical procedure for the natural vibration analysis of plates with openings and carlings based on the assumed mode method is extended to assess their forced response. Firstly, natural response of plates with openings and carlings is calculated from the eigenvalue equation derived by using Lagrange's equation of motion. Secondly, the mode superposition method is applied to determine frequency response. Mindlin theory is adopted for plate modelling and the effect of openings is taken into account by subtracting their potential and kinetic energies from the corresponding plate energies. Natural and frequency response of plates with openings and carlings subjected to point excitation force and enforced acceleration at boundaries, respectively, is analysed by using developed in-house code. For the validation of the developed method and the code, extensive numerical results, related to plates with different opening shape, carlings and boundary conditions, are compared with numerical data from the relevant literature and with finite element solutions obtained by general finite element tool.

Surface effects on the electroelastic responses of a thin piezoelectric plate with nanoscale thickness

International Nuclear Information System (INIS)

Yan Zhi; Jiang Liying

2012-01-01

This work aims to investigate the electroelastic responses of a thin piezoelectric plate under mechanical and electrical loads with the consideration of surface effects. Surface effects, including surface elasticity, residual surface stress and surface piezoelectricity, are incorporated into the conventional Kirchhoff plate theory for a piezoelectric plate via the surface piezoelectricity model and the generalized Young-Laplace equations. Different from the results predicted by the conventional plate theory ignoring the surface effects, the proposed model predicts size-dependent behaviours of the piezoelectric thin plate with nanoscale thickness. It is found that surface effects have significant influence on the electroelastic responses of the piezoelectric nanoplate. This work is expected to provide more accurate predictions on characterizing nanofilm or nanoribbon based piezoelectric devices in nanoelectromechanical systems. (paper)

Experimental and numerical simulation the effect of distribution plates in a mobile electrostatic precipitator

International Nuclear Information System (INIS)

Noorpoor, A. R.; Sadeghi, M.

2003-01-01

In this investigation, behaviour of airflow inside an electrostatic precipitator with three different distribution plates has been considered by means of numerical and experimental methods and results have been compared together. This device has been designed and produced in this center for the first time in Iran, and its ability to absorb particles, haze and soot is good. But for increasing the efficiency there must be some changes to an miscellaneous sections. Therefore, here we consider the effect of distribution plates to increase performance, because when distribution flow at cross sections of precipitator is uniform, the efficiency will increase. To have a numerical simulation, fluent software version 5.3 was and for modeling turbulence the RNG k-Σ turbulent model applied. This program after discretization governing equations on a body fitted coordinate system, that is produced in preprocessor, integrates this equations on control volumes and determines the rate of quantities on control volume faces using order two (upwind)approximations. Finally by means of a pitot tube velocity magnitude of fluid in two sections of domain was measured and compared with numerical results which shows a good agreement. After simulation the three model, e.g. without distribution plate, with a distribution plate after inlet duct and with two distribution plates (one after inlet duct and before outlet duct), and taking some results and by comparing them, we conclude that use of combined distribution plate can give a good result

Active damping of multiferroic composite plates using 1-3 piezoelectric composites

Science.gov (United States)

Kattimani, S. C.

2017-12-01

A layer-wise shear deformation theory is used to analyze the smart damping of multiferroic composite or magneto-electro-elastic (MEE) plates. The intent of this analysis is to investigate the need for incorporating additional smart elements for controlling the vibrations of multiferroic composite plates. Active constrained layer damping (ACLD) treatment has been incorporated to alleviate the vibration of MEE plate. A layer of viscoelastic material is used as constrained layer for the ACLD treatment. The coupled constitutive equations of multiferroic (ferroelectric and ferromagnetic) composite materials along with the total potential energy principle are used to derive the finite element formulation for the overall multiferroic or MEE plate. Maxwell’s electrostatic and electromagnetic relations are used to compute the electric and magnetic potential distribution. Influence of obliquely reinforced piezoelectric fibers in the piezoelectric layer of the ACLD treatment has also been investigated. In order to investigate the importance of using ACLD treatment for an active damping of multiferroic or MEE plate, an active control of MEE plate has also been analyzed by providing the control voltage directly to the piezoelectric layers of the MEE substrate plate without using the ACLD treatment. The present study suggests that for an optimal control of MEE plates, the smartness element such as the ACLD treatment is essentially required.

Numerical study on the effects of absorptivity on performance of flat plate solar collector of a water heater

Science.gov (United States)

Tambunan, D. R. S.; Sibagariang, Y. P.; Ambarita, H.; Napitupulu, F. H.; Kawai, H.

2018-03-01

The characteristics of absorber plate of a flat plate solar collector play an important role in the improvement of the performance. In this work, a numerical analysis is carried out to explore the effect of absorptivity and emissivity of absorber plate to the performance of the solar collector of a solar water heater. For a results comparison, a simple a simple solar box cooker with absorber area of 0.835 m × 0.835 m is designed and fabricated. It is employed to heat water in a container by exposing to the solar radiation in Medan city of Indonesia. The transient governing equations are developed. The governing equations are discretized and solved using the forward time step marching technique. The results reveal that the experimental and numerical results show good agreement. The absorptivity of the plate absorber and emissivity of the glass cover strongly affect the performance of the solar collector.

Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

KAUST Repository

Le Maitre, Olivier

2014-01-06

In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

KAUST Repository

Le Maitre, Olivier

2014-01-01

In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

Two-dimensional simulations of steady perforated-plate stabilized premixed flames

KAUST Repository

Altay, H. Murat

2010-03-17

The objective of this work is to examine the impact of the operating conditions and the perforated-plate design on the steady, lean premixed flame characteristics. We perform two-dimensional simulations of laminar flames using a reduced chemical kinetics mechanism for methane-air combustion, consisting of 20 species and 79 reactions. We solve the heat conduction problem within the plate, allowing heat exchange between the gas mixture and the solid plate. The physical model is based on a zero-Mach-number formulation of the axisymmetric compressible conservation equations. The results suggest that the flame consumption speed, the flame structure, and the flame surface area depend significantly on the equivalence ratio, mean inlet velocity, the distance between the perforated-plate holes and the plate thermal conductivity. In the case of an adiabatic plate, a conical flame is formed, anchored near the corner of the hole. When the heat exchange between themixture and the plate is finite, the flame acquires a Gaussian shape stabilizing at a stand-off distance, that grows with the plate conductivity. The flame tip is negatively curved; i.e. concave with respect to the reactants. Downstream of the plate, the flame base is positively curved; i.e. convex with respect to the reactants, stabilizing above a stagnation region established between neighboring holes. As the plate\\'s thermal conductivity increases, the heat flux to the plate decreases, lowering its top surface temperature. As the equivalence ratio increases, the flame moves closer to the plate, raising its temperature, and lowering the flame stand-off distance. As the mean inlet velocity increases, the flame stabilizes further downstream, the flame tip becomes sharper, hence raising the burning rate at that location. The curvature of the flame base depends on the distance between the neighboring holes; and the flame there is characterized by high concentration of intermediates, like carbon monoxide. © 2010 Taylor

thermoelastic waves without energy dissipation in an elastic plate ...

African Journals Online (AJOL)

cistvr

The first generalization, for isotropic bodies, is due to Lord & Shulman (1967) who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier's law. ...... In this paper we have studied the thermoelastic interactions due to the punching of a cylindrical hole in an elastic plate ...

Numerical investigation of the effects of compressibility on the flutter of a cantilevered plate in an inviscid, subsonic, open flow

Science.gov (United States)

Colera, Manuel; Pérez-Saborid, Miguel

2018-06-01

We have carried out a numerical study of the influence of the upstream Mach number on the flutter of a two-dimensional, cantilevered, flexible plate subject to a subsonic, inviscid, open flow. We have assumed a linear elastic model for the plate and that the fluid flow is governed by the linearized potential theory. The fluid equations are solved with a novel frequency-domain, finite differences method to obtain the generalized aerodynamic forces as a function of the plate displacements. Then, these generalized forces are coupled to the equation of motion of the plate and an eigenvalue analysis is performed to find the flutter point. The obtained results are in good agreement with those of related theoretical and experimental studies found in the literature. To the best of our knowledge, the analysis performed here is the first self-consistent, parametric study of the influence of the compressibility on the flutter point of a two-dimensional cantilevered plate in subsonic flow.

EXACT SOLUTION FOR TEMPERATURE-DEPENDENT BUCKLING ANALYSIS OF FG-CNT-REINFORCED MINDLIN PLATES

Directory of Open Access Journals (Sweden)

Seyed Mohammad Mousavi

2016-03-01

Full Text Available This research deals with the buckling analysis of nanocomposite polymeric temperature-dependent plates reinforced by single-walled carbon nanotubes (SWCNTs. For the carbon-nanotube reinforced composite (CNTRC plate, uniform distribution (UD and three types of functionally graded (FG distribution patterns of SWCNT reinforcements are assumed. The material properties of FG-CNTRC plate are graded in the thickness direction and estimated based on the rule of mixture. The CNTRC is located in a elastic medium which is simulated with temperature-dependent Pasternak medium. Based on orthotropic Mindlin plate theory, the governing equations are derived using Hamilton’s principle and solved by Navier method. The influences of the volume fractions of carbon nanotubes, elastic medium, temperature and distribution type of CNTs are considered on the buckling of the plate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the stiffness of plates.

Free vibration response of a multilayer smart hybrid composite plate with embedded SMA wires

Directory of Open Access Journals (Sweden)

K. Malekzadeh

Full Text Available In this paper, free vibration response of a hybrid composite plate was studied. Effects of some geometrical, physical and material parameters on response of the composite plates embedded with shape memory alloy (SMA wires were investigated, which have not been reported in the literature thus far. Some of these parameters included important factors affecting free vibration response of the smart hybrid composite plates. The SMA wires were embedded within the layers of the composite laminate. First-order shear deformation theory (FSDT was utilized to obtain the governing equations of hybrid composite plates. Transverse shear and rotary inertia effects of the plate were taken into consideration. For simply-supported boundary conditions, systematic closed form solutions were obtained by Navier's technique. It was established that dynamic behavior of the smart hybrid composite plate depended on various parameters such as volume fraction, temperature dependent recovery stress and tensile pre-strain of SMA wires and aspect ratio of the laminated hybrid plate.

Calibration of a laboratory spectrophotometer for specular light by means of stacked glass plates.

Science.gov (United States)

Allen, W. A.; Richardson, A. J.

1971-01-01

Stacked glass plates have been used to calibrate a laboratory spectrophotometer, over the spectral range 0.5-2.5 microns, for specular light. The uncalibrated instrument was characterized by systematic errors when used to measure the reflectance and transmittance of stacked glass plates. Calibration included first, a determination of the reflectance of a standard composed of barium sulfate paint deposited on an aluminum plate; second, the approximation of the reflectance and transmittance residuals between observed and computed values by means of cubic equations; and, finally, the removal of the systematic errors by a computer. The instrument, after calibration, was accurate to 1% when used to measure the reflectance and transmittance of stacked glass plates.

Control of Flowing Liquid Films By Electrostatic Fields in Space

Science.gov (United States)

Bankoff, S. George; Miksis, Michael J.; Kim, Hyo

1996-01-01

A novel type of lightweight space radiator has been proposed which employs internal electrostatic fields to stop coolant leaks from punctures caused by micrometeorites or space debris. Extensive calculations have indicated the feasibility of leak stoppage without film destabilization for both stationary and rotating designs. Solutions of the evolution equation for a liquid-metal film on an inclined plate, using lubrication theory for low Reynolds numbers, Karman-Pohlhausen quadratic velocity profiles for higher Reynolds numbers, and a direct numerical solution are shown. For verification an earth-based falling-film experiment on a precisely-vertical wall with controllable vacuum on either side of a small puncture is proposed. The pressure difference required to start and to stop the leak, in the presence and absence of a strong electric field, will be measured and compared with calculations. Various parameters, such as field strength, film Reynolds number, contact angle, and hole diameter will be examined. A theoretical analysis will be made of the case where the electrode is close enough to the film surface that the electric field equation and the surface dynamics equations are coupled. Preflight design calculations will be made in order to transfer the modified equipment to a flight experiment.

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Chaos control for the plates subjected to subsonic flow

Science.gov (United States)

Norouzi, Hamed; Younesian, Davood

2016-07-01

The suppression of chaotic motion in viscoelastic plates driven by external subsonic air flow is studied. Nonlinear oscillation of the plate is modeled by the von-Kármán plate theory. The fluid-solid interaction is taken into account. Galerkin's approach is employed to transform the partial differential equations of the system into the time domain. The corresponding homoclinic orbits of the unperturbed Hamiltonian system are obtained. In order to study the chaotic behavior of the plate, Melnikov's integral is analytically applied and the threshold of the excitation amplitude and frequency for the occurrence of chaos is presented. It is found that adding a parametric perturbation to the system in terms of an excitation with the same frequency of the external force can lead to eliminate chaos. Variations of the Lyapunov exponent and bifurcation diagrams are provided to analyze the chaotic and periodic responses. Two perturbation-based control strategies are proposed. In the first scenario, the amplitude of control forces reads a constant value that should be precisely determined. In the second strategy, this amplitude can be proportional to the deflection of the plate. The performance of each controller is investigated and it is found that the second scenario would be more efficient.

The influence of retention on the plate height in ion-exchange chromatography

DEFF Research Database (Denmark)

Hansen, Ernst; Mollerup, Jørgen

2004-01-01

The plate heights for the amino acid tyrosine (anion exchange) and the polypeptide aprotinin (cation exchange) were determined on a porous media (Resource 15) and a get filled media (HyperD 20) at salt concentrations ranging from weak to strong retention. At a constant velocity, measurements showed....... In this article, the rate of mass transfer in the particles is described by three different rate mechanisms, pore diffusion, solid diffusion, and parallel diffusion. The van Deemter equation was used to model the data to determine the mass-transfer properties. The development of the plate height with increasing...... retention revealed a characteristic behavior for each rate mechanism. In the pore diffusion model, the plate height increased toward a constant value at strong retention, while the plate height in the solid diffusion model decreased, approaching a constant value at strong retention. In the parallel...

Hydrodynamics of a flexible plate between pitching rigid plates

Science.gov (United States)

Kim, Junyoung; Kim, Daegyoum

2017-11-01

The dynamics of a flexible plate have been studied as a model problem in swimming and flying of animals and fluid-structure interaction of plants and flags. Motivated by fish schooling and an array of sea grasses, we investigate the dynamics of a flexible plate closely placed between two pitching rigid plates. In most studies on passive deformation of the flexible plate, the plate is immersed in a uniform flow or a wavy flow. However, in this study, the flexible plate experiences periodic deformation by the oscillatory flow generated by the prescribed pitching motion of the rigid plates. In our model, the pitching axes of the rigid plates and the clamping position of the flexible plate are aligned on the same line. The flexible plate shows various responses depending on length and pitching frequency of rigid plates, thickness of a flexible plate, and free-stream velocity. To find the effect of each variable on the response of the flexible plate, amplitude of a trailing edge and modal contribution of a flapping motion are compared, and flow structure around the flexible plate is examined.

Aligned Magnetic Field, Radiation, and Rotation Effects on Unsteady Hydromagnetic Free Convection Flow Past an Impulsively Moving Vertical Plate in a Porous Medium

Directory of Open Access Journals (Sweden)

Sandeep Naramgari

2014-01-01

Full Text Available We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases.

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Viscous dissipation effects on heat transfer in flow past a continuous moving plate

Digital Repository Service at National Institute of Oceanography (India)

Soundalgekar, V.M.; Murty, T.V.R.

The study of thermal boundary layer on taking into account the viscous dissipative heat, on a continuously moving semi-infinite flat plate is presented here.Similarity solutions are derived and the resulting equations are integrated numerically...

Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory

Directory of Open Access Journals (Sweden)

Yuwaraj Marotrao Ghugal

Full Text Available Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to nonlinear thermal load through the thickness of laminated plates are presented by using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.

Transient convective heat transfer to laminar flow from a flat plate with constant heat capacity

International Nuclear Information System (INIS)

Hanawa, Juichi

1980-01-01

Most basic transient heat transfer problem is the transient response characteristics of forced convection heat transfer in the flow along a flat plate or in a tube. In case of the laminar flow along a flat plate, the profile method using steady temperature distribution has been mostly adopted, but its propriety has not been clarified yet. About the unsteady heat transfer in the laminar flow along a flat plate, the analysis or experiment evaluating the heat capacity of the flat plate exactly was never carried out. The purpose of this study is to determine by numerical calculation the unsteady characteristics of the boundary layer in laminar flow and to confirm them by experiment concerning the unsteady heat transfer when a flat plate with a certain heat capacity is placed in parallel in uniform flow and given a certain quantity of heat generation suddenly. The basic equation and the solution are given, and the method of numerical calculation and the result are explained. The experimental setup and method, and the experimental results are shown. Both results were in good agreement, and the response of wall temperature, the response of Nusselt number and the change of temperature distribution in course of time were able to be determined by applying Laplace transformation and numerical Laplace inverse transformation to the equation. (Kako, I.)

Mass transfer effects on vertical oscillating plate with heat flux

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2007-01-01

Full Text Available Theoretical solution of unsteady viscous incompressible flow past an infinite vertical oscillating plate with uniform heat flux and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. The temperature from the plate to the fluid at an uniform rate and the mass is diffused uniformly. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle chemical reaction parameter, thermal Grashof number, mass Grashof number Schmidt number and time are studied. The so­lutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter.

Polymer concentration and properties of elastic turbulence in a von Karman swirling flow

Science.gov (United States)

Jun, Yonggun; Steinberg, Victor

2017-10-01

We report detailed experimental studies of statistical, scaling, and spectral properties of elastic turbulence (ET) in a von Karman swirling flow between rotating and stationary disks of polymer solutions in a wide, from dilute to semidilute entangled, range of polymer concentrations ϕ . The main message of the investigation is that the variation of ϕ just weakly modifies statistical, scaling, and spectral properties of ET in a swirling flow. The qualitative difference between dilute and semidilute unentangled versus semidilute entangled polymer solutions is found in the dependence of the critical Weissenberg number Wic of the elastic instability threshold on ϕ . The control parameter of the problem, the Weissenberg number Wi, is defined as the ratio of the nonlinear elastic stress to dissipation via linear stress relaxation and quantifies the degree of polymer stretching. The power-law scaling of the friction coefficient on Wi/Wic characterizes the ET regime with the exponent independent of ϕ . The torque Γ and pressure p power spectra show power-law decays with well-defined exponents, which has values independent of Wi and ϕ separately at 100 ≤ϕ ≤900 ppm and 1600 ≤ϕ ≤2300 ppm ranges. Another unexpected observation is the presence of two types of the boundary layers, horizontal and vertical, distinguished by their role in the energy pumping and dissipation, which has width dependence on Wi and ϕ differs drastically. In the case of the vertical boundary layer near the driving disk, wvv is independent of Wi/Wic and linearly decreases with ϕ /ϕ * , while in the case of the horizontal boundary layer wvh its width is independent of ϕ /ϕ * , linearly decreases with Wi/Wic , and is about five times smaller than wvv. Moreover, these Wi and ϕ dependencies of the vertical and horizontal boundary layer widths are found in accordance with the inverse turbulent intensity calculated inside the boundary layers Vθh/Vθh rms and Vθv/Vθv rms , respectively

Solution of the Bagley Torvik equation by fractional DTM

Science.gov (United States)

Arora, Geeta; Pratiksha

2017-07-01

In this paper, fractional differential transform method(DTM) is implemented on the Bagley Torvik equation. This equation models the viscoelastic behavior of geological strata, metals, glasses etc. It explains the motion of a rigid plate immersed in a Newtonian fluid. DTM is a simple, reliable and efficient method that gives a series solution. Caputo fractional derivative is considered throughout this work. Two examples are given to demonstrate the validity and applicability of the method and comparison is made with the existing results.

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

Damping mathematical modelling and dynamic responses for FRP laminated composite plates with polymer matrix

Science.gov (United States)

Liu, Qimao

2018-02-01

This paper proposes an assumption that the fibre is elastic material and polymer matrix is viscoelastic material so that the energy dissipation depends only on the polymer matrix in dynamic response process. The damping force vectors in frequency and time domains, of FRP (Fibre-Reinforced Polymer matrix) laminated composite plates, are derived based on this assumption. The governing equations of FRP laminated composite plates are formulated in both frequency and time domains. The direct inversion method and direct time integration method for nonviscously damped systems are employed to solve the governing equations and achieve the dynamic responses in frequency and time domains, respectively. The computational procedure is given in detail. Finally, dynamic responses (frequency responses with nonzero and zero initial conditions, free vibration, forced vibrations with nonzero and zero initial conditions) of a FRP laminated composite plate are computed using the proposed methodology. The proposed methodology in this paper is easy to be inserted into the commercial finite element analysis software. The proposed assumption, based on the theory of material mechanics, needs to be further proved by experiment technique in the future.

Flow induced deformation and collapse of a thin rectangular plate with application to the Engineering Test Reactor nuclear fuel elements

International Nuclear Information System (INIS)

Davis, C.D.

1981-01-01

This work examines a single flat fuel plate bounded by two channels and determines static plate deflections, resultant forces and bending stresses due to pressure differential and hydrodynamic loadings. The classical then reactangular plate equations are used to model the fuel plate. These equations contain as an input the hydrodynamic loading function for modeling the fluid-structural interaction. Two models of the channel flow are developed. One assumes the accelerating potential core flow is laminar with developing two-dimensional laminar boundary layers being formed on the channel walls. The Schlichting entry length solution for developing laminar flow is found to be valid the entire length of the channel. The second model assumes the core flow is fully-developed turbulent the entire length of the channel. Hydrodynamic loading functions are developed for both flow models containing parameters for fluid density, fluid velocity, Reynolds number and channel and plate dimensions. Hence the effects of each parameter can be examined independently. A criterion is developed for predicting ETR fuel plate collapse at high channel flow velocities, 1067 cm/s (420 in/sec) (R/sub e/ = 60,000). The criterion predicts that in order to prevent ETR plate collapse the inlet velocities between channels must not differ by more than 2%

Pyrolysis and Boundary Layer Combustion of a Non-Charring Solid Plate Under Forced Flow

National Research Council Canada - National Science Library

Ananth, Ramagopal

2003-01-01

Solutions of Navier-Stokes (NS) equations were obtained for burning rate Nu and temperature distributions for a flat PMMA plate using an iterative method to impose steady-state, pyrolysis kinetics at the surface...

Multipactor saturation in parallel-plate waveguides

International Nuclear Information System (INIS)

Sorolla, E.; Mattes, M.

2012-01-01

The saturation stage of a multipactor discharge is considered of interest, since it can guide towards a criterion to assess the multipactor onset. The electron cloud under multipactor regime within a parallel-plate waveguide is modeled by a thin continuous distribution of charge and the equations of motion are calculated taking into account the space charge effects. The saturation is identified by the interaction of the electron cloud with its image charge. The stability of the electron population growth is analyzed and two mechanisms of saturation to explain the steady-state multipactor for voltages near above the threshold onset are identified. The impact energy in the collision against the metal plates decreases during the electron population growth due to the attraction of the electron sheet on the image through the initial plate. When this growth remains stable till the impact energy reaches the first cross-over point, the electron surface density tends to a constant value. When the stability is broken before reaching the first cross-over point the surface charge density oscillates chaotically bounded within a certain range. In this case, an expression to calculate the maximum electron surface charge density is found whose predictions agree with the simulations when the voltage is not too high.

Effect of partial heating at mid of vertical plate adjacent to porous medium

Science.gov (United States)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets

Science.gov (United States)

Sahmani, Saeid; Aghdam, Mohammad Mohammadi; Rabczuk, Timon

2018-04-01

By gradually changing of the porosity across a specific direction, functionally graded porous materials (FGPMs) are produced which can impart desirable mechanical properties. To enhance these properties, it is common to reinforce FGPMs with nanofillers. The main aim of the current study is to investigate the size-dependent nonlinear axial postbuckling characteristics of FGPM micro/nano-plates reinforced with graphene platelets. For this purpose, the theory of nonlocal strain gradient elasticity incorporating the both stiffness reduction and stiffness enhancement mechanisms of size effects is applied to the refined exponential shear deformation plate theory. Three different patterns of porosity dispersion across the plate thickness in conjunction with the uniform one are assumed for FGPM as an open-cell metal foam is utilized associated with the coefficients of the relative density and porosity. With the aid of the virtual work’s principle, the non-classical governing differential equations are constructed. Thereafter, an improved perturbation technique is employed to capture the size dependencies in the nonlinear load-deflection and load-shortening responses of the reinforced FGPM micro/nano-plates with and without initial geometric imperfection. It is indicated that by increasing the value of porosity coefficient, the size-dependent critical buckling loads of reinforced FGPM micro/nano-plates with all types of porosity dispersion pattern reduce, but the associated shortening may increase or decrease which depends on the type of dispersion pattern.

An experimental and theoretical investigation of the mechanical behavior of multilayer initially curved microplates under electrostatic actuation

KAUST Repository

Saghir, Shahid

2017-04-07

We investigate the static and dynamic behavior of a multilayer clamped-free-clamped-free (CFCF) microplate, which is made of polyimide, gold, chromium, and nickel. The microplate is slightly curved away from a stationary electrode and is electrostatically actuated. The free and forced vibrations of the microplate are examined. First, we experimentally investigate the variation of the first natural frequency under the electrostatic DC load. Then, the forced dynamic behavior is investigated by applying a harmonic AC voltage superimposed to a DC voltage. Results are shown demonstrating the transition of the dynamic response of the microplate from hardening to softening as the DC voltage is changed as well the dynamic pull-in phenomenon. For theoretical model, we adopt a dynamic analog of the von-Karman governing equations accounting for initial curvature imperfection. These equations are then used to develop a reduced order model based on the Galerkin procedure to simulate the mechanical behavior of the microplate. We compare the theoretical results with experimental data and show excellent agreement among the results. We also examine the effect of the initial rise on the natural frequencies of first three symmetric-symmetric modes of the plate.

The Nonlinear Dynamic Response of an Elastic-Plastic Thin Plate under Impulsive Loading,

Science.gov (United States)

1987-06-11

Among those numerical methods, the finite element method is the most effective one. The method presented in this paper is an " influence function " numerical...computational time is much less than the finite element method. Its precision is higher also. II. Basic Assumption and the Influence Function of a Simple...calculation. Fig. 1 3 2. The Influence function of a Simple Supported Plate The motion differential equation of a thin plate can be written as DV’w+ _.eluq() (1

Fire resistance of a steel plate reinforced concrete bearing wall

International Nuclear Information System (INIS)

Kodaira, Akio; Kanchi, Masaki; Fujinaka, Hideo; Akita, Shodo; Ozaki, Masahiko

2003-01-01

Samples from a steel plate reinforced concrete bearing wall composed of concrete slab sandwiched between studded steel plates, were subjected to loaded fire resistance tests. There were two types of specimens: some were 1800 mm high while the rest were 3000 mm high ; thickness and width were the same for all specimens, at 200 mm and 800 mm, respectively. Under constant load conditions, one side of each specimen was heated along the standard fire-temperature curve. The results enabled us to approximate the relationship between the ratio of working load to concrete strength N/(Ac x c σ b) and the fire resistance time (t: minutes), as equation (1) for the 1800 mm - high specimen, and equation (2) for the 3000 mm - high specimen. N/(Ac x c σ b) = 2.21 x (1/t) 0.323 (1), .N/(Ac x c σ b) 2.30 x (1/t) 0.378 (2) In addition, the temperature of the unheated side of the specimens was 100degC at 240 minutes of continuous heating, clearly indicating that there was sufficient heat insulation. (author)

Parametric Studies of Flat Plate Trajectories Using VIC and Penalization

Directory of Open Access Journals (Sweden)

François Morency

2018-01-01

Full Text Available Flying debris is generated in several situations: when a roof is exposed to a storm, when ice accretes on rotating wind turbines, or during inflight aircraft deicing. Four dimensionless parameters play a role in the motion of flying debris. The goal of the present paper is to investigate the relative importance of four dimensionless parameters: the Reynolds number, the Froude number, the Tachikawa number, and the mass moment of inertia parameters. Flying debris trajectories are computed with a fluid-solid interaction model formulated for an incompressible 2D laminar flow. The rigid moving solid effects are modelled in the Navier-Stokes equations using penalization. A VIC scheme is used to solve the flow equations. The aerodynamic forces and moments are used to compute the acceleration and the velocity of the solid. A database of 64 trajectories is built using a two-level full factorial design for the four factors. The dispersion of the plate position at a given horizontal position decreases with the Froude number. Moreover, the Tachikawa number has a significant effect on the median plate position.

Mathematical model of temperature field distribution in thin plates during polishing with a free abrasive

Directory of Open Access Journals (Sweden)

Avilov Alex

2017-01-01

Full Text Available The purpose of this paper is to estimate the dynamic characteristics of the heating process of thin plates during polishing with a free abrasive. A mathematical model of the temperature field distribution in space and time according to the plate thickness is based on Lagrange equation of the second kind in the thermodynamics of irreversible processes (variation principle Bio. The research results of thermo elasticity of thin plates (membranes will allow to correct the modes of polishing with a free abrasive to receive the exact reflecting surfaces of satellites reflector, to increase temperature stability and the ability of radio signal reflection, satellite precision guidance. Calculations of temperature fields in thin plates of different thicknesses (membranes is held in the Excel, a graphical characteristics of temperature fields in thin plates (membranes show non-linearity of temperature distribution according to the thickness of thin plates (membranes.

Development of novel segmented-plate linearly tunable MEMS capacitors

International Nuclear Information System (INIS)

Shavezipur, M; Khajepour, A; Hashemi, S M

2008-01-01

In this paper, novel MEMS capacitors with flexible moving electrodes and high linearity and tunability are presented. The moving plate is divided into small and rigid segments connected to one another by connecting beams at their end nodes. Under each node there is a rigid step which selectively limits the vertical displacement of the node. A lumped model is developed to analytically solve the governing equations of coupled structural-electrostatic physics with mechanical contact. Using the analytical solver, an optimization program finds the best set of step heights that provides the highest linearity. Analytical and finite element analyses of two capacitors with three-segmented- and six-segmented-plate confirm that the segmentation technique considerably improves the linearity while the tunability remains as high as that of a conventional parallel-plate capacitor. Moreover, since the new designs require customized fabrication processes, to demonstrate the applicability of the proposed technique for standard processes, a modified capacitor with flexible steps designed for PolyMUMPs is introduced. Dimensional optimization of the modified design results in a combination of high linearity and tunability. Constraining the displacement of the moving plate can be extended to more complex geometries to obtain smooth and highly linear responses

Modal radiation patterns of baffled circular plates and membranes.

Science.gov (United States)

Christiansen, Thomas Lehrmann; Hansen, Ole; Thomsen, Erik Vilain; Jensen, Jørgen Arendt

2014-05-01

The far field velocity potential and radiation pattern of baffled circular plates and membranes are found analytically using the full set of modal velocity profiles derived from the corresponding equation of motion. The derivation is valid for a plate or membrane subjected to an external excitation force, which is used as a sound receiver in any medium or as a sound transmitter in a gaseous medium. A general, concise expression is given for the radiation pattern of any mode of the membrane and the plate with arbitrary boundary conditions. Specific solutions are given for the four special cases of a plate with clamped, simply supported, and free edge boundary conditions as well as for the membrane. For all non-axisymmetric modes, the velocity potential along the axis of the radiator is found to be strictly zero. In the long wavelength limit, the radiation pattern of all axisymmetric modes approaches that of a monopole, while the non-axisymmetric modes exhibit multipole behavior. Numerical results are also given, demonstrating the implications of having non-axisymmetric excitation using both a point excitation with varying eccentricity and a homogeneous excitation acting on half of the circular radiator.

Modeling of damage evaluation in thin composite plate loaded by pressure loading

Directory of Open Access Journals (Sweden)

Dudinský M.

2012-12-01

Full Text Available This article presents the results of numerical analysis of elastic damage of thin laminated long fiber-reinforced composite plate consisting of unidirectional layers which is loaded by uniformly distributed pressure. The analysis has been performed by means of the finite element method (FEM. The numerical implementation uses layered plate finite elements based on the Kirchhoff plate theory. System of nonlinear equations has been solved by means of the Newton- Raphson procedure. Evolution of damage has been solved using the return-mapping algorithm based on the continuum damage mechanics (CDM. The analysis was performed using own program created in MATLAB. Problem of laminated fiber-reinforced composite plate fixed on edges for two different materials and three different laminate stacking sequences (LSS was simulated. Evolution of stresses vs. strains and also evolution of damage variables in critical points of the structure are shown.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

Science.gov (United States)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

CREATION OF MATHEMATICAL MODEL OF EXTRACTION BY CHEESE WHEY FROM A LUPINE IN THE FORM OF A PLATE

Directory of Open Access Journals (Sweden)

Y. I. Shishatskii

2015-01-01

Full Text Available Prerequisites for creation of model are stated. At a problem definition consideration of a particle of a lupine as unlimited plate is proved. The main assumptions are formulated, regional conditions are written out. Partial solutions of the differential equation, and also the common decision for the current value of a concentration pressure С'(x,у. Distribution of concentration is symmetric concerning ordinate axis. Final expression for a field of concentration at extraction of a flat plate in a dimensionless look is written out. It is shown that distribution of concentration is rather precisely described by the first member of a row. Th e conclusion is drawn that for any timepoint under the set boundary conditions the field of concentration has an appearance of a symmetric curve with a maximum on a plate axis (Х=0. For each subsequent timepoint there will be the curve which is monotonously decreasing to a plate surface. It is proved that it is possible to define nature of change of concentration in a body at a preset value the case when strives for infinity at the set physical parameters, thickness of a plate and the organization of high intensity of branch of extractive substances from a surface Is considered. For this case the equations of rather dimensionless concentration and Fourier's numb er are received. Also the equation for definition of final time of extraction is written out. It is shown that the received solutions of the eq uations of model are found in a good consent with experimental data.

Investigation of free vibration characteristics for skew multiphase magneto-electro-elastic plate

Science.gov (United States)

Kiran, M. C.; Kattimani, S.

2018-04-01

This article presents the investigation of skew multiphase magneto-electro-elastic (MMEE) plate to assess its free vibration characteristics. A finite element (FE) model is formulated considering the different couplings involved via coupled constitutive equations. The transformation matrices are derived to transform local degrees of freedom into the global degrees of freedom for the nodes lying on the skew edges. Effect of different volume fraction (Vf) on the free vibration behavior is explicitly studied. In addition, influence of width to thickness ratio, the aspect ratio, and the stacking arrangement on natural frequencies of skew multiphase MEE plate investigated. Particular attention has been paid to investigate the effect of skew angle on the non-dimensional Eigen frequencies of multiphase MEE plate with simply supported edges.

Magnetohydrodynamic mixed convective slip flow over an inclined porous plate with viscous dissipation and Joule heating

Directory of Open Access Journals (Sweden)

S. Das

2015-06-01

Full Text Available The combined effects of viscous dissipation and Joule heating on the momentum and thermal transport for the magnetohydrodynamic flow past an inclined plate in both aiding and opposing buoyancy situations have been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the plate. The results show that there are significant effects of pertinent parameters on the flow fields.

A Numerical Study on Laminar Free Convection between Vertical Flat Plates with Symmetric Heating

Directory of Open Access Journals (Sweden)

Ameer A. Jadoaa

2012-06-01

Full Text Available The development of free convection in a viscous fluid between heated plates is investigated. The basic governing continuity, momentum, and energy equations are solved numerically by finite difference method. Results are obtained for the variations of Nusselt number, velocity, temperature, and pressure throughout the flow field assuming the fluid to enter the channel with ambient temperature and a flat velocity profile. The flow and heat-transfer characteristics of the channel are studied and a development height established. Heating plate condition is (C.W.T and C.H.F. An correlation equation has been deduced for the average Nusselt number as a function of Rayligt number. A comparison is made between the results of this theoretical investigation and theoretical work of (Bodoia, J.R 1962[1].

Multimedia in physics education: teaching videos about aero and fluid dynamics

International Nuclear Information System (INIS)

Wagner, Andreas; Altherr, Stefan; Eckert, Bodo; Jodl, Hans Joerg

2007-01-01

In a series of letters, we present teaching videos on topics which are difficult to understand for students, or which are difficult to realize experimentally in school, if at all. These videos can be used for quantitative analysis or visualization of phenomena. Here we present videos on aero and fluid dynamics which deal with the Navier-Stokes equation, the continuity equation and Karman's vortex street. (letters and comments)

Investigation of Three-Dimensional Axisymmetric Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

OpenAIRE

ali shokrgozar abbasi; Asghar Baradaran Rahimi; Hamidreza Mozayeni

2016-01-01

General formulation and solution of Navier-Stokes and energy equations are sought in the study of threedimensional axisymmetric unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration towards the main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z - directi...

Dynamic Response of a Rigid Pavement Plate Based on an Inertial Soil.

Science.gov (United States)

Gibigaye, Mohamed; Yabi, Crespin Prudence; Alloba, I Ezéchiel

2016-01-01

This work presents the dynamic response of a pavement plate resting on a soil whose inertia is taken into account in the design of pavements by rational methods. Thus, the pavement is modeled as a thin plate with finite dimensions, supported longitudinally by dowels and laterally by tie bars. The subgrade is modeled via Pasternak-Vlasov type (three-parameter type) foundation models and the moving traffic load is expressed as a concentrated dynamic load of harmonically varying magnitude, moving straight along the plate with a constant acceleration. The governing equation of the problem is solved using the modified Bolotin method for determining the natural frequencies and the wavenumbers of the system. The orthogonal properties of eigenfunctions are used to find the general solution of the problem. Considering the load over the center of the plate, the results showed that the deflections of the plate are maximum about the middle of the plate but are not null at its edges. It is therefore observed that the deflection decreased 18.33 percent when the inertia of the soil is taken into account. This result shows the possible economic gain when taking into account the inertia of soil in pavement dynamic design.

Flow over a traveling wavy foil with a passively flapping flat plate

Science.gov (United States)

Liu, Nansheng; Peng, Yan; Liang, Youwen; Lu, Xiyun

2012-05-01

Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The study reveals that the passively oscillating flat plate contributes half of the propulsive force. The flexibility, represented by the nondimensional natural frequency F, plays a very important role in the movement and propulsive force generation of the whole body. When the plate is too flexible, the drag force is observed. As the flat plate becomes more rigid, the propulsive force that is generated when the undulation is confined to last part of the wavy foil becomes larger. The steady movement occurs at F=5. These results are consistent with the observations of some swimming animals in nature.

Nonlinear Aeroelastic Analysis of the HIAD TPS Coupon in the NASA 8' High Temperature Tunnel: Theory and Experiment

Science.gov (United States)

Goldman, Benjamin D.; Scott, Robert C,; Dowell, Earl H.

2014-01-01

The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments.

Optimum Energy Extraction from Coherent Vortex Rings Passing Tangentially Over Flexible Plates

Science.gov (United States)

Pirnia, Alireza; Browning, Emily A.; Peterson, Sean D.; Erath, Byron D.

2017-11-01

Coherent vortical structures can incite self-sustained oscillations in flexible membranes. This concept has recently gained interest for energy extraction from ambient environments. In this study the special case of a vortex ring passing tangentially over a cantilevered flexible plate is investigated. This problem is governed by the Kirchhoff-Love plate equation, which can be expressed in terms of a non-dimensional mass parameter of the plate, non-dimensional pressure loading induced by the vortex ring, and a Strouhal (St) number which expresses the duration of pressure loading relative to the period of plate oscillation. For a plate with a fixed mass parameter immersed in a fluid environment, the St number specifies the beam dynamics and the energy exchange process. The aim of this study is to identify the St number corresponding to maximum energy exchange between plates and vortex rings. The energy exchange process between the vortex ring and the plate is investigated over a range of 0.3 transfer is reported in each case and an empirical correlation is provided for predictive purposes. Supported by the National Science Foundation (NSF) under Grant No. CBET-1511761, and the Natural Sciences and Engineering Research Council of Canada (NSERC), under Grant No. 05778-2015.

Heat and mass transfer effects on moving vertical plate in the presence of thermal radiation

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2004-01-01

Full Text Available Thermal radiation effects on moving infinite vertical plate in the presence variable temperature and mass diffusion is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature and the concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity and skin-friction are studied for different parameters like thermal Grashof number, mass Grashof number, time and radiation parameter. It is observed that the velocity slightly decreases with increasing value of the radiation parameter.

An Experimental and Analytical Study of a Radiative Cooling System with Unglazed Flat Plate Collectors

DEFF Research Database (Denmark)

Hosseinzadeh, Elham; Taherian, Hessam

2012-01-01

plate solar collectors in a humid area, Babol, Iran, is assessed both experimentally and numerically. Different methods available in the literature are reviewed and by using a widely accepted model, the sky temperature is determined. The mathematical model for a flat plate solar collector is used...... as a guideline to derive the governing equations of a night sky radiator. Then, a cooling loop, including a storage tank, pump, connecting pipes, and a radiator has been studied experimentally. The water is circulated through the unglazed flat-plate radiator having 4 m2 of collector area at night to be cooled...

Theoretical study of chemical reaction effects on vertical oscillating plate with variable temperature

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Muthucumaraswamy R.

2006-01-01

Full Text Available An exact solution to the flow of a viscous incompressible unsteady flow past an infinite vertical oscillating plate with variable temperature and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. Both the plate temperature and the concentration level near the plate are raised linearly with respect to time. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time are studied. The solutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter. .

Asymmetric Vibrations of a Circular Elastic Plate on an Elastic Half Space

DEFF Research Database (Denmark)

Schmidt, H.; Krenk, Steen

1982-01-01

The asymmetric problem of a vibrating circular elastic plate in frictionless contact with an elastic half space is solved by an integral equation method, where the contact stress appears as the unknown function. By a trigonometric expansion, the problem is reduced to a number of uncoupled two...

The structure of Karman vortex streets in the atmospheric boundary layer derived from large eddy simulation

Energy Technology Data Exchange (ETDEWEB)

Heinze, Rieke; Raasch, Siegfried; Etling, Dieter [Hannover Univ. (Germany). Inst. fuer Meteorologie und Klimatologie

2012-06-15

Karman vortex streets generated in the wake of an idealized island are studied using large eddy simulation (LES). Simulations were carried out under conditions of a dry convective boundary layer, capped by an inversion below the island top. These conditions are more realistic compared to previous studies in which mesoscale models with a uniform stable stratification were used. Several properties of the vortex streets like the shedding period of the vortices and the distances between cyclonic and anti-cyclonic vortices were determined for various values of Froude number and surface heat flux. The main focus of the study was to identify the azimuthally averaged structure of fully developed single vortices, which is presented here for the first time. For this purpose a tracking mechanism was developed which allows to detect and to follow vortices automatically. Because the capping inversion is located below the obstacle top, the vortices extend throughout the whole depth of the mixed layer and their features are almost constant with height. They have a nearly upright vertical axis with a warm core, which is feeded by a convergent near-surface inflow of warm air. The vortex core is dominated by a continuous updraft in the order of 10 cm s{sup -1}, which is associated with a divergent outflow of air at the vortex' top. This flow divergence creates an additional increase in temperature due to a locally sinking inversion, which is probably responsible for the cloud-free eye of many observed vortices. An increase in the surface heat flux is causing a faster decay of the vortices due to stronger boundary layer turbulence. Other vortex features derived from the simulations are very similar to those from previous studies. (orig.)

Critical impact energy for the perforation of metallic plates

International Nuclear Information System (INIS)

Aly, S.Y.; Li, Q.M.

2008-01-01

This paper investigates the empirical formulae used in engineering practice to predict the critical perforation energy of metallic plates struck by rigid projectiles in the sub-ordnance regime. Main factors affecting the critical perforation energy are identified and valid conditions for each empirical formula are compared. Dimensional analysis is conducted to show the dependence of the non-dimensional critical impact energy on other influential non-dimensional numbers. Available empirical formulae are re-expressed in non-dimensional forms. A modified Jowett/AEA equation is proposed to predict the critical perforation energy of a flat-ended short projectile. The present work increases the confidence of using these empirical formulae and can be regarded as a quick guide for ballistic protection design of metallic shields and steel armour plates

A new strain based brick element for plate bending

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L. Belounar

2014-03-01

Full Text Available This paper presents the development of a new three-dimensional brick finite element by the use of the strain based approach for the linear analysis of plate bending. The developed element has the three essential external degrees of freedom (U, V and W at each of the eight corner nodes as well as at the centroidal node. The displacement field of the developed element is based on assumed functions for the various strains satisfying the compatibility equations and the static condensation technique is used for the internal node. The performance of this element is evaluated on several problems related to thick and thin plate bending in linear analysis. The obtained results show the good performances and accuracy of the present element.

Oscillations of a spring-magnet system damped by a conductive plate

Science.gov (United States)

Ladera, C. L.; Donoso, G.

2013-09-01

We study the motion of a spring-magnet system that oscillates with very low frequencies above a circular horizontal non-magnetizable conductive plate. The magnet oscillations couple with the plate via the Foucault currents induced therein. We develop a simple theoretical model for this magneto-mechanical oscillator, a model that leads to the equation of a damped harmonic oscillator, whose weak attenuation constant depends upon the system parameters, e.g. the electrical conductivity of the constituent material of the plate and its thickness. We present a set of validating experiments, the results of which are predicted with good accuracy by our analytical model. Additional experiments can be performed with this oscillating system or its variants. This oscillator is simple and low-cost, easy to assemble, and can be used in experiments or project works in physics teaching laboratories at the undergraduate level.

Oscillations of a spring–magnet system damped by a conductive plate

International Nuclear Information System (INIS)

Ladera, C L; Donoso, G

2013-01-01

We study the motion of a spring–magnet system that oscillates with very low frequencies above a circular horizontal non-magnetizable conductive plate. The magnet oscillations couple with the plate via the Foucault currents induced therein. We develop a simple theoretical model for this magneto-mechanical oscillator, a model that leads to the equation of a damped harmonic oscillator, whose weak attenuation constant depends upon the system parameters, e.g. the electrical conductivity of the constituent material of the plate and its thickness. We present a set of validating experiments, the results of which are predicted with good accuracy by our analytical model. Additional experiments can be performed with this oscillating system or its variants. This oscillator is simple and low-cost, easy to assemble, and can be used in experiments or project works in physics teaching laboratories at the undergraduate level. (paper)

Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

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Shaochong Yang

2017-01-01

Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.

Application of viscoplastic constitutive equations in finite element programs

International Nuclear Information System (INIS)

Hornberger, K.; Stamm, H.

1987-04-01

The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de

Refined Modeling of Flexural Deformation of Layered Plates with a Regular Structure Made from Nonlinear Hereditary Materials

Science.gov (United States)

Yankovskii, A. P.

2018-01-01

On the basis of constitutive equations of the Rabotnov nonlinear hereditary theory of creep, the problem on the rheonomic flexural behavior of layered plates with a regular structure is formu-lated. Equations allowing one to describe, with different degrees of accuracy, the stress-strain state of such plates with account of their weakened resistance to transverse shear were ob-tained. From them, the relations of the nonclassical Reissner- and Reddytype theories can be found. For axially loaded annular plates clamped at one edge and loaded quasistatically on the other edge, a simplified version of the refined theory, whose complexity is comparable to that of the Reissner and Reddy theories, is developed. The flexural strains of such metal-composite annular plates in shortterm and long-term loadings at different levels of heat action are calcu-lated. It is shown that, for plates with a relative thickness of order of 1/10, neither the classical theory, nor the traditional nonclassical Reissner and Reddy theories guarantee reliable results for deflections even with the rough 10% accuracy. The accuracy of these theories decreases at elevated temperatures and with time under long-term loadings of structures. On the basic of relations of the refined theory, it is revealed that, in bending of layered metal-composite heat-sensitive plates under elevated temperatures, marked edge effects arise in the neighborhood of the supported edge, which characterize the shear of these structures in the transverse direction

Resolution of Laplace equation in a region containing plane and cylindrical charged plates

International Nuclear Information System (INIS)

Jesus Paes, A.C. de.

1986-05-01

A computational program to solve the Laplace equation, in two dimensions, was developed. Cylindrical coordinates were used and the electric potential was calculated in a region bounded by an eccentric circunference that is grounded and in this region there were electrodes at known potential. The iterative method of Gauss-Seidel was used to solve the equation and the matrix of the coefficients, a sparse matrix, was stored in a compacted form in three line matrices. The distribution of this electric field were obtained from the potential and a subroutine to draw was developed. (author) [pt

About one counterexample of applying method of splitting in modeling of plating processes

Science.gov (United States)

Solovjev, D. S.; Solovjeva, I. A.; Litovka, Yu V.; Korobova, I. L.

2018-05-01

The paper presents the main factors that affect the uniformity of the thickness distribution of plating on the surface of the product. The experimental search for the optimal values of these factors is expensive and time-consuming. The problem of adequate simulation of coating processes is very relevant. The finite-difference approximation using seven-point and five-point templates in combination with the splitting method is considered as solution methods for the equations of the model. To study the correctness of the solution of equations of the mathematical model by these methods, the experiments were conducted on plating with a flat anode and cathode, which relative position was not changed in the bath. The studies have shown that the solution using the splitting method was up to 1.5 times faster, but it did not give adequate results due to the geometric features of the task under the given boundary conditions.

Heat transfer in flow past a continuously moving porous flat plate with heat flux

Digital Repository Service at National Institute of Oceanography (India)

Murty, T.V.R.; Sarma, Y.V.B.

The analysis of the heat transfer in flow past a continuously moving semi-infinite plate in the presence of suction/ injection with heat flux has been presented. Similarity solutions have been derived and the resulting equations are integrated...

Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM

Energy Technology Data Exchange (ETDEWEB)

Hatami, M., E-mail: m.hatami@tue.nl [Esfarayen University of Technology, Mechanical Engineering Department, Esfarayen, North Khorasan (Iran, Islamic Republic of); Jing, Dengwei; Song, Dongxing [International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi' an 710049 (China); Sheikholeslami, M.; Ganji, D.D. [Department of Mechanical Engineering, Babol University of Technology, Babol (Iran, Islamic Republic of)

2015-12-15

In this study, effect of variable magnetic field on nanofluid flow and heat transfer analysis between two parallel disks is investigated. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy perturbation method. The analytical investigation is carried out for different governing parameters namely: squeeze number, suction parameter, Hartmann number, Brownian motion parameter, thermophrotic parameter and Lewis number. Results show that Nusselt number has direct relationship with Brownian motion parameter and thermophrotic parameter but it is a decreasing function of squeeze number, suction parameter, Hartmann number and Lewis number. - Highlights: • Heat and mass transfer of nanofluids between parallel plates investigated. • A variable magnetic field is applied on the plates. • Governing equations are solved analytically. • Effects of physical parameters are discussed on the Nusselt number.

Heat transfer and flow analysis of nanofluid flow between parallel plates in presence of variable magnetic field using HPM

International Nuclear Information System (INIS)

Hatami, M.; Jing, Dengwei; Song, Dongxing; Sheikholeslami, M.; Ganji, D.D.

2015-01-01

In this study, effect of variable magnetic field on nanofluid flow and heat transfer analysis between two parallel disks is investigated. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy perturbation method. The analytical investigation is carried out for different governing parameters namely: squeeze number, suction parameter, Hartmann number, Brownian motion parameter, thermophrotic parameter and Lewis number. Results show that Nusselt number has direct relationship with Brownian motion parameter and thermophrotic parameter but it is a decreasing function of squeeze number, suction parameter, Hartmann number and Lewis number. - Highlights: • Heat and mass transfer of nanofluids between parallel plates investigated. • A variable magnetic field is applied on the plates. • Governing equations are solved analytically. • Effects of physical parameters are discussed on the Nusselt number

Heat transfer effects on flow past an exponentially accelerated vertical plate with variable temperature

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2008-01-01

Full Text Available An exact solution to the problem of flow past an exponentially accelerated infinite vertical plate with variable temperature is analyzed. The temperature of the plate is raised linearly with time t. The dimensionless governing equations are solved using Laplace-transform technique. The velocity and temperature profiles are studied for different physical parameters like thermal Grashof number Gr, time and an accelerating parameter a. It is observed that the velocity increases with increasing values of a or Gr.

Optimization Design of Bipolar Plate Flow Field in PEM Stack

Science.gov (United States)

Wen, Ming; He, Kanghao; Li, Peilong; Yang, Lei; Deng, Li; Jiang, Fei; Yao, Yong

2017-12-01

A new design of bipolar plate flow field in proton exchange membrane (PEM) stack was presented to develop a high-performance transfer efficiency of the two-phase flow. Two different flow fields were studied by using numerical simulations and the performance of the flow fields was presented. the hydrodynamic properties include pressure gap between inlet and outlet, the Reynold’s number of the two types were compared based on the Navier-Stokes equations. Computer aided optimization software was implemented in the design of experiments of the preferable flow field. The design of experiments (DOE) for the favorable concept was carried out to study the hydrodynamic properties when changing the design parameters of the bipolar plate.

MHD free convection flow past an oscillating plate in the presence of ...

African Journals Online (AJOL)

The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow past an infinite vertical oscillating plate through porous medium, taking account of the presence of free convection and mass transfer. The energy and chemical species equations are solved in closed form by Laplace-transform technique and ...

Cold plate

Energy Technology Data Exchange (ETDEWEB)

Marroquin, Christopher M.; O' Connell, Kevin M.; Schultz, Mark D.; Tian, Shurong

2018-02-13

A cold plate, an electronic assembly including a cold plate, and a method for forming a cold plate are provided. The cold plate includes an interface plate and an opposing plate that form a plenum. The cold plate includes a plurality of active areas arranged for alignment over respective heat generating portions of an electronic assembly, and non-active areas between the active areas. A cooling fluid flows through the plenum. The plenum, at the non-active areas, has a reduced width and/or reduced height relative to the plenum at the active areas. The reduced width and/or height of the plenum, and exterior dimensions of cold plate, at the non-active areas allow the non-active areas to flex to accommodate surface variations of the electronics assembly. The reduced width and/or height non-active areas can be specifically shaped to fit between physical features of the electronics assembly.

Trefftz method in solving Fourier-Kirchhoff equation for two-phase flow boiling in a vertical rectangular minichannel

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Hożejowska Sylwia

2017-01-01

Full Text Available This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.

An optimal approach to active damping of nonlinear vibrations in composite plates using piezoelectric patches

International Nuclear Information System (INIS)

Saviz, M R

2015-01-01

In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain–displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman–type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations. (paper)

Damping mathematical modelling and dynamic responses for FRP laminated composite plates with polymer matrix

Directory of Open Access Journals (Sweden)

Liu Qimao

2018-02-01

Full Text Available This paper proposes an assumption that the fibre is elastic material and polymer matrix is viscoelastic material so that the energy dissipation depends only on the polymer matrix in dynamic response process. The damping force vectors in frequency and time domains, of FRP (Fibre-Reinforced Polymer matrix laminated composite plates, are derived based on this assumption. The governing equations of FRP laminated composite plates are formulated in both frequency and time domains. The direct inversion method and direct time integration method for nonviscously damped systems are employed to solve the governing equations and achieve the dynamic responses in frequency and time domains, respectively. The computational procedure is given in detail. Finally, dynamic responses (frequency responses with nonzero and zero initial conditions, free vibration, forced vibrations with nonzero and zero initial conditions of a FRP laminated composite plate are computed using the proposed methodology. The proposed methodology in this paper is easy to be inserted into the commercial finite element analysis software. The proposed assumption, based on the theory of material mechanics, needs to be further proved by experiment technique in the future.

MHD and radiation effects on moving isothermal vertical plate with variable mass diffusion

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Muthucumaraswamy R.

2006-01-01

Full Text Available An analysis is performed to study the effects of thermal radiation on unsteady free convective flow over a moving vertical plate with mass transfer in the presence of magnetic field. The fluid considered here is a gray, absorbing-emitting radiation but a non- scattering medium. The plate temperature is raised to T 0 and the concentration level near the plate is also raised linearly with time. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature and concentration are studied for different parameters like the magnetic field parameter, radiation parameter, thermal Grashof number, mass Grashof number and time. It is observed that the velocity decreases with increasing magnetic field parameter or radiation parameter. .

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

Science.gov (United States)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-04-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Earth Reflected Solar Radiation Incident upon an Arbitrarily Oriented Spinning Flat Plate

Science.gov (United States)

Cunningham, Fred G.

1963-01-01

A general derivation is given for the earth reflected solar radiation input to a flat plate--a solar cell paddle, for example--which is spinning about an axis coincident with the axis of symmetry of the satellite to which it is affixed. The resulting equations are written for the general case so that arbitrary orientations of the spin axis with respect to the earth-satellite line and arbitrary orientations of the normal to the plate with respect to the spin axis can be treated. No attempt is made to perform the resulting integrations because of the complexity of the equations; nor is there any attempt to delineate the integration limits for the general case. However, the equations governing these limits are given. The appendixes contain: the results, in graphical form, of two representative examples; the general computer program for the calculation is given in Fortran notation; and the results of a calculation of the distribution of albedo energy on the proposed Echo II satellite. The value of the mean solar constant used is 1.395 times 10 (sup 4) ergs per centimeters-squared per second; the mean albedo of the earth is assumed to be 0.34; and the earth is assumed to be a diffuse reflector.

Effect of geometric and process variables on the performance of inclined plate settlers in treating aquacultural waste.

Science.gov (United States)

Sarkar, Sudipto; Kamilya, Dibyendu; Mal, B C

2007-03-01

Inclined plate settlers are used in treating wastewater due to their low space requirement and high removal rates. The prediction of sedimentation efficiency of these settlers is essential for their performance evaluation. In the present study, the technique of dimensional analysis was applied to predict the sedimentation efficiency of these inclined plate settlers. The effect of various geometric parameters namely, distance between plates (w(p)), plate angle (alpha), length of plate (l(p)), plate roughness (epsilon(p)), number of plates (n(p)) and particle diameter (d(s)) on the dynamic conditions, influencing the sedimentation process was studied. From the study it was established that neither the Reynolds criterion nor the Froude criterion was singularly valid to simulate the sedimentation efficiency (E) for different values of w(p) and flow velocity (v(f)). Considering the prevalent scale effect, simulation equations were developed to predict E at different dynamic conditions. The optimum dynamic condition producing the maximum E is also discussed.

Three-Dimensional Elasticity Solutions for Sound Radiation of Functionally Graded Materials Plates considering State Space Method

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Tieliang Yang

2016-01-01

Full Text Available This paper presents an analytical study for sound radiation of functionally graded materials (FGM plate based on the three-dimensional theory of elasticity. The FGM plate is a mixture of metal and ceramic, and its material properties are assumed to have smooth and continuous variation in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. Based on the three-dimensional theory of elasticity and state space method, the governing equations with variable coefficients of the FGM plate are derived. The sound radiation of the vibration plate is calculated with Rayleigh integral. Comparisons of the present results with those of solutions in the available literature are made and good agreements are achieved. Finally, some parametric studies are carried out to investigate the sound radiation properties of FGM plates.

Forced and free convection hydromagnetic flow past a vertical flat plate

International Nuclear Information System (INIS)

Abdelkhalek, M.M.

2004-01-01

The effects of magnetic field and temperature heat source on the free and forced convection flow past an infinite vertical plate is studied analytically. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using perturbation technique. The expression for the velocity field, skin friction and Nusselt number have been obtained

Asymmetric free vibrations of laminated annular cross-ply circular plates including the effects of shear deformation and rotary inertia. Spline method

Energy Technology Data Exchange (ETDEWEB)

Viswanathan, K.K.; Kim, Kyung Su; Lee, Jang Hyun [Inha Univ., Incheon (Korea). Dept. of Naval Architecture and Ocean Engineering

2009-12-15

Asymmetric free vibrations of annular cross-ply circular plates are studied using spline function approximation. The governing equations are formulated including the effects of shear deformation and rotary inertia. Assumptions are made to study the cross-ply layered plates. A system of coupled differential equations are obtained in terms of displacement functions and rotational functions. These functions are approximated using Bickley- type spline functions of suitable order. Then the system is converted into the eigenvalue problem by applying the point collocation technique and suitable boundary conditions. Parametric studies have been made to investigate the effect of transverse shear deformation and rotary inertia on frequency parameter with respect to the circumferential node number, radii ratio and thickness to radius ratio for both symmetric and anti-symmetric cross-ply plates using various types of material properties. (orig.)

Properties of local equations for a separation column

International Nuclear Information System (INIS)

Hodor, I.

1992-01-01

An overall theory of column separation is developed. A general expression for fully-developed concentration fields is found. For close-separation processes, a simple method to derive the theoretical plate height and the stage efficiency from local equations are given. Application of separation-of-variables to linearized systems is discussed and a partial range completeness of the eigenfunctions is found. (author)

Calculation of the heat flow peak in case of local defect of the fuel plate of a nuclear reactor

International Nuclear Information System (INIS)

Fabrega, Serge

1965-11-01

The author reports the calculation of the local thermal flow which exits a fuel plate in a nuclear reactor, where a fabrication defect creates a much localized peak of the power density released in the plate. He first reports the development of the problem equations: hypotheses and data, equation elaboration, simplification and resolution. He presents the results of a numeric application to actual cases, and describes how the conduction in the sheath is taken into account (study of the influence of peak width and shape), and gives a synthetic presentation of the formula for the approximate calculation of the heat flow in case of local defect [fr

Time dependent shear stress and temperature distribution over an insulated flat plate moving at hypersonic speed.

Science.gov (United States)

Rodkiewicz, C. M.; Gupta, R. N.

1971-01-01

The laminar two-dimensional flow over a stepwise accelerated flat plate moving with hypersonic speed at zero angle of attack is analysed. The governing equations in the self-similar form are linearized and solved numerically for small times. The solutions obtained are the deviations of the velocity and the temperature profiles from those of steady state. The presented results may be used to find the first order boundary layer induced pressure on the plate.

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

2014-01-01

Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

On the contact interaction of two identical stringers with an elastic semi-infinite continuous or vertically cracked plate

Science.gov (United States)

Grigoryan, M. S.

2018-04-01

This paper considers two connected contact problems on the interaction of stringers with an elastic semi-infinite plate. In the first problem, an elastic half-infinite continuous plate is reinforced on its boundary by two identical stringers exposed to a tensile external force. In the second problem, in the presence of the same stringers, the plate contains a collinear system of cracks on its vertical axis. The solution of both problems is reduced to the solution of singular integral equations (SIE) that are solved by a known numerical-analytical method.

J-integral and limit load analysis of semi-elliptical surface cracks in plates under bending

International Nuclear Information System (INIS)

Lei, Y.

2004-01-01

Systematic detailed linear and non-linear finite element (FE) analyses are performed for semi-elliptical surface cracks in plates under bending. Limit load (moment) solutions are obtained from the FE J results via the reference stress method. The FE results show that the Newman and Raju stress intensity factor equation is reasonably accurate and the Yagawa et al. J solution may significantly under estimate J for bending load. The relationship between J and the limit load is found to be dependent on the ratio a/t and a/c, where a and c are the depth and the half-length of the crack and t is the plate thickness. For a/t≤0.5 with a/c=0.2, J for any position along a crack front can be predicted by the reference stress method using a single limit load value except for the points very close to the plate surface. For all other cases, it can only be approximately estimated by the reference stress method because a limit load value that can satisfy all the FE J solutions along the crack front cannot be found. However, for all the cases examined, the maximum J along the crack front can be well predicted by the reference stress method when a proper global limit load is used. The Goodall and Webster global limit load equation is extended to any crack depth. The limit load data obtained in this paper can be well reproduced by the extended equation

Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation

KAUST Repository

Saghir, Shahid

2016-12-01

The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear static and dynamic behavior of rectangular microplates under small and large actuating forces. In the first part, we present and compare various approaches to develop reduced order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. In the second part, we present an investigation of the static and dynamic behavior of a fully clamped microplate. We investigate the effect of different non-dimensional design parameters on the static response. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of midplane stretching. However, the behavior switches to softening as the DC load is increased. Next, near-square plates are studied to understand the effect of geometric imperfections of microplates. In the final part of the dissertation, we investigate the mechanical behavior of

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

Science.gov (United States)

Cheng, Yong; Ji, Chun-yan; Zhai, Gang-jun; Oleg, Gaidai

2018-03-01

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy's law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.

Scaling of mean inertia and theoretical basis for a log law in turbulent boundary layers

Science.gov (United States)

Philip, Jimmy; Morrill-Winter, Caleb; Klewicki, Joseph

2017-11-01

Log law in the mean streamwise velocity (U) for pipes/channels is well accepted based on the derivation from the mean momentum balance (MMB) equation and support from experimental data. For flat plate turbulent boundary layers (TBLs), however, there is only empirical evidence and a theoretical underpinning of the kind available for pipes/channels in lacking. The main difficultly is the mean inertia (MI) term in the MMB equation, which, unlike in pipes/channels, is not a constant in TBLs. We present results from our paper (JFM `` 2017, Vol 813, pp 594-617), where the MI term for TBL is transformed so as to render it invariant in the outer region, corroborated with high Re (δ+) data from Melbourne Wind Tunnel and New Hampshire Flow Physics Facility. The transformation is possible because the MI term in the TBL has a `shape' which becomes invariant with increasing δ+ and a `magnitude' which is proportional to 1 /δ+ . The transformed equation is then employed to derive a log law for U with κ an order one (von-Karman) constant. We also show that the log law begins at y+ =C1√{δ+} , and the peak location of the Reynolds shear stress, ym+ =C2√{δ+} , where, C1 3.6 and C2 2.17 are from high Re data. Australian Research Council and the US National Science Foundation.

Inelastic damage using continuum damage mechanics in composite plate reinforced by unidirectional fibers

Directory of Open Access Journals (Sweden)

Žmindák Milan

2018-01-01

Full Text Available It is well that a finite element method is very popular simulation method to predict the physical behavior of systems and structures. In the last years an increase of interest in a new type of numerical methods known as meshless methods was observed. The paper deals with application of radial basis functions on modelling of inelastic damage using continuum damage mechanics of layered plate composite structures reinforced with long unidirectional fibers. For numerical simulations of elastic-plastic damage of layered composite plates own computational programs were implemented in MATLAB programming language. We will use the Newton-Raphson method to solve nonlinear systems of equations. Evaluation damage during plasticity has been solved using return mapping algorithm. The results of elastic-plastic damage analysis of composite plate with unsymmetrical laminate stacking sequence are presented.

Heat transfer in porous medium embedded with vertical plate: Non-equilibrium approach - Part A

Energy Technology Data Exchange (ETDEWEB)

Badruddin, Irfan Anjum [Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 (Malaysia); Quadir, G. A. [School of Mechatronic Engineering, University Malaysia Perlis, Pauh Putra, 02600 Arau, Perlis (Malaysia)

2016-06-08

Heat transfer in a porous medium embedded with vertical flat plate is investigated by using thermal non-equilibrium model. Darcy model is employed to simulate the flow inside porous medium. It is assumed that the heat transfer takes place by natural convection and radiation. The vertical plate is maintained at isothermal temperature. The governing partial differential equations are converted into non-dimensional form and solved numerically using finite element method. Results are presented in terms of isotherms and streamlines for various parameters such as heat transfer coefficient parameter, thermal conductivity ratio, and radiation parameter.

Heat transfer in porous medium embedded with vertical plate: Non-equilibrium approach - Part A

International Nuclear Information System (INIS)

Badruddin, Irfan Anjum; Quadir, G. A.

2016-01-01

Heat transfer in a porous medium embedded with vertical flat plate is investigated by using thermal non-equilibrium model. Darcy model is employed to simulate the flow inside porous medium. It is assumed that the heat transfer takes place by natural convection and radiation. The vertical plate is maintained at isothermal temperature. The governing partial differential equations are converted into non-dimensional form and solved numerically using finite element method. Results are presented in terms of isotherms and streamlines for various parameters such as heat transfer coefficient parameter, thermal conductivity ratio, and radiation parameter

Study of flow past an exponentially accelerated isothermal vertical plate in the presence of chemical reaction

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2010-01-01

Full Text Available Theoretical study of unsteady flow past an exponentially accelerated infinite isothermal vertical plate with variable mass diffusion has been presented in the presence of homogeneous chemical reaction of first order. The plate temperature is raised to Tw and species concentration level near the plate is made to rise linearly with time. The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles are studied for different physical parameters like chemical reaction parameter, thermal Grashof number, mass Grashof number, a and time. It is observed that the velocity increases with increasing values of a or t. But the trend is just reversed with respect to K.

Exact solution of thermal radiation on vertical oscillating plate with variable temperature and mass flux

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2010-01-01

Full Text Available Thermal radiation effects on unsteady flow past an infinite vertical oscillating plate in the presence of variable temperature and uniform mass flux is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with time and the mass is diffused from the plate to the fluid at an uniform rate. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, concentration and temperature are studied for different physical parameters like the phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing phase angle ωt.

Vibrations And Deformations Of Moderately Thick Plates In Stochastic Finite Element Method

Directory of Open Access Journals (Sweden)

Grzywiński Maksym

2015-12-01

Full Text Available The paper deals with some chosen aspects of stochastic dynamical analysis of moderately thick plates. The discretization of the governing equations is described by the finite element method. The main aim of the study is to provide the generalized stochastic perturbation technique based on classical Taylor expansion with a single random variable.

HEAT AND MASS TRANSFER FOR VISCO-ELASTIC MHD BOUNDARY LAYER FLOW PAST A VERTICAL FLAT PLATE

OpenAIRE

Rita Choudhury; Hridi Ranjan Deb

2012-01-01

The two-dimensional free convection flow of visco-elastic and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to ordinary differential equation by introducing appropriate co-ordinate transformation. The analytical expressions for the velocity, temperature and species concentration fields have been obtained. The corresponding expressions for the non-dimensional rates of he...

The interaction of thermal radiation on vertical oscillating plate with variable temperature and mass diffusion

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2006-01-01

Full Text Available Thermal radiation effects on unsteady free convective flow of a viscous incompressible flow past an infinite vertical oscillating plate with variable temperature and mass diffusion has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with respect to time and the concentration level near the plate is also raised linearly with respect to time. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity, temperature and concentration are studied for different parameters like phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time are studied. It is observed that the velocity increases with decreasing phase angle ωt. .

Motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates

Energy Technology Data Exchange (ETDEWEB)

Abd Elkhalek, M M [Nuclear Research Center-Atomic Energy Authority, Cairo (Egypt)

1997-12-31

The motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates is discussed. The equation of motion of a suspended particle was suggested by Closkin. The equations of motion are reduced to ordinary differential equations by similarity transformation and solved numerically by using Runge-Kutta method. The trajectories of particles are calculated by integrating the equation of motion of a single particle. The present simulation requires some empirical parameters concerning the collision of the particles with the wall. The effect of solid particles on flow properties are discussed. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically. 4 figs.

Motion of Charged Suspended Particle in a Non-Newtonian Fluid between Two Long Parallel Plated

International Nuclear Information System (INIS)

Abd-El Khalek, M.M.

1998-01-01

The motion of charged suspended particle in a non-Newtonian fluid between two long parallel plates is discussed. The equation of motion of a suspended particle was suggested by Closkin. The equations of motion are reduced to ordinary differential equations by similarity transformations and solved numerically by using the Runge-Kutta method. The trajectories of particles are calculated by integrating the equation of motion of a single particle. The present simulation requires some empirical parameters concerning the collision of the particles with the wall. The effects of solid particles on flow properties are discussed. Some typical results for both fluid and particle phases and density distributions of the particles are presented graphically

First general solutions for unidirectional motions of rate type fluids over an infinite plate

Directory of Open Access Journals (Sweden)

Constantin Fetecau

2015-09-01

Full Text Available Based on a simple but important remark regarding the governing equation for the non-trivial shear stress corresponding to the motion of a fluid over an infinite plate, exact solutions are established for the motion of Oldroyd-B fluids due to the plate that applies an arbitrary time-dependent shear stress to the fluid. These solutions, that allow us to provide the first exact solutions for motions of rate type fluids produced by an infinite plate that applies constant, constantly accelerating or oscillating shears stresses to the fluid, can easily be reduced to the similar solutions for Maxwell, second grade or Newtonian fluids performing the same motion. Furthermore, the obtained solutions are used to develop general solutions for the motion induced by a moving plate and to correct or recover as special cases different known results from the existing literature. Consequently, the motion problem of such fluids over an infinite plate that is moving in its plane or applies a shear stress to the fluid is completely solved.

Radiation shielding plate

International Nuclear Information System (INIS)

Kobayashi, Torakichi; Sugawara, Takeo.

1983-01-01

Purpose: To reduce the weight and stabilize the configuration of a radiation shielding plate which is used in close contact with an object to be irradiated with radiation rays. Constitution: The radiation shielding plate comprises a substrate made of lead glass and a metallic lead coating on the surface of the substrate by means of plating, vapor deposition or the like. Apertures for permeating radiation rays are formed to the radiation shielding plate. Since the shielding plate is based on a lead glass plate, a sufficient mechanical strength can be obtained with a thinner structure as compared with the conventional plate made of metallic lead. Accordingly, if the shielding plate is disposed on a soft object to be irradiated with radiation rays, the object and the plate itself less deform to obtain a radiation irradiation pattern with distinct edges. (Moriyama, K.)

Plating on difficult-to-plate metals: what's new

International Nuclear Information System (INIS)

Wiesner, H.J.

1980-01-01

Some of the changes since 1970 in procedures for plating on such materials as titanium, molybdenum, silicon, aluminum, and gallium arsenide are summarized. While basic procedures for plating some of these materials were developed as many as 30 to 40 years ago, changes in the end uses of the plated products have necessitated new plating processes. In some cases, vacuum techniques - such as ion bombardment, ion implantation, and vacuum metallization - have been introduced to improve the adhesion of electrodeposits. In other cases, these techniques have been used to deposit materials upon which electrodeposits are required

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

Directory of Open Access Journals (Sweden)

Bazhenov V.A.

2014-06-01

Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Effect of plate shapes in orifice plate type flowmeters

International Nuclear Information System (INIS)

Moeller, S.V.

1984-01-01

The study of unusual plate shapes in orifice plate type flowmeters is presented, with a view to providing data for the substitution of the plate with one centered circular orifice in those applications where its use is not possible. For this purpose, six pairs of plates with different forms, with and without chamfered edges, were made and tested in a closed water loop. Results show that, generally, the use of chamfers improves the results and, in the case of perforated and slotlike orificed plates, the narrow-ness of the fluid passage tends to make unnecessary its use. (Author) [pt

Plating laboratory

International Nuclear Information System (INIS)

Seamster, A.G.; Weitkamp, W.G.

1984-01-01

The lead plating of the prototype resonator has been conducted entirely in the plating laboratory at SUNY Stony Brook. Because of the considerable cost and inconvenience in transporting personnel and materials to and from Stony Brook, it is clearly impractical to plate all the resonators there. Furthermore, the high-beta resonator cannot be accommodated at Stony Brook without modifying the set up there. Consequently the authors are constructing a plating lab in-house

Nonlinear morphoelastic plates I: Genesis of residual stress

KAUST Repository

McMahon, J.

2011-04-28

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. © SAGE Publications 2011.

Nonlinear morphoelastic plates I: Genesis of residual stress

KAUST Repository

McMahon, J.; Goriely, A.; Tabor, M.

2011-01-01

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established. © SAGE Publications 2011.

Exact result in strong wave turbulence of thin elastic plates

Science.gov (United States)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

Create Your Plate

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Full Text Available ... Plate Share Create Your Plate ! Share: Seven Simple Steps to Create Your Plate It's simple and effective ... foods within each food category. Try these seven steps to get started: Using your dinner plate, put ...

Numerical analysis of viscoelastic boundary layers : the case of plate withdrawal in a Maxwellian fluid

International Nuclear Information System (INIS)

Sadeghy, K.; Sharifi, M.

2002-01-01

The effect of a fluid's elasticity on the characteristics of its boundary layer was investigated in this work. A viscoelastic fluid of Maxwellian type was selected for this purpose and the flow induced in this fluid by a plate withdrawing at a constant velocity was studied. Conventional boundary layer assumptions were invoked to reduce the equations of motion to a simple form incorporating an elastic term in addition to the familiar inertial, viscous and pressure terms. It was shown that for elastic effects to be of an importance in a boundary layer, the fluid's relaxation time should be of an order much larger than its kinematic viscosity. By introducing a stream function, the governing equation was transformed into a nonlinear ODE with x-coordinate still appearing in the equation demonstrating that no similarity solution existed for this flow. The resulting equation was then solved numerically for Deborah numbers as large as 1.0. The results showed a marked formation of boundary layer adjacent to a moving wall for a Maxwellian fluid. The boundary layer thickness and the wall shear stress were found to scale with fluid's elasticity - both decreasing the higher the fluid's elasticity. It is thus anticipated that in free coating processes, the force required to impart a constant velocity to a withdrawing belt or plate would be lower if fluid's elasticity is significant. (author)

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

Science.gov (United States)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation

Vibration Analysis of Rectangular Plates with One or More Guided Edges via Bicubic B-Spline Method

Directory of Open Access Journals (Sweden)

W.J. Si

2005-01-01

Full Text Available A simple and accurate method is proposed for the vibration analysis of rectangular plates with one or more guided edges, in which bicubic B-spline interpolation in combination with a new type of basis cubic B-spline functions is used to approximate the plate deflection. This type of basis cubic B-spline functions can satisfy simply supported, clamped, free, and guided edge conditions with easy numerical manipulation. The frequency characteristic equation is formulated based on classical thin plate theory by performing Hamilton's principle. The present solutions are verified with the analytical ones. Fast convergence, high accuracy and computational efficiency have been demonstrated from the comparisons. Frequency parameters for 13 cases of rectangular plates with at least one guided edge, which are possible by approximate or numerical methods only, are presented. These results are new in literature.

Similarity Solution for Combined Free-Forced Convection Past a Vertical Porous Plate in a Porous Medium with a Convective Surface Boundary Condition

Directory of Open Access Journals (Sweden)

Garg P.

2016-12-01

Full Text Available This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

Hall effects on unsteady MHD reactive flow of second grade fluid through porous medium in a rotating parallel plate channel

Science.gov (United States)

Krishna, M. Veera; Swarnalathamma, B. V.

2017-07-01

We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.

Analysis of Heat Transfer and Pressure Drop for a Gas Flowing Through a set of Multiple Parallel Flat Plates at High Temperatures

Science.gov (United States)

Einstein, Thomas H.

1961-01-01

Equations were derived representing heat transfer and pressure drop for a gas flowing in the passages of a heater composed of a series of parallel flat plates. The plates generated heat which was transferred to the flowing gas by convection. The relatively high temperature level of this system necessitated the consideration of heat transfer between the plates by radiation. The equations were solved on an IBM 704 computer, and results were obtained for hydrogen as the working fluid for a series of cases with a gas inlet temperature of 200 R, an exit temperature of 5000 0 R, and exit Mach numbers ranging from 0.2 to O.8. The length of the heater composed of the plates ranged from 2 to 4 feet, and the spacing between the plates was varied from 0.003 to 0.01 foot. Most of the results were for a five- plate heater, but results are also given for nine plates to show the effect of increasing the number of plates. The heat generation was assumed to be identical for each plate but was varied along the length of the plates. The axial variation of power used to obtain the results presented is the so-called "2/3-cosine variation." The boundaries surrounding the set of plates, and parallel to it, were assumed adiabatic, so that all the power generated in the plates went into heating the gas. The results are presented in plots of maximum plate and maximum adiabatic wall temperatures as functions of parameters proportional to f(L/D), for the case of both laminar and turbulent flow. Here f is the Fanning friction factor and (L/D) is the length to equivalent diameter ratio of the passages in the heater. The pressure drop through the heater is presented as a function of these same parameters, the exit Mach number, and the pressure at the exit of the heater.

Study on the stress and strain during welding of plate-to-pipe joint

Energy Technology Data Exchange (ETDEWEB)

Na, S.J.; Kim, H.W.

1986-09-01

In manufacturing of pipe walls for boiler units, distortion can result in pipe-to-pipe joints from the nonuniform expansion and contraction of the weld metal and the adjacent base metal during heating and cooling cycle of the welding process. In this study, the stresses and strains during longitudinal welding of the plate-to-pipe joint were investigated. Using the method of sucessive elastic solution, longitudinal stresses and strains during and after welding were calculated from the information of temperature distributions obtained by Rosenthal's equations. In order to confirm the validity of the numerical results, the temperature and residual stress distributions were measured and compared with the calculated results. In spite of some assumptions, the one-dimensional analytical results of residual stresses were in fairly good agreement with the experimental ones. The residual stresses due to welding of plate-to-pipe joints are tensile near the weld line and compressive in the base metal as in the welding of plates. The amount and distribution of residual stresses were deeply dependent on the heat input ratio of the plate and pipe.

Equilibrium paths of an imperfect plate with respect to its aspect ratio

Science.gov (United States)

Psotny, Martin

2017-07-01

The stability analysis of a rectangular plate loaded in compression is presented, a specialized code based on FEM has been created. Special finite element with 48 degrees of freedom has been used for analysis. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To trace the complete nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used, load versus displacement control was changed during the calculation process. The peculiarities of the effects of the initial imperfections on the load-deflection paths are investigated with respect to aspect ratio of the plate. Special attention is paid to the influence of imperfections on the post-critical buckling mode.

Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

Directory of Open Access Journals (Sweden)

Havran Jozef

2015-12-01

Full Text Available The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

Transient heat transfer to laminar flow from a flat plate with heat capacity

International Nuclear Information System (INIS)

Hanawa, Juichi

1975-01-01

As the most basic problem in transient heat transfer, a plate with heat capacity was studied, which is placed in uniform laminar flow in parallel with it, is initially at the same temperature as that of the fluid, and then abruptly is given a specific heating value. The equation of transient heat transfer in this case was solved by numerical calculation. The following matters were revealed. (1) The equation was able to be solved by the application of Laplace transformation and numerical inverse transformation. (2) Wall temperature when the heat capacity of a plate was zero initially agreed well with heat conduction solution. With increase of the heat capacity, the delay in wall temperature rise was increased. (3) Heat transfer rate in case of the heat capacity of zero initially agreed well with the heat-conduction solution. With increase of the heat capacity, the Nusselt number increased. (4) Temperature distribution in case of the heat capacity of zero initially agreed well with the heat-conduction solution. (Mori, K.)

Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems

Directory of Open Access Journals (Sweden)

Xuehai Huang

2013-01-01

Full Text Available Based on stress-deflection variational formulation, we propose a family of local projection-based stabilized mixed finite element methods for Kirchhoff plate bending problems. According to the error equations, we obtain the error estimates of the approximation to stress tensor in energy norm. And by duality argument, error estimates of the approximation to deflection in H1-norm are achieved. Then we design an a posteriori error estimator which is closely related to the equilibrium equation, constitutive equation, and nonconformity of the finite element spaces. With the help of Zienkiewicz-Guzmán-Neilan element spaces, we prove the reliability of the a posteriori error estimator. And the efficiency of the a posteriori error estimator is proved by standard bubble function argument.

Paper microzone plates.

Science.gov (United States)

Carrilho, Emanuel; Phillips, Scott T; Vella, Sarah J; Martinez, Andres W; Whitesides, George M

2009-08-01

This paper describes 96- and 384-microzone plates fabricated in paper as alternatives to conventional multiwell plates fabricated in molded polymers. Paper-based plates are functionally related to plastic well plates, but they offer new capabilities. For example, paper-microzone plates are thin (approximately 180 microm), require small volumes of sample (5 microL per zone), and can be manufactured from inexpensive materials ($0.05 per plate). The paper-based plates are fabricated by patterning sheets of paper, using photolithography, into hydrophilic zones surrounded by hydrophobic polymeric barriers. This photolithography used an inexpensive formulation photoresist that allows rapid (approximately 15 min) prototyping of paper-based plates. These plates are compatible with conventional microplate readers for quantitative absorbance and fluorescence measurements. The limit of detection per zone loaded for fluorescence was 125 fmol for fluorescein isothiocyanate-labeled bovine serum albumin, and this level corresponds to 0.02 the quantity of analyte per well used to achieve comparable signal-to-noise in a 96-well plastic plate (using a solution of 25 nM labeled protein). The limits of detection for absorbance on paper was approximately 50 pmol per zone for both Coomassie Brilliant Blue and Amaranth dyes; these values were 0.4 that required for the plastic plate. Demonstration of quantitative colorimetric correlations using a scanner or camera to image the zones and to measure the intensity of color, makes it possible to conduct assays without a microplate reader.

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

Science.gov (United States)

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

2018-04-01

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

Unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid

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Deka Rudra Kt.

2009-01-01

Full Text Available An exact solution to one-dimensional unsteady natural convection flow past an infinite vertical accelerated plate, immersed in a viscous thermally stratified fluid is investigated. Pressure work term and the vertical temperature advection are considered in the thermodynamic energy equation. The dimensionless governing equations are solved by Laplace Transform techniques for the Prandtl number unity. The velocity and temperature profiles as well as the skin-friction and the rate of heat transfer are presented graphically and discussed the effects of the Grashof number Gr, stratification parameter S at various times t.

Laminar dispersion in parallel plate sections of flowing systems used in analytical chemistry and chemical engineering

NARCIS (Netherlands)

Kolev, S.D.; Kolev, Spas D.; van der Linden, W.E.

1991-01-01

An exact solution of the convective-diffusion equation for fully developed parallel plate laminar flow was obtained. It allows the derivation of theoretical relationships for calculating the Peclet number in the axially dispersed plug flow model and the concentration distribution perpendicular to

Rate effects in resistive plate chambers

International Nuclear Information System (INIS)

Lippmann, C.; Riegler, W.; Kalweit, A.

2006-01-01

The resistive plates in RPCs cause a drop of the electric field in the gas gap at high particle rates or large gas gain, which affects efficiency and time resolution. This effect is typically estimated by assuming the particle flux to be a DC current that causes a voltage drop when it passes through the resistive plate. In an improved model by Abbrescia (Nucl. Instr. Meth. A 533 (2004) 7), the fluctuation of the field in the gas gap is modelled by assuming that the avalanche partially discharges a small capacitor which gets recharged with a time constant characteristic for the given RPC. In our approach, the effect is calculated by using the exact analytic solution for the time dependent electric field of a point charge sitting on the surface of a resistive plate in an RPC. This is, by definition, the best possible approximation to reality. The solution is obtained using the quasi-static approximation of Maxwell's equations. The formulas are presented as integral representations with 'cured' integrands, which allow easy numerical evaluation for Monte Carlo simulations. The solutions show that the charges in RPCs are 'destroyed' with a continuous distribution of time constants which are related in a very intuitive way to some limiting cases. Using these formulas we present a Monte Carlo simulation of rate effects, proving the applicability of this approach. Finally, we compare the Monte Carlo results to analytical calculations, similar to the ones proposed by Gonzalez-Diaz et al. (see proceedings of this conference)

Vibration Characteristics of Axially Moving Titanium- Polymer Nanocomposite Faced Sandwich Plate Under Initial Tension

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Ali Ghorbanpour Arani

2017-07-01

Full Text Available In the present research, vibration and instability of axially moving sandwich plate made of soft core and composite face sheets under initial tension is investigated. Single-walled carbon nano-tubes (SWCNTs are selected as a reinforcement of composite face sheets inside Poly methyl methacrylate (PMMA matrix. Higher order shear deformation theory (HSDT is utilized due to its accuracy of polynomial functions than other plate theories. Based on extended rule of mixture, the structural properties of composite face sheets are taken into consideration. Motion equations are obtained by means of Hamilton’s principle and solved analytically. Influences of various parameters such as axially moving speed, volume fraction of CNTs, pre-tension, thickness and aspect ratio of sandwich plate on the vibration characteristics of moving system are discussed in details. The results indicated that the critical speed of moving sandwich plate is strongly dependent on the volume fraction of CNTs. Therefore, the critical speed of moving sandwich plate can be improved by adding appropriate values of CNTs. The results of this investigation can be used in design and manufacturing of marine vessels and aircrafts.

Kirchhoff plate theory-based electromechanically-coupled analytical model considering inertia and stiffness effects of a surface-bonded piezoelectric patch

International Nuclear Information System (INIS)

Yoon, Heonjun; Youn, Byeng D; Kim, Heung Soo

2016-01-01

As a compact and durable design concept, piezoelectric energy harvesting skin (PEH skin) has been recently proposed for self-powered electronic device applications. This study aims to develop an electromechanically-coupled analytical model of PEH skin considering the inertia and stiffness effects of a piezoelectric patch. Based on Kirchhoff plate theory, Hamilton’s principle is used to derive the electromechanically-coupled differential equation of motion. Due to the geometric discontinuity of the piezoelectric patch, the Rayleigh–Ritz method is applied to calculate the natural frequency and corresponding mode shapes. The electrical circuit equation is derived from Gauss’s law. Output voltage is estimated by solving the equation of motion and electrical circuit equation, simultaneously. For the purpose of evaluating the predictive capability, the results of the electromechanically-coupled analytical model are compared with those of the finite element method in a hierarchical manner. The outstanding merits of the electromechanically-coupled analytical model of PEH skin are three-fold: (1) consideration of the inertia and stiffness effects of the piezoelectric patches; (2) physical parameterization between the two-dimensional mechanical configuration and piezoelectric transduction; (3) manipulability of the twisting modes of a cantilever plate with a small aspect ratio. (paper)

A solution for the Graetz problem in parallel plates, with axial heat conduction in the fluid and in the wall

International Nuclear Information System (INIS)

Biage, M.

1983-04-01

A heat transfer problem in parallel plates with infinite with has been solved, with axial heat conduction in the fluid and in the wall, considering steady-state laminar flow for a Newtonian fluid and a fully developed velocity profile. The duct consists of an infinite inicial part, insulated on both plates, an intermediale part of finite length, with a prescribed heat flux in the upper plate and insulated on the botton plate, and by another infinite part also insulated on both plates. The problem has been solved by a numerical combination of the integral equation method and the variational method. Both, the performance of the numerical technique employed and results obtained are analyzed in this work. It is demostrated that the heat conduction in the wall significantly modifies the heat transfer parameters. (Author) [pt

Microstructure and Mechanical Property of Aluminum Alloy Plate AA 7055

Directory of Open Access Journals (Sweden)

CHEN Junzhou

2017-10-01

Full Text Available Through-thickness microstructure and mechanical property of AA 7055-T7751 aluminum alloy plate were investigated by using electron backscattered diffraction (EBSD, transmission electron microscope (TEM and small angle X-ray scattering(SAXS. The results indicate an inhomogeneous distribution of microstructure through the thickness. The degree of recrystallization decreases gradually from 69% to 19.1%, as deepening from the surface to the center of the plate. The size of subgrains decreases from 10 μm at the surface to around 2 μm at the center. Strong texture of rolling type is observed near the center but the intensity decreases gradually as nearing the surface and the shear texture becomes the dominant. High density of plate-like η' phases are observed in the alloy, indicating the sufficient precipitation. η' precipitates of this condition are around 3.7 nm in radius, 1-3 nm in thickness and are found coherent with the Al matrix with a coherent strain of 0.0133, showing a strong strengthening effect. The heterogeneity in grain scale does not influence the distribution and the morphology of precipitates. The yield strength (L direction varies linearly along the thickness direction of the plate, fitting an equation of σy=-38.7S+604.8 (0≤S≤1. The variation of yield strength is related to the heterogeneity of grain structure.

Prediction of macroscopic and local stress-strain behaviors of perforated plates under primary and secondary creep conditions

International Nuclear Information System (INIS)

Igari, Toshihide; Tokiyoshi, Takumi; Mizokami, Yorikata

2000-01-01

Prediction methods of macroscopic and local creep behaviors of perforated plates are examined in order to apply these methods to the structural design of perforated structures such as heat exchangers used in elevated temperatures. Both primary and secondary creeps are considered for predicting macroscopic and local creep behaviors of perorated plates which are made of actual structural materials. Both uniaxial and multiaxial loading of perforated plates are taken into consideration. The concept of effective stress is applied to the prediction of macroscopic creep behaviors of perforated plates, and the predicted results are compared with the numerical results by FEM for the unit section of perorated plated under creep, in order to confirm the propriety of the proposed method. Based on the idea that stress exponents in creep equations govern the stress distribution of perforated plates, a modified Neuber's rule is used for predicting local stress and strain concentrations. The propriety of this prediction method is shown through a comparison of the prediction with the numerical results by FEM for the unit section of perforated plates under creep, and experimental results by the Moire method. (author)

Ground cross-modal impedance as a tool for analyzing ground/plate interaction and ground wave propagation.

Science.gov (United States)

Grau, L; Laulagnet, B

2015-05-01

An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.

Simulation Study on the Deflection Response of the 921A Steel thin plate under Explosive Impact Load

Science.gov (United States)

Zhang, Yu-Xiang; Chen, Fang; Han, Yan

2018-03-01

The Ship cabin would be subject to high-intensity shock wave load when it is attacked by anti-ship weapons, causing its side board damaged. The time course of the deflection of the thin plate made of 921A steel in different initial conditions under the impact load is researched by theoretical analysis and numerical simulation. According to the theory of elastic-plastic deformation of the thin plate, the dynamic response equation of the thin plate under the explosion impact load is established with the method of energy, and the theoretical calculation value is compared with the result from the simulation method. It proved that the theoretical calculation method has better reliability and accuracy in different boundary size.

Thermal resistance of a convectively cooled plate with applied heat flux and variable internal heat generation

International Nuclear Information System (INIS)

Venkataraman, N.S.; Cardoso, H.P.; Oliveira Filho, O.B. de

1981-01-01

The conductive heat transfer in a rectangular plate with nonuniform internal heat generation, with one end convectively cooled and a part of the opposite end subjected to external heat flux is considered. The remaining part of this end as well as the other two sides are thermally insulated. The governing differential equation is solved by a finite difference scheme. The variation of the thermal resistance with Biot modulus, the plate geometry, the internal heat generation parameter and the type of profile of internal heat generation is discussed. (author) [pt

Locking screw-plate interface stability in carbon-fibre reinforced polyetheretherketone proximal humerus plates.

Science.gov (United States)

Hak, David J; Fader, Ryan; Baldini, Todd; Chadayammuri, Vivek B S

2017-09-01

Carbon-fibre reinforced polyetheretherketone (CFR-PEEK) plates have recently been introduced for proximal humerus fracture treatment. The purpose of this study was to compare the locking screw-plate interface stability in CFR-PEEK versus stainless steel (SS) proximal humerus plates. Locking screw mechanical stability was evaluated independently in proximal and shaft plate holes. Stiffness and load to failure were tested for three conditions: (1) on-axis locking screw insertion in CFR-PEEK versus SS plates, (2) on-axis locking screw insertion, removal, and reinsertion in CFR-PEEK plates, and (3) 10-degree off-axis locking screw insertion in CFR-PEEK plates. Cantilever bending at a rate of 1 mm/minute was produced by an Instron machine and load-displacement data recorded. Shaft locking screw load to failure was significantly greater in CFR-PEEK plates compared to SS plates (746.4 ± 89.7 N versus 596.5 ± 32.6 N, p PEEK plates (p PEEK plates. The mechanical stability of locking screws in CFR-PEEK plates is comparable or superior to locking screws in SS plates.

Voltage-current characteristics of a pin-plate system with different plate configurations

International Nuclear Information System (INIS)

Feng, Zhuangbo; Long, Zhengwei

2013-01-01

In this paper, the voltage-current (V-I) characteristics of a pin-plate system with four types of collection plate configurations are studied experimentally. The collection plates consider a single metal plate, a metal plate with a fly ash cake layer, a metal plate with a clean filter media and a metal plate with a dirty filter media. The results show that the clean filter media has no obvious effect on the V-I characteristics. But the dirty filter media reduces the current density because of its high resistance. The thick fly ash cake layer increase current density because of the anti-corona effect but the increment is not very obvious.

Electromagnetic pulse coupling through an aperture into a two-parallel-plate region

Science.gov (United States)

Rahmat-Samii, Y.

1978-01-01

Analysis of electromagnetic-pulse (EMP) penetration via apertures into cavities is an important study in designing hardened systems. In this paper, an integral equation procedure is developed for determining the frequency and consequently the time behavior of the field inside a two-parallel-plate region excited through an aperture by an EMP. Some discussion of the numerical results is also included in the paper for completeness.

Study of Boundary Layer Convective Heat Transfer with Low Pressure Gradient Over a Flat Plate Via He's Homotopy Perturbation Method

International Nuclear Information System (INIS)

Fathizadeh, M.; Aroujalian, A.

2012-01-01

The boundary layer convective heat transfer equations with low pressure gradient over a flat plate are solved using Homotopy Perturbation Method, which is one of the semi-exact methods. The nonlinear equations of momentum and energy solved simultaneously via Homotopy Perturbation Method are in good agreement with results obtained from numerical methods. Using this method, a general equation in terms of Pr number and pressure gradient (λ) is derived which can be used to investigate velocity and temperature profiles in the boundary layer.

Predicting lower body power from vertical jump prediction equations for loaded jump squats at different intensities in men and women.

Science.gov (United States)

Wright, Glenn A; Pustina, Andrew A; Mikat, Richard P; Kernozek, Thomas W

2012-03-01

The purpose of this study was to determine the efficacy of estimating peak lower body power from a maximal jump squat using 3 different vertical jump prediction equations. Sixty physically active college students (30 men, 30 women) performed jump squats with a weighted bar's applied load of 20, 40, and 60% of body mass across the shoulders. Each jump squat was simultaneously monitored using a force plate and a contact mat. Peak power (PP) was calculated using vertical ground reaction force from the force plate data. Commonly used equations requiring body mass and vertical jump height to estimate PP were applied such that the system mass (mass of body + applied load) was substituted for body mass. Jump height was determined from flight time as measured with a contact mat during a maximal jump squat. Estimations of PP (PP(est)) for each load and for each prediction equation were compared with criterion PP values from a force plate (PP(FP)). The PP(est) values had high test-retest reliability and were strongly correlated to PP(FP) in both men and women at all relative loads. However, only the Harman equation accurately predicted PP(FP) at all relative loads. It can therefore be concluded that the Harman equation may be used to estimate PP of a loaded jump squat knowing the system mass and peak jump height when more precise (and expensive) measurement equipment is unavailable. Further, high reliability and correlation with criterion values suggest that serial assessment of power production across training periods could be used for relative assessment of change by either of the prediction equations used in this study.

Parametrices and exact paralinearization of semi-linear boundary problems

DEFF Research Database (Denmark)

Johnsen, Jon

2008-01-01

The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization...... of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....

Three-dimensional inverse transient heat transfer analysis of thick functionally graded plates

Energy Technology Data Exchange (ETDEWEB)

Haghighi, M.R. Golbahar; Malekzadeh, P. [Department of Mechanical Engineering, School of Engineering, Persian Gulf University, Bushehr 75168 (Iran); Eghtesad, M. [Department of Mechanical Engineering, School of Engineering, Shiraz University, Shiraz 71348-51154 (Iran); Necsulescu, D.S. [Department of Mechanical Engineering, Faculty of Engineering, University of Ottawa, Ottawa, Ontario (Canada)

2009-03-15

In this paper, a three-dimensional transient inverse heat conduction (IHC) procedure is presented to estimate the unknown boundary heat flux of thick functionally graded (FG) plates. For this purpose, the conjugate gradient method (CGM) in conjunction with adjoint problem is used. A recently developed three-dimensional efficient hybrid method is employed to solve variable-coefficient initial-boundary-value differential equations of direct problem as a part of the inverse solution. The accuracy of the inverse analysis is examined by simulating the exact and noisy data for problems with different types of boundary conditions and material properties. In addition to rectangular domain, skew plates are considered. The results obtained show good accuracy for the estimation of boundary heat fluxes. (author)

Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate

Directory of Open Access Journals (Sweden)

S. Das

2015-03-01

Full Text Available An investigation of the hydromagnetic boundary layer flow past a moving vertical plate in nanofluids in the presence of a uniform transverse magnetic field and thermal radiation has been carried out. Three different types of water-based nanofluids containing copper, aluminum oxide and titanium dioxide are taken into consideration. The governing equations are solved using Laplace transform technique and the solutions are presented in closed form. The numerical values of nanofluid temperature, velocity, the rate of heat transfer and the shear stress at the plate are presented graphically for several values of the pertinent parameters. The present study finds applications in engineering devices.

Simulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models

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Flávio Luiz de Silva Bussamra

Full Text Available Abstract Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from Papkovitch-Neuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term "quasi". In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical p-refinement is exploited.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

Science.gov (United States)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Entropy Generation on Nanofluid Flow through a Horizontal Riga Plate

Directory of Open Access Journals (Sweden)

Tehseen Abbas

2016-06-01

Full Text Available In this article, entropy generation on viscous nanofluid through a horizontal Riga plate has been examined. The present flow problem consists of continuity, linear momentum, thermal energy, and nanoparticle concentration equation which are simplified with the help of Oberbeck-Boussinesq approximation. The resulting highly nonlinear coupled partial differential equations are solved numerically by means of the shooting method (SM. The expression of local Nusselt number and local Sherwood number are also taken into account and discussed with the help of table. The physical influence of all the emerging parameters such as Brownian motion parameter, thermophoresis parameter, Brinkmann number, Richardson number, nanoparticle flux parameter, Lewis number and suction parameter are demonstrated graphically. In particular, we conferred their influence on velocity profile, temperature profile, nanoparticle concentration profile and Entropy profile.

Effects of Velocity-Slip and Viscosity Variation in Squeeze Film Lubrication of Two Circular Plates

Directory of Open Access Journals (Sweden)

R.R. Rao

2013-03-01

Full Text Available A generalized form of Reynolds equation for two symmetrical surfaces is taken by considering velocity-slip at the bearing surfaces. This equation is applied to study the effects of velocity-slip and viscosity variation for the lubrication of squeeze films between two circular plates. Expressions for the load capacity and squeezing time obtained are also studied theoretically for various parameters. The load capacity and squeezing time decreases due to slip. They increase due to the presence of high viscous layer near the surface and decrease due to low viscous layer.

The Effect of Material Property on the Critical Velocity of Randomly Excited Nonlinear Axially Travelling Functionally Graded Plates

Directory of Open Access Journals (Sweden)

M. Abedi

Full Text Available Abstract In this paper, the critical axial speeds of three types of sigmoid, power law and exponential law functionally graded plates for both isotropic and orthotropic cases are obtained via a completely analytic method. The plates are subjected to lateral white noise excitation and show evidence of large deformations. Due to randomness, the conventional deterministic methods fail and a statistical approach must be selected. Here, the probability density function is evaluated analytically for prescribed plates and used to investigate the critical axial velocity of them. Specifically the effect of in-plane forces, mean value of lateral load and the material property on the critical axial speed are studied and discussed for both isotropic and orthotropic functionally graded plates. Since the governing equation is transformed to a non dimensional format, the results can be used for a wide range of plate dimensions. It is shown that the material heterogeneity palys an essential and significant role in increasing or decreasing the critical speed of both isotropic and orthotropic functionally graded plates.

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

Science.gov (United States)

Guenanou, A.; Houmat, A.

2018-05-01

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange's method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.

Vortex molecule in a nanoscopic square superconducting plate

International Nuclear Information System (INIS)

Suematsu, Hisataka; Kato, Masaru; Ishida, Takekazu; Koyama, Tomio; Machida, Masahiko

2010-01-01

Using the finite element method and solving the Bogoliubov-de Gennes equation, we have investigated magnetic field dependence of the stable vortex structures in a mesoscopic superconducting plate at low temperature (T = 0.1T c ). Because of the compactness of vortex configuration, there is interference between bound states around vortices and such quasi-particle structure affects the vortex configuration. Especially in two-vortices state, vortices form a molecule-like state, where bound states of each vortex form molecular orbital like bonding and anti-bonding states. The vortex configuration is different from that, which is expected from the repulsive interaction between vortices. (author)

Diffraction of a plane electromagnetic wave on a dielectric plate of variable density. [Field equatios, diffracted-wave angular distributions

Energy Technology Data Exchange (ETDEWEB)

Aivazyan, Yu M; Mergelyan, O S; Poulatov, M P

1974-01-01

Aproblem for the diffraction of a plane electromagnetic wave on a dielectric plate between two other dielectrics is solved. The dielectric constant of the plate depends periodically on three coordinates. From this solution it is possible to obtain the equations for fields and the angular distribution of diffracted waves for the particular cases of a crystal plate and a dielectric surface fluted in all directions. If the expansion is made in the variable of the electron density in crystals, the results will correspond to the problem for the X-ray diffraction on a crystal lattice, the values of the coefficient ..cap alpha -->..sub(tau) being determined by the lattice parameters.

Finite element analysis of actively controlled smart plate with patched actuators and sensors

Directory of Open Access Journals (Sweden)

M. Yaqoob Yasin

Full Text Available The active vibration control of smart plate equipped with patched piezoelectric sensors and actuators is presented in this study. An equivalent single layer third order shear deformation theory is employed to model the kinematics of the plate and to obtain the shear strains. The governing equations of motion are derived using extended Hamilton's principle. Linear variation of electric potential across the piezoelectric layers in thickness direction is considered. The electrical variable is discretized by Lagrange interpolation function considering two-noded line element. Undamped natural frequencies and the corresponding mode shapes are obtained by solving the eigen value problem with and without electromechanical coupling. The finite element model in nodal variables are transformed into modal model and then recast into state space. The dynamic model is reduced for further analysis using Hankel norm for designing the controller. The optimal control technique is used to control the vibration of the plate.

Evaluation of a Rising Plate Meter for Use in Multispecies Swards

Directory of Open Access Journals (Sweden)

S. Leanne Dillard

2016-11-01

Full Text Available The rising plate meter (RPM provides rapid estimates of herbage mass (HM. Accurate calibration of the RPM is difficult due to variability in forage management, growth, and species composition. The RPM is typically calibrated by linear regression of HM and RPM height; however, the is usually low. Curvilinear regression, with the intercept set to zero, could provide a more robust calibration equation and decrease variability in RPM estimates. Three Pennsylvania organic dairy farms grazing lactating dairy cattle on multispecies pastures were used to determine measured HM and estimated HM using a RPM. Removal of the intercept increased the adjusted of all equations between 42.8 and 89.0%. Use of quadratic and cubic regression only resulted in 0.01 to 0.02 increase in adjusted . Linear regression remains the simplest and preferred method of calibration; however, error can be reduced by setting calibration equations so that zero RPM height is associated with zero HM.

Natural convection in an asymmetrically heated vertical channel with an adiabatic auxiliary plate

International Nuclear Information System (INIS)

Taieb, Soumaya; Hatem, Laatar Ali; Balti, Jalloul

2013-01-01

The effect of an auxiliary plate on natural convection in an asymmetrically heated channel is studied numerically in laminar regime. The computational procedure is made by solving the unsteady two dimensional Navier-Stokes and energy equations. This nonlinear system is integrated by a finite volume approach and then solved in time using the projection method, allowing the decoupling pressure from velocity. More than hundred simulations are performed to determine the best positions of the auxiliary plate that enhance the induced mass flow and the heat transfer rate for modified Rayleigh numbers ranging from Ra m = 10 2 to Ra m = 10 5 . Contour maps are plotted and then used to precise the enhancement rates of the mass flow and the heat transfer for any position of the auxiliary plate in the channel. The numerical results (velocity, pressure and temperature fields) provide detailed information about the evolution of the flow structure according to the geometry considered in this study. In addition, they permit to explain why the mass flow rate and Nusselt number are enhanced for certain positions of the auxiliary plate and are on the contrary deteriorated for others. (authors)

An analysis of the relaxation of laminar boundary layer on a flat plate after passage of an interface with application to expansion-tube flows

Science.gov (United States)

Gupta, R. N.

1972-01-01

The relaxation of the accelerating-gas boundary layer to the test-gas boundary layer over a flat plate in an expansion tube is analyzed. Several combinations of test gas and acceleration gas are considered. The problem is treated in two conically similar limits: (1) when the time lag between the arrival of the shock and the interface at the leading edge of the plate is very large, and (2) when this lag is negligible. The time-dependent laminar-boundary-layer equations of a binary mixture of perfect gases are taken as the flow-governing equations. This coupled set of differential equations, written in terms of the Lam-Crocco variables, has been solved by a line-relaxation finite-difference techniques. The results presented include the Stanton number and the local skin-friction coefficient as functions of shock Mach number and the nondimensional distance-time variable. The results indicate that more than 95 percent of the test-gas boundary layer exists over a length, measured from the leading edge of the plate, equal to about three-tenths of the distance traversed by the interface in the free stream.

Heat transfer in flow past a continuously moving semi-infinite flat plate in transverse magnetic field with heat flux

Digital Repository Service at National Institute of Oceanography (India)

Murty, T.V.R.

Thermal boundary layer on a continuously moving semi-infinite flat plate in the presence of transverse magnetic field with heat flux has been examined. Similarity solutions have been derived and the resulting equations are integrated numerically...

A Possible Differentially Shortened Strike-slip Plate Boundary: the Okhotsk Plate Example.

Science.gov (United States)

Hindle, D.; Egorov, V.; Mackey, K. G.; Fujita, K.

2004-12-01

The Okhotsk plate has been postulated based on a combination of GPS geodetic inversions (REVEL1), seimsicity, geologic and lineament data. Lying between the North American and Eurasian plates, its northwestern corner would appear to be undergoing compression in a scissors motion between the two bounding plates. Extrusion tectonics along multiple, large strike-slip faults within the Okhotsk plate itself have been suggested to allow the escape of material away from the apex of Eurasia-North America. The plate boundary between Okhotsk and North America has been suggested to be diffuse, based on widely scattered minor seismicity. However, the large, left lateral, Ulakhan fault has also been suggested as a candidate plate boundary. We present field geological and geomorphological evidence of the partitioning of deformation between the Ulakhan fault, and several parallel and oblique, linked faults. The Ulakhan fault strand appears to have a maximum displacement of 24 km based on river valley offsets and closing large pull apart basins. Some of the displacement from the Ulakhan fault appears relayed into the plate margin along oblique trending, thrust/oblique slip faults. Estimated shortening over these faults is equivalent to the amount of shortening relayed into the plate margin from the plate boundary. There may be several thrust/oblique slip faults along the Ulakhan fault, which leads to the interesting situation of a segmented, strike-slip plate boundary being actively shortened in a margin parallel direction. This may be the result of postulated extrusion of the Okhotsk plate due to North America/Eurasia convergence. Such a situation would have important consequences for the interpretation of GPS data in a plate tectonic context.

Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics

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Dang Quang A

2013-02-01

Full Text Available In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments.

Effects of rotation on MHD flow past an accelerated isothermal vertical plate with heat and mass diffusion

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Muthucumaraswamy R.

2010-01-01

Full Text Available An exact analysis of rotation effects on unsteady flow of an incompressible and electrically conducting fluid past a uniformly accelerated infinite isothermal vertical plate, under the action of transversely applied magnetic field has been presented. The plate temperature is raised to Tw and the concentration level near the plate is also raised to C′w . The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles, temperature and concentration are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number and time. It is observed that the velocity increases with increasing values of thermal Grashof number or mass Grashof number. It is also observed that the velocity increases with decreasing magnetic field parameter.

Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current

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Ping Wang

2017-01-01

Full Text Available Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM, consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect.

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Science.gov (United States)

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

1992-01-01

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

13 September 2013 - Chairman of the Board of Directors of the von Karman Institute Kingdom of Belgium J.-P. Contzen visiting the ATLAS experimental cavern with ATLAS Former Spokesperson P. Jenni; visiting the LHC tunnel at Point 1 with Technology Department N. Delruelle and signing the guest book with Technology Department Head F. Bordry. International Relations Adviser T. Kurtyka present.

CERN Multimedia

Laurent Egli (visit)

2013-01-01

13 September 2013 - Chairman of the Board of Directors of the von Karman Institute Kingdom of Belgium J.-P. Contzen visiting the ATLAS experimental cavern with ATLAS Former Spokesperson P. Jenni; visiting the LHC tunnel at Point 1 with Technology Department N. Delruelle and signing the guest book with Technology Department Head F. Bordry. International Relations Adviser T. Kurtyka present.

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

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Maria Cinefra

2015-04-01

Full Text Available The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic. The refined models used are derived from Carrera’s Unified Formulation (CUF and they permit the vibration modes along the thickness to be accurately described. The finite-element method is employed and the plate element implemented has nine nodes, and the mixed interpolation of tensorial component (MITC method is used to contrast the membrane and shear locking phenomenon. The related governing equations are derived from the principle of virtual displacement, extended to the analysis of electromechanical problems. An isotropic plate with piezoelectric patches is analyzed, with clamped-free boundary conditions and subjected to open- and short-circuit configurations. The results, obtained with different theories, are compared with the higher-order type solutions given in the literature. The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.

Plane wave diffraction by a finite plate with impedance boundary conditions.

Science.gov (United States)

Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal

2014-01-01

In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.

Multiple solutions and stability of the steady transonic small-disturbance equation

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Ya Liu

2017-09-01

Full Text Available Numerical solutions of the steady transonic small-disturbance (TSD potential equation are computed using the conservative Murman−Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.

Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary

Science.gov (United States)

Khan, W. A.; Khan, Z. H.; Rahi, M.

2014-06-01

Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302-307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Effect of Plate Curvature on Blast Response of Structural Steel Plates

Science.gov (United States)

Veeredhi, Lakshmi Shireen Banu; Ramana Rao, N. V.; Veeredhi, Vasudeva Rao

2018-04-01

In the present work an attempt is made, through simulation studies, to determine the effect of plate curvature on the blast response of a door structure made of ASTM A515 grade 50 steel plates. A door structure with dimensions of 5.142 m × 2.56 m × 10 mm having six different radii of curvatures is analyzed which is subjected to blast load. The radii of curvature investigated are infinity (flat plate), 16.63, 10.81, 8.26, 6.61 and 5.56 m. In the present study, a stand-off distance of 11 m is considered for all the cases. Results showed that the door structure with smallest radius of curvature experienced least plastic deformation and yielding when compared to a door with larger radius of curvature with same projected area. From the present Investigation, it is observed that, as the radius of curvature of the plate increases, the deformation mode gradually shifts from indentation mode to flexural mode. The plates with infinity and 16.63 m radius of curvature have undergone flexural mode of deformation and plates with 6.61 and 5.56 m radius of curvature undergo indentation mode of deformation. Whereas, mixed mode of deformation that consists of both flexural and indentation mode of deformations are seen in the plates with radius of curvature 10.81 and 8.26 m. As the radius of curvature of the plate decreases the ability of the plate to mitigate the effect the blast loads increased. It is observed that the plate with smaller radius of curvature deflects most of the blast energy and results in least indentation mode of deformation. The most significant observation made in the present investigation is that the strain energy absorbed by the steel plate gets reduced to 1/3 rd when the radius of curvature is approximately equal to the stand-off distance which could be the critical radius of curvature.

The Okhotsk Plate and the Eurasia-North America plate boundary zone.

Science.gov (United States)

Hindle, David; Mackey, Kevin

2014-05-01

The Eurasia-North America plate boundary zone transitions from spreading at rates of ~ 25mm/yr in the North Atlantic, to compression at rates of ~ 5mm/yr in the region of the Okhotsk plate. Because the pole of rotation between Eurasia and North America lies more or less on their mutual boundary, there is a linear change in rate along the boundary, and regions near the euler pole are subject to extremely low deformation rates. The Okhotsk - Eurasia - North America triple junction lies slightly south of the rotation pole, placing the Okhotsk plate entirely in a weakly contractional setting. Regions near the triple junction absorb 1mm/yr contraction. Further south, towards the shoreline of the Okhotsk sea, up to 5 mm/yr contraction may be absorbed within the plate. How shortening is accommodated across the boundary remains an open question. One possibility is wholesale extrusion of the entire Okhotsk plate (or possibly its northwestern corner) along two plate boundary strike slip faults (Eurasia-Okhostk and North America Okhotsk). The problem with this model is that the seismic record does not presently clearly support it, with the largest events distributed both within the plate interior and on its boundaries. This may suggest that instead, the Okhotsk plate, and particularly its north-western end, consists of a series of smaller blocks which shuffle against each other, partially accommodating extrusion, but also permitting some internal deformation and change of shape of the Okhotsk plate itself. We present analyses of the very sparse seismic record from the region, as well as geometric-kinematic, tectonic models of the possible deformation of northwest Okhotsk to try to better understand the different probabilities of how this slowly deforming plate boundary zone is behaving.

Free vibration analysis of multi directional functionally graded circular and annular plates

Energy Technology Data Exchange (ETDEWEB)

Kermani, Iman Davoodi; Ghayour, Mostafa; Mirdamadi, Hamid Reza [Isfahan Univ. of Technology, Isfahan (Iran, Islamic Republic of)

2012-11-15

This paper addresses the free vibration of multi directional functionally graded circular and annular plates using a semianalytical/numerical method, called state space based differential quadrature method. Three-dimensional elasticity equations are derived for multi directional functionally graded plates and a solution is given by the semi-analytical/numerical method. This method gives an analytical solution along the thickness direction, using a state space method and a numerical solution using differential quadrature method. Some numerical examples are presented to show the accuracy and convergence of the method. The most of simulations of the present study have been validated by the existing literature. The non dimensional frequencies and corresponding displacements mode shapes are obtained. Then the influences of thickness ratio and graded indexes are demonstrated on the non dimensional natural frequencies.

A globally convergent and closed analytical solution of the Blasius equation with beneficial applications

Science.gov (United States)

Zheng, Jun; Han, Xinyue; Wang, ZhenTao; Li, Changfeng; Zhang, Jiazhong

2017-06-01

For about a century, people have been trying to seek for a globally convergent and closed analytical solution (CAS) of the Blasius Equation (BE). In this paper, we proposed a formally satisfied solution which could be parametrically expressed by two power series. Some analytical results of the laminar boundary layer of a flat plate, that were not analytically given in former studies, e.g. the thickness of the boundary layer and higher order derivatives, could be obtained based on the solution. Besides, the heat transfer in the laminar boundary layer of a flat plate with constant temperature could also be analytically formulated. Especially, the solution of the singular situation with Prandtl number Pr=0, which seems impossible to be analyzed in prior studies, could be given analytically. The method for finding the CAS of Blasius equation was also utilized in the problem of the boundary layer regulation through wall injection and slip velocity on the wall surface.

A New Approach for Studying Nonlinear Dynamic Response of a Thin Plate with Internal Resonance in a Fractional Viscoelastic Medium

Directory of Open Access Journals (Sweden)

Yury A. Rossikhin

2015-01-01

Full Text Available In the previous analysis, the dynamic behaviour of a nonlinear plate embedded into a fractional derivative viscoelastic medium has been studied by the method of multiple time scales under the conditions of the internal resonances two-to-one and one-to-one, as well as the internal combinational resonances for the case when the linear parts of nonlinear equations of motion occur to be coupled. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. It has been shown that for some internal resonances there exist such particular cases when it is possible to obtain two first integrals, namely, the energy integral and the stream function, which allows one to reduce the problem to the calculation of elliptic integrals. The new approach enables one to solve the problems of vibrations of thin bodies more efficiently.

Finite element analysis of a solar collector plate using two plate geometries

Directory of Open Access Journals (Sweden)

Diego Manuel Medina Carril

2016-09-01

Full Text Available The thermal behavior of an absorber plate in a solar collector is investigated using finite element analysis. The thermal behavior and efficiency of two absorber plate geometries are studied, using a typical solar collector with a rectangular profile as reference, and a proposed absorber plate with curved geometry. An analysis of the most important parameters involved in the design of the absorber plate was carried out, indicating that the curved geometry of the absorber plate yields an average efficiency ~25% higher than the conventional rectangular geometry. The results suggest that a curved profile made of materials such as aluminum with thermal conductivity higher than 200W/m°C, plate thickness of the order of 2-3mm and with a large density of tubes per unit area of the collector´s plate greatly benefits the thermal efficiency of the solar collector.

Dynamic Stress Concentration at the Boundary of an Incision at the Plate Under the Action of Weak Shock Waves

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Mikulich Olena

2017-09-01

Full Text Available This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of weak shock waves. For solution of the problem it uses the integral and discrete Fourier transforms. Calculation of transformed dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the developed algorithm is based on the method of mechanical quadratures and collocation technique. For calculation of originals of the dynamic stresses it uses modified discrete Fourier transform. The algorithm is effective in the analysis of the dynamic stress state of defective plates.

Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates

CERN Document Server

Kitahara, M

1985-01-01

The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro

A numerical analysis of a reciprocating Active Magnetic Regenerator with a parallel-plate regenerator geometry

DEFF Research Database (Denmark)

Petersen, Thomas Frank; Pryds, Nini; Smith, Anders

2007-01-01

We have developed a two-dimensional model of a reciprocating Active Magnetic Regenerator(AMR) with a regenerator made of parallel plates arranged in a stack configuration. The time dependent,two-dimensional model solves the Navier-Stokes equations for the heat transfer fluid and the coupled heat...... transfer equations for the regenerator and the fluid. The model is implemented using the Finite Element Method. The model can be used to study both transient and steady-state phenomena in the AMR for any ratio of regenerator to fluid heat capacity. Results on the AMR performance for different design...

Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature

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Asma Khalid

2015-01-01

Full Text Available The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, J. L.; Tannehill, J. C.; Chaussee, D. S.

1984-01-01

MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Thermal-hydraulic behavior of physical quantities at critical velocities in a nuclear research reactor core channel using plate type fuel

Directory of Open Access Journals (Sweden)

Sidi Ali Kamel

2012-01-01

Full Text Available The thermal-hydraulic study presented here relates to a channel of a nuclear reactor core. This channel is defined as being the space between two fuel plates where a coolant fluid flows. The flow velocity of this coolant should not generate vibrations in fuel plates. The aim of this study is to know the distribution of the temperature in the fuel plates, in the cladding and in the coolant fluid at the critical velocities of Miller, of Wambsganss, and of Cekirge and Ural. The velocity expressions given by these authors are function of the geometry of the fuel plate, the mechanical characteristics of the fuel plate’s material and the thermal characteristics of the coolant fluid. The thermal-hydraulic study is made under steady-state; the equation set-up of the thermal problem is made according to El Wakil and to Delhaye. Once the equation set-up is validated, the three critical velocities are calculated and then used in the calculations of the different temperature profiles. The average heat flux and the critical heat flux are evaluated for each critical velocity and their ratio reported. The recommended critical velocity to be used in nuclear channel calculations is that of Wambsganss. The mathematical model used is more precise and all the physical quantities, when using this critical velocity, stay in safe margins.

Plate removal following orthognathic surgery.

Science.gov (United States)

Little, Mhairi; Langford, Richard Julian; Bhanji, Adam; Farr, David

2015-11-01

The objectives of this study are to determine the removal rates of orthognathic plates used during orthognathic surgery at James Cook University Hospital and describe the reasons for plate removal. 202 consecutive orthognathic cases were identified between July 2004 and July 2012. Demographics and procedure details were collected for these patients. Patients from this group who returned to theatre for plate removal between July 2004 and November 2012 were identified and their notes were analysed for data including reason for plate removal, age, smoking status, sex and time to plate removal. 3.2% of plates were removed with proportionally more plates removed from the mandible than the maxilla. 10.4% of patients required removal of one or more plate. Most plates were removed within the first post-operative year. The commonest reasons for plate removal were plate exposure and infection. The plate removal rates in our study are comparable to those seen in the literature. Copyright © 2015 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

OpenAIRE

Wu, Lei

2014-01-01

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

Unsteady MHD blood flow through porous medium in a parallel plate channel

Science.gov (United States)

Latha, R.; Rushi Kumar, B.

2017-11-01

In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.

Simulation on Natural Convection of a Nanofluid along an Isothermal Inclined Plate

Science.gov (United States)

Mitra, Asish

2017-08-01

A numerical algorithm is presented for studying laminar natural convection flow of a nanofluid along an isothermal inclined plate. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a set of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless velocity, temperature profiles and nanoparticle concentration for various angles of inclination are illustrated graphically. The effects of Prandtl number, Brownian motion parameter and thermophoresis parameter on Nusselt number are also discussed. The results of the present simulation are then compared with previous one available in literature with good agreement.

Plane wave diffraction by a finite plate with impedance boundary conditions.

Directory of Open Access Journals (Sweden)

Rab Nawaz

Full Text Available In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.

Hydrogen Recombination Rates of Plate-type Passive Auto-catalytic Recombiner

Energy Technology Data Exchange (ETDEWEB)

Kim, Jongtae; Hong, Seong-Wan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Kim, Gun Hong [Kyungwon E-C Co., Seongnam (Korea, Republic of)

2014-10-15

The hydrogen mitigation system may include igniters, passive autocatalytic recombiner (PAR), and venting or dilution system. Recently PAR is commonly used as a main component of HMS in a NPP containment because of its passive nature. PARs are categorized by the shape and material of catalytic surface. Catalytic surface coated by platinum is mostly used for the hydrogen recombiners. The shapes of the catalytic surface can be grouped into plate type, honeycomb type and porous media type. Among them, the plate-type PAR is well tested by many experiments. PAR performance analysis can be approached by a multi-scale method which is composed of micro, meso and macro scales. The criterion of the scaling is the ratio of thickness of boundary layer developed on a catalytic surface to representative length of a computational domain. Mass diffusion in the boundary layer must be resolved in the micro scale analysis. In a lumped parameter (LP) analysis using a system code such as MAAP or MELCOR, the chamber of the PAR is much smaller than a computational node. The hydrogen depletion by a PAR is modeled as a source of mass and energy conservation equations. Te catalytic surface reaction of hydrogen must be modeled by a volume-averaged correlation. In this study, a micro scale analysis method is developed using libraries in OpenFOAM to evaluate a hydrogen depletion rate depending on parameters such as size and number of plates and plate arrangement. The analysis code is validated by simulating REKO-3 experiment. And hydrogen depletion analysis is conducted by changing the plate arrangement as a trial of the performance enhancement of a PAR. In this study, a numerical code for an analysis of a PAR performance in a micro scale has been developed by using OpenFOAM libraries. The physical and numerical models were validated by simulating the REKO-3 experiment. As a try to enhance the performance of the plate-type PAR, it was proposed to apply a staggered two-layer arrangement of the

Hydrogen Recombination Rates of Plate-type Passive Auto-catalytic Recombiner

International Nuclear Information System (INIS)

Kim, Jongtae; Hong, Seong-Wan; Kim, Gun Hong

2014-01-01

The hydrogen mitigation system may include igniters, passive autocatalytic recombiner (PAR), and venting or dilution system. Recently PAR is commonly used as a main component of HMS in a NPP containment because of its passive nature. PARs are categorized by the shape and material of catalytic surface. Catalytic surface coated by platinum is mostly used for the hydrogen recombiners. The shapes of the catalytic surface can be grouped into plate type, honeycomb type and porous media type. Among them, the plate-type PAR is well tested by many experiments. PAR performance analysis can be approached by a multi-scale method which is composed of micro, meso and macro scales. The criterion of the scaling is the ratio of thickness of boundary layer developed on a catalytic surface to representative length of a computational domain. Mass diffusion in the boundary layer must be resolved in the micro scale analysis. In a lumped parameter (LP) analysis using a system code such as MAAP or MELCOR, the chamber of the PAR is much smaller than a computational node. The hydrogen depletion by a PAR is modeled as a source of mass and energy conservation equations. Te catalytic surface reaction of hydrogen must be modeled by a volume-averaged correlation. In this study, a micro scale analysis method is developed using libraries in OpenFOAM to evaluate a hydrogen depletion rate depending on parameters such as size and number of plates and plate arrangement. The analysis code is validated by simulating REKO-3 experiment. And hydrogen depletion analysis is conducted by changing the plate arrangement as a trial of the performance enhancement of a PAR. In this study, a numerical code for an analysis of a PAR performance in a micro scale has been developed by using OpenFOAM libraries. The physical and numerical models were validated by simulating the REKO-3 experiment. As a try to enhance the performance of the plate-type PAR, it was proposed to apply a staggered two-layer arrangement of the

Influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach

Directory of Open Access Journals (Sweden)

R. Massabò

2014-07-01

Full Text Available Stress and displacement fields in multilayered composites with interfacial imperfections, such as imperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowing relative motion, have large variations in the thickness, with characteristic zigzag patterns and jumps at the layer interfaces. These effects are well captured by a model recently formulated by the author for multilayered plates with imperfect interfaces and affine interfacial traction laws (Massabò & Campi, Meccanica, 2014, in press; Compos Struct, 2014, 116, 311-324. The model defines a homogenized displacement field, which satisfies interfacial continuity, and uses a variational technique to derive equilibrium equations depending on only six generalized displacement functions, for any arbitrary numbers of layers and interfaces. The model accurately predicts stresses and displacements in simply supported, highly anisotropic, thick plates with continuous, sliding interfaces. In this paper the model is applied to wide plates with clamped edges and some inconsistencies, which have been noted in the literature for models based on similar approaches and have limited their utilization, are explained. A generalized transverse shear force is introduced as the gross stress resultant which is directly related to the bending moment in the equilibrium equations of multilayered structures with imperfect interfaces and substitutes for the shear force of single-layer theory. An application to a delaminated wide plate highlights the potential and limitations of the proposed model for the solution of fracture mechanics problems.

Dynamics of second order in time evolution equations with state-dependent delay

Czech Academy of Sciences Publication Activity Database

Chueshov, I.; Rezunenko, Oleksandr

123-124, č. 1 (2015), s. 126-149 ISSN 0362-546X R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor Subject RIV: BD - Theory of Information Impact factor: 1.125, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf

Active Vibration Control of Plate Partly Treated with ACLD Using Hybrid Control

Directory of Open Access Journals (Sweden)

Dongdong Zhang

2014-01-01

Full Text Available A finite element model of plate partly treated with ACLD treatments is developed based on the constitutive equations of elastic, piezoelectric, viscoelastic materials and Hamilton’s principle. The Golla-Hughes-Mctavish (GHM method is employed to describe the frequency-dependent characteristics of viscoelastic material (VEM. A model reduction is completed by using iterative dynamic condensation and balance model reduction method to design an effective control system. The emphasis is concerned on hybrid (combined feedback/feedforward control system to attenuate the vibration of plates with ACLD treatments. The optimal linear quadratic Gaussian (LQG controller is considered as a feedback channel and the adaptive filtered-reference LMS (FxLMS controller is used as a feedforward channel. They can be utilized individually or in a hybrid way to suppress the vibration of plate/ACLD system. The results show that the hybrid controller which combines feedback/feedforward together can reduce the displacement amplitude of plate/ACLD system subjected to a complicated disturbance substantially without requiring more control effort. Furthermore, the hybrid controller has more rapid and stable convergence rate than the adaptive feedforward FxLMS controller. Meanwhile, perfect robustness to phase error of the cancellation path in feedforward controller and the weight matrices in feedback LQG controller is demonstrated in proposed hybrid controller. Therefore, its application in structural engineering can be highly appreciated.

Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA Approach

Directory of Open Access Journals (Sweden)

Zheng Ling

2011-01-01

Full Text Available Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an

Comparison of the application of plate and beam theories to the elastic dilation and interaction of PFR sub-assembly wrappers

International Nuclear Information System (INIS)

Moss, R.L.

1977-10-01

A wrapper face is assumed to be a long, narrow, rectangular plate. The mechanical interaction between adjacent dilating wrappers in contact along an axial line is discussed in terms of the theory of the bending of plates. A variational method is used to obtain neat and concise equations that determine both the interaction load and the length of the line of contact. The prime objective of the work is to compare the results obtained from plate theory with corresponding expressions from much simpler calculations based on beam theory. Numerical results indicate that the elastic dilation of a wrapper and its interaction with a neighbouring wrapper can be calculated to adequate accuracy by simple beam theory. (author)

Heat transfer analysis to investigate the core catcher plate assembly in SFR

International Nuclear Information System (INIS)

Patil, Swapnil; Sharma, Anil Kumar; Velusamy, K.; Nashine, B.K.; Selvaraj, P.

2015-01-01

Severe accident scenario in Sodium Cooled Fast Reactor (SFR) is the major concern for public acceptance. After severe accident, the molten core continuously generates substantial decay heat. However, an in-vessel core catcher plate is provided to remove the decay heat passively. The numerical investigation of pool hydraulics phenomena in sodium pool of typical Indian SFR has been carried out. The debris may form a heap with different angle over the core catcher plate due to molten fuel density and interaction force. Therefore, the debris bed with different heap angle has been analyzed for steady and transient state conditions. The governing equation of fluid flow and heat transfer are solved by finite volume method based solver with the k-ε turbulent model. The time period Δ for which temperature is exceeding above safety limit with different debris heap angle have been established. (author)

PERFORMANCE DETERIORATION OF THERMOSIPHON SOLAR FLAT PLATE WATER HEATER DUE TO SCALING

OpenAIRE

arunachala umesh chandavar

2011-01-01

The performance of Flat plate Solar Water Heater deteriorates within five to twelve years of their installation due to factors related to manufacturing, operating conditions, lack of maintenance etc. Especially, problem due to scaling is significant as it is based on quality of water used. The remaining factors are system dependent and could be overcome by quality production. Software is developed by incorporating Hottel Whillier Bliss (H-W-B) equation to ascertain the effect of scaling o...

Cadmium plating replacements

Energy Technology Data Exchange (ETDEWEB)

Nelson, M.J.; Groshart, E.C.

1995-03-01

The Boeing Company has been searching for replacements to cadmium plate. Two alloy plating systems seem close to meeting the needs of a cadmium replacement. The two alloys, zinc-nickel and tin-zinc are from alloy plating baths; both baths are neutral pH. The alloys meet the requirements for salt fog corrosion resistance, and both alloys excel as a paint base. Currently, tests are being performed on standard fasteners to compare zinc-nickel and tin-zinc on threaded hardware where cadmium is heavily used. The Hydrogen embrittlement propensity of the zinc-nickel bath has been tested, and just beginning for the tin-zinc bath. Another area of interest is the electrical properties on aluminum for tin-zinc and will be discussed. The zinc-nickel alloy plating bath is in production in Boeing Commercial Airplane Group for non-critical low strength steels. The outlook is promising that these two coatings will help The Boeing Company significantly reduce its dependence on cadmium plating.

History of internal fixation with plates (part 2): new developments after World War II; compressing plates and locked plates.

Science.gov (United States)

Hernigou, Philippe; Pariat, Jacques

2017-07-01

The first techniques of operative fracture with plates were developed in the 19th century. In fact, at the beginning these methods consisted of an open reduction of the fracture usually followed by a very unstable fixation. As a consequence, the fracture had to be opened with a real risk of (sometimes lethal) infection, and due to unstable fixation, protection with a cast was often necessary. During the period between World Wars I and II, plates for fracture fixation developed with great variety. It became increasingly recognised that, because a fracture of a long bone normally heals with minimal resorption at the bone ends, this may result in slight shortening and collapse, so a very rigid plate might prevent such collapse. However, as a consequence, delayed healing was observed unless the patient was lucky enough to have the plate break. One way of dealing with this was to use a slotted plate in which the screws could move axially, but the really important advance was recognition of the role of compression. After the first description of compression by Danis with a "coapteur", Bagby and Müller with the AO improved the technique of compression. The classic dynamic compression plates from the 1970s were the key to a very rigid fixation, leading to primary bone healing. Nevertheless, the use of strong plates resulted in delayed union and the osteoporosis, cancellous bone, comminution, and/or pathological bone resulted in some failures due to insufficient stability. Finally, new devices represented by locking plates increased the stability, contributing to the principles of a more biological osteosynthesis while giving enough stability to allow immediate full weight bearing in some patients.

Investigation of the nonlinear static and dynamic behaviour of rectangular microplates under electrostatic actuation

KAUST Repository

Saghir, Shahid; Younis, Mohammad I.

2016-01-01

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary resonance. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased.

Investigation of the nonlinear static and dynamic behaviour of rectangular microplates under electrostatic actuation

KAUST Repository

Saghir, Shahid

2016-11-16

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary resonance. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased.

Optimizing the longitudinal and transverse electroosmotic pumping in a rectangular channel with horizontal baffle plates

Science.gov (United States)

Lai, Anison K. R.; Chang, Chien-Cheng; Wang, Chang-Yi

2018-04-01

This paper presents a continued study to our previous work on electroosmotic (EO) flow in a channel with vertical baffle plates by further investigating EO flow through an array of baffle plates arranged in parallel to the channel walls. The flow may be driven either in the direction along or in the direction transverse to the plates, thus distinguishing the longitudinal EO pumping (LEOP) and the transverse EO pumping (TEOP). In both types of EO pumping, it is more interesting to examine the cases when the baffle plates develop a higher zeta potential (denoted by α) than that on the channel walls (β). This semi-analytical study enables us to compare between LEOP and TEOP in the pumping efficiency under similar conditions. The TEOP case is more difficult to solve due to the higher order governing partial differential equations caused by the induced non-uniform pressure gradient distribution. In particular, we examine how the EO pumping rates deviate from those predicted by the Helmholtz-Smoluchowski velocity and illustrate the general trend of optimizing the EO pumping rates with respect to the physical and geometric parameters involved.

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

Science.gov (United States)

Somogyi, D.; Yen, H. H.

1973-01-01

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

STEADY STATE AND PSEUDO-TRANSIENT ELECTRIC POTENTIAL USING THE POISSONBOLTZMANN EQUATION

Directory of Open Access Journals (Sweden)

L. C. dos Santos

2015-03-01

Full Text Available A method for analysis of the electric potential profile in saline solutions was developed for systems with one or two infinite flat plates. A modified Poisson-Boltzmann equation, taking into account nonelectrostatic interactions between ions and surfaces, was used. To solve the stated problem in the steady-state approach the finite-difference method was used. For the formulated pseudo-transient problem, we solved the set of ordinary differential equations generated from the algebraic equations of the stationary case. A case study was also carried out in relation to temperature, solution concentration, surface charge and salt-type. The results were validated by the stationary problem solution, which had also been used to verify the ionic specificity for different salts. The pseudo-transient approach allowed a better understanding of the dynamic behavior of the ion-concentration profile and other properties due to the surface charge variation.

The Importance of Lower Mantle Structure to Plate Stresses and Plate Motions

Science.gov (United States)

Holt, W. E.; Wang, X.; Ghosh, A.

2016-12-01

Plate motions and plate stresses are widely assumed as the surface expression of mantle convection. The generation of plate tectonics from mantle convection has been studied for many years. Lithospheric thickening (or ridge push) and slab pull forces are commonly accepted as the major driving forces for the plate motions. However, the importance of the lower mantle to plate stresses and plate motions remains less clear. Here, we use the joint modeling of lithosphere and mantle dynamics approach of Wang et al. (2015) to compute the tractions originating from deeper mantle convection and follow the method of Ghosh et al. (2013) to calculate gravitational potential energy per unit area (GPE) based on Crust 1.0 (Laske et al., 2013). Absolute values of deviatoric stresses are determined by the body force distributions (GPE gradients and traction magnitudes applied at the base of the lithosphere). We use the same relative viscosity model that Ghosh et al. (2013) used, and we solve for one single adjustable scaling factor that multiplies the entire relative viscosity field to provide absolute values of viscosity throughout the lithosphere. This distribution of absolute values of lithosphere viscosities defines the magnitudes of surface motions. In this procedure, the dynamic model first satisfies the internal constraint of no-net-rotation of motions. The model viscosity field is then scaled by the single factor until we achieve a root mean square (RMS) minimum between computed surface motions and the kinematic no-net-rotation (NNR) model of Kreemer et al. (2006). We compute plate stresses and plate motions from recently published global tomography models (over 70 based on Wang et al., 2015). We find that RMS misfits are significantly reduced when details of lower mantle structure from the latest tomography models are added to models that contain only upper and mid-mantle density distributions. One of the key reasons is that active upwelling from the Large Low Shear

The electrical MHD and Hall current impact on micropolar nanofluid flow between rotating parallel plates

Science.gov (United States)

Shah, Zahir; Islam, Saeed; Gul, Taza; Bonyah, Ebenezer; Altaf Khan, Muhammad

2018-06-01

The current research aims to examine the combined effect of magnetic and electric field on micropolar nanofluid between two parallel plates in a rotating system. The nanofluid flow between two parallel plates is taken under the influence of Hall current. The flow of micropolar nanofluid has been assumed in steady state. The rudimentary governing equations have been changed to a set of differential nonlinear and coupled equations using suitable similarity variables. An optimal approach has been used to acquire the solution of the modelled problems. The convergence of the method has been shown numerically. The impact of the Skin friction on velocity profile, Nusslet number on temperature profile and Sherwood number on concentration profile have been studied. The influences of the Hall currents, rotation, Brownian motion and thermophoresis analysis of micropolar nanofluid have been mainly focused in this work. Moreover, for comprehension the physical presentation of the embedded parameters that is, coupling parameter N1 , viscosity parameter Re , spin gradient viscosity parameter N2 , rotating parameter Kr , Micropolar fluid constant N3 , magnetic parameter M , Prandtl number Pr , Thermophoretic parameter Nt , Brownian motion parameter Nb , and Schmidt number Sc have been plotted and deliberated graphically.

Catalysts characteristics of Ni/YSZ core-shell according to plating conditions using electroless plating

Science.gov (United States)

Park, Hyun-Wook; Jang, Jae-Won; Lee, Young-Jin; Kim, Jin-Ho; Jeon, Dae-Woo; Lee, Jong-Heun; Hwang, Hae-jin; Lee, Mi-Jai

2017-11-01

This study aims to develop an anode catalyst for a solid oxide fuel cell (SOFC) using electroless nickel plating. We have proposed a new method for electroless plating of Ni metal on yttria-stabilized zirconia (YSZ) particles. We examine the uniformity of the Ni layer on the plated core-shell powder, in addition to the content of Ni and the reproducibility of the plating. We have also evaluated the carbon deposition rate and characteristics of the SOFC anode catalyst. To synthesize Ni-plated YSZ particles, the plated powder is heat-treated at 1200 °C. The resultant particles, which have an average size of 50 μm, were subsequently used in the experiment. The size of the Ni particles and the Ni content both increase with increasing plating temperature and plating time. The X-ray diffraction pattern reveals the growth of Ni particles. After heat-treatment, Ni is oxidized to NiO, leading to the co-existence of Ni and NiO; Ni3P is also observed due to the presence of phosphorous in the plating solution. Following heat treatment for 1 h at 1200 °C, Ni is mostly oxidized to NiO. The carbon deposition rate of the reference YSZ powder is 135%, while that of the Ni-plated YSZ is 1%-6%.

Numerical Investigation of Jet Impingement Heat Transfer on a Flat plate

Directory of Open Access Journals (Sweden)

Asem Nabadavis

2016-12-01

Full Text Available The numerical investigation emphasizes on studying the heat transfer characteristics when a high velocity air jet impinges upon a flat plate having constant heat flux. Numerical analysis has been conducted by solving conservation equations of momentum, mass and energy with two equations based k- ε turbulence model to determine the wall temperature and Nu of the plate considering the flow to be incompressible. It was found from the investigation that the heat transfer rate increases with the increase of Reynolds number of the jet (Rej. It was also found that there is an optimum value for jet distance to nozzle diameter ratio (H/d for maximum heat transfer when all the other parameters were kept fixed. Similar results as above were found when two jets of air were used instead of one jet keeping the mass flow rate constant. For a two jets case it was also found that heat transfer rate over the surface increases when the jets are inclined outward compared to vertical and inward jets and also there exists an optimum angle of jet for maximum heat transfer. Further investigation was carried out for different jetto-jet separation distance for a twin jet impingement model where it was noted that heat transfer is more distributed in case of larger values of L and the rate of heat transfer increases as the separation between the jet increases till a certain point after which the rate of heat transfer decreases.

Unsteady MHD free convection flow of casson fluid over an inclined vertical plate embedded in a porous media

Science.gov (United States)

Manideep, P.; Raju, R. Srinivasa; Rao, T. Siva Nageswar; Reddy, G. Jithender

2018-05-01

This paper deals, an unsteady magnetohydrodynamic heat transfer natural convection flow of non-Newtonian Casson fluid over an inclined vertical plate embedded in a porous media with the presence of boundary conditions such as oscillating velocity, constant wall temperature. The governing dimensionless boundary layer partial differential equations are reduced to simultaneous algebraic linear equation for velocity, temperature of Casson fluid through finite element method. Those equations are solved by Thomas algorithm after imposing the boundary conditions through MATLAB for analyzing the behavior of Casson fluid velocity and temperature with various physical parameters. Also analyzed the local skin-friction and rate of heat transfer. Compared the present results with earlier reported studies, the results are comprehensively authenticated and robust FEM.

Fuel cell end plate structure

Science.gov (United States)

Guthrie, Robin J.; Katz, Murray; Schroll, Craig R.

1991-04-23

The end plates (16) of a fuel cell stack (12) are formed of a thin membrane. Pressure plates (20) exert compressive load through insulation layers (22, 26) to the membrane. Electrical contact between the end plates (16) and electrodes (50, 58) is maintained without deleterious making and breaking of electrical contacts during thermal transients. The thin end plate (16) under compressive load will not distort with a temperature difference across its thickness. Pressure plate (20) experiences a low thermal transient because it is insulated from the cell. The impact on the end plate of any slight deflection created in the pressure plate by temperature difference is minimized by the resilient pressure pad, in the form of insulation, therebetween.

A Mathematical Model for the Non-Stationary Process of Compression Molding of Plates from Granulate of Thermoplastic Composites

Directory of Open Access Journals (Sweden)

Vladimir N. Vodyakov

2017-12-01

Full Text Available Introduction: Mathematical modeling allows assigning optimal parameters for the process of compression molding of plates and calculating the dimensions of the mold without costly and long-term experiments. The options ensure the required precision of pressing. The disadvantages of the known models are the assumptions about the process isothermicity and independence of the thermal-physical coefficients from temperature. The models do not take into account the dependence of the pressure in the cavity of the mold on the excess of the melt; the problem of calculating the dimensions of the mold cavity for given plate dimensions is not posed. The known models do not give a complete description of all stages of the process. The aim of this paper is to develop a perfect mathematical model without limitations for the compression molding of plates from a granulate of highly filled thermoplastic composites. Materials and Methods: The paper proposes a non-stationary mathematical model. The model takes into account the presence of physical states transitions and dependence of the thermophysical characteristics of composites on temperature. The model is based on the known equations of thermal physics and continuum mechanics. Results: Initial and boundary conditions, rheological equations, systems of equations for the material, thermal, and power balance are determined for three stages of the process. The calculation problems are determined too. A program of iterative numerical calculation has been developed because of the resulting system of equations has no analytical solution. A convergence of experimental and theoretical results with the correlation coefficient confirms the adequacy of the developed mathematical model and the calculation program. Discussion and Conclusions: The results of the study allow calculating the dimensions of the mold cavity, the initial granulate required mass, technological losses, the time functions of pressure and temperature

Irreversibility analysis for gravity driven non-Newtonian liquid film along an inclined isothermal plate

International Nuclear Information System (INIS)

Makinde, O.D.

2005-10-01

In this paper, the first and second law of thermodynamics are employed in order to study the inherent irreversibility for a gravity driven non-Newtonian Ostwald-de Waele power law liquid film along an inclined isothermal plate. Based on some simplified assumptions, the governing equations are obtained and solved analytically. Expressions for fluid velocity, temperature, volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number are also determined. (author)

Heat insulating plates

Energy Technology Data Exchange (ETDEWEB)

Allan, J.A.F.

1976-10-28

Micro-porous insulation plates are dealt with, for example, how they are used in the insulation of heat storage devices. Since one side of such plates is exposed to a temperature of over 700/sup 0/C, a shrinkage of the glass texture of the covering can occur, which can exceed the shrinkage of the inner micro-porous material, so that cracks and splits in the high temperature side of the covering can come about. The task of the invention is to design the plate in such a way as to prevent this from happening. For this purpose the plate is provided, according to invention specifications, with flutes, waves, ribs, waffle or grid patterns and the covering is set into the recesses originating from this.

Recent developments in multi-parametric three-dimensional stress field representation in plates weakened by cracks and notches

Directory of Open Access Journals (Sweden)

P. Lazzarin

2013-07-01

Full Text Available The paper deals with the three-dimensional nature and the multi-parametric representation of the stress field ahead of cracks and notches of different shape. Finite thickness plates are considered, under different loading conditions. Under certain hypotheses, the three-dimensional governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. The analytical frame is applied to some notched and cracked geometries and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE models.

Fuel cell cooler-humidifier plate

Science.gov (United States)

Vitale, Nicholas G.; Jones, Daniel O.

2000-01-01

A cooler-humidifier plate for use in a proton exchange membrane (PEM) fuel cell stack assembly is provided. The cooler-humidifier plate combines functions of cooling and humidification within the fuel cell stack assembly, thereby providing a more compact structure, simpler manifolding, and reduced reject heat from the fuel cell. Coolant on the cooler side of the plate removes heat generated within the fuel cell assembly. Heat is also removed by the humidifier side of the plate for use in evaporating the humidification water. On the humidifier side of the plate, evaporating water humidifies reactant gas flowing over a moistened wick. After exiting the humidifier side of the plate, humidified reactant gas provides needed moisture to the proton exchange membranes used in the fuel cell stack assembly. The invention also provides a fuel cell plate that maximizes structural support within the fuel cell by ensuring that the ribs that form the boundaries of channels on one side of the plate have ends at locations that substantially correspond to the locations of ribs on the opposite side of the plate.

Various methods of determining the natural frequencies and damping of composite cantilever plates. 3. The Ritz method

Science.gov (United States)

Ekel'chik, V. S.; Ryabov, V. M.

1997-03-01

The Ritz method was used to determine the frequencies and forms of free vibrations of rectangular cantilever plates made of anisotropic laminated composites. Orthogonal Jacobi and Legendre polynomials were used as coordinate functions. The results of the calculations are in good agreement with the published experimental and calculated data of other authors for plates made of boron and carbon fiber reinforced plastics with different angles of reinforcement of unidirectional layers and different sequence of placing the layers, and also of isotropic plates. The dissipative characteristics in vibrations were determined on the basis of the concept of complex moduli. The solution of the frequency equation with complex coefficients yields a complex frequency; the loss factors are determined from the ratio of the imaginary component of the complex frequency to the real component. For plates of unidirectionally reinforced carbon fiber plastic with different relative length a detailed analysis of the influence of the angle of reinforcement on the interaction and frequency transformation and on the loss factor was carried out. The article shows that the loss factor of a plate depends substantially on the type of vibration mode: bending or torsional. It also examines the asymptotics of the loss factors of plates when their length is increased, and it notes that the binomial model of deformation leads to a noticeable error in the calculation of the loss factor of long plates when the angle of reinforcement lies in the range 20°<φ<70°.

Nonlinear streak computation using boundary region equations

Energy Technology Data Exchange (ETDEWEB)

Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

2012-08-01

The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes; Solucion de la ecuacion de transporte de Boltzmann-Fokker-Planck usando esquemas nodales exponenciales

Energy Technology Data Exchange (ETDEWEB)

Ortega J, R.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: roj@correo.azc.uam.mx

2003-07-01

There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S{sub 4} with expansions of the dispersion cross sections until P{sub 3} order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

Topology optimization for elastic base under rectangular plate subjected to moving load

Directory of Open Access Journals (Sweden)

Jilavyan Samvel H.

2015-09-01

Full Text Available Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two- dimensional Heaviside‘s function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.

An analytical erosion model for divertor plates and limiter experiments in CHS

International Nuclear Information System (INIS)

Sagara, A.; Noda, N.; Akiyama, R.; Arimoto, H.; Idei, H.; Iguchi, H.; Kaneko, O.; Kohmoto, T.; Kubo, S.; Matsuoka, K.; Morita, S.; Motojima, O.; Nishimura, K.; Okamura, S.; Takahasi, C.; Takita, Y.; Yamada, I.; Matsunami, N.; Rice, J.; Yamada, H.; Shoji, T.; Ueda, M.

1992-01-01

A self-consistent analytical solution for net erosion of a divertor plate which is set perpendicular to magnetic field lines is presented. The primary flux profile of hydrogen and impurities except redepositing particles is externally given as well as the return ratio of sputtered atoms to the plate. In the direction along the divertor trace, all conditions are uniform. The ionization mean free path is assumed constant to simplify equations. The analytical solution is compared with net erosion experiments carried out in compact helical system (CHS) by exposing a graphite target to a neutral beam heated plasma column introduced perpendicularly to the target along the magnetic field lines through a 2 cm slit opend on a graphite limiter. After exposure to 98 discharges, the target surface is analyzed with Rutherford backscattering method. Deposition profiles of Ti and O impurities are very well explained with the analytical predictions. (orig.)

CFD SIMULATION OF THE HEAT TRANSFER PROCESS IN A CHEVRON PLATE HEAT EXCHANGER USING THE SST TURBULENCE MODEL

Directory of Open Access Journals (Sweden)

Jan Skočilas

2015-08-01

Full Text Available This paper deals with a computational fluid dynamics (CFD simulation of the heat transfer process during turbulent hot water flow between two chevron plates in a plate heat exchanger. A three-dimensional model with the simplified geometry of two cross-corrugated channels provided by chevron plates, taking into account the inlet and outlet ports, has been designed for the numerical study. The numerical model was based on the shear-stress transport (SST k-! model. The basic characteristics of the heat exchanger, as values of heat transfer coefficient and pressure drop, have been investigated. A comparative analysis of analytical calculation results, based on experimental data obtained from literature, and of the results obtained by numerical simulation, has been carried out. The coefficients and the exponents in the design equations for the considered plates have been arranged by using simulation results. The influence on the main flow parameters of the corrugation inclination angle relative to the flow direction has been taken into account. An analysis of the temperature distribution across the plates has been carried out, and it has shown the presence of zones with higher heat losses and low fluid flow intensity.

Modeling of parallel-plate regenerators with non-uniform plate distributions

DEFF Research Database (Denmark)

Jensen, Jesper Buch; Engelbrecht, Kurt; Bahl, Christian Robert Haffenden

2010-01-01

plate spacing distributions are presented in order to understand the impact of spacing non-uniformity. Simulations of more realistic distributions where the plate spacings follow normal distributions are then discussed in order to describe the deviation of the performance of a regenerator relative...

Highly conductive composites for fuel cell flow field plates and bipolar plates

Science.gov (United States)

Jang, Bor Z; Zhamu, Aruna; Song, Lulu

2014-10-21

This invention provides a fuel cell flow field plate or bipolar plate having flow channels on faces of the plate, comprising an electrically conductive polymer composite. The composite is composed of (A) at least 50% by weight of a conductive filler, comprising at least 5% by weight reinforcement fibers, expanded graphite platelets, graphitic nano-fibers, and/or carbon nano-tubes; (B) polymer matrix material at 1 to 49.9% by weight; and (C) a polymer binder at 0.1 to 10% by weight; wherein the sum of the conductive filler weight %, polymer matrix weight % and polymer binder weight % equals 100% and the bulk electrical conductivity of the flow field or bipolar plate is at least 100 S/cm. The invention also provides a continuous process for cost-effective mass production of the conductive composite-based flow field or bipolar plate.

Radiation effects on flow past an impulsively started vertical plate with variable temperature and mass flux

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2005-01-01

Full Text Available An analysis is performed to study the thermal radiation effects on unsteady free convective flow over a moving vertical plate in the presence of variable temperature and uniform mass flux. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The temperature is raised linearly with time and the concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace transform technique. The velocity and skinfriction are studied for different parameters like the radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing radiation parameter.

Analysis of a rectangular ceramic plate in electrically forced thickness-twist vibration as a piezoelectric transformer.

Science.gov (United States)

Yang, Jiashi; Liu, Jinjin; Li, Jiangyu

2007-04-01

A rectangular ceramic plate with appropriate electrical load and operating mode is analyzed for piezoelectric transformer application. An exact solution from the three-dimensional equations of linear piezoelectricity is obtained. The solution simulates the real operating situation of a transformer as a vibrating piezoelectric body connected to a circuit. Transforming ratio, input admittance, and efficiency of the transformer are obtained.

Software development for a orifice plate characterization used in the oil and gas industry; Desenvolvimento de um 'software' para caracterizacao de placas de orificio utilizadas na industria do petroleo

Energy Technology Data Exchange (ETDEWEB)

Andreas, N. Andreas [Universidade Federal de Itajuba (UNIFEI), MG (Brazil)

2008-07-01

The petroleum industry is an economic area that has a strong impact, because this, the information precision is one of the most important facts and it is able to be defined with software simulation. The knowledge of the exactly quantify of petroleum is fundamental, and then the instrumentation is essential for this measurement. There are many mechanisms to measure the volume flow, and one of the most used is the Orifice Plates, which has been more common in the Natural Gas Industry. The software development goal is the characterization of these Orifice Plates, allowing that the constant, which characterizes certain Plate, to be determined without Labor instruments, for that the software has an actualized database. But, the software needs some variables, that are responsible for the environment characteristics and the used material, to calculate the constant of the Orifice Plate, for example, fluid viscosity, environment temperature and kind of the Orifice Plate. The utilized equations in this software are based on the Stolz II equations. This tool is able to facilitate the work in petroleum industry, besides it is done for mobile applications, allowing analyses in real time. (author)

Ni-based amorphous alloy-coating for bipolar plate of PEM fuel cell by electrochemical plating

International Nuclear Information System (INIS)

Yamaura, S; Kim, S C; Inoue, A

2013-01-01

In this study, the Ni-Cr-P amorphous alloy-coated bipolar plates were produced by electro-plating on the Cu base plates with a flow field. The power generation tests of a single fuel cell with those Ni-Cr-P bipolar plates were conducted at 353 K. It was found that the single fuel cell with those Ni-Cr-P bipolar plates showed excellent I-V performance as well as that with the carbon graphite bipolar plates. It was also found that the single cell with those Ni-Cr-P bipolar plates showed better I-V performance than that with the Ni-P amorphous alloy-coated bipolar plates. Furthermore, the long-time operation test was conducted for 440 h with those Ni-Cr-P bipolar plates at the constant current density of 200 mA·cm −2 . As a result, it was found that the cell voltage gradually decreased at the beginning of the measurement before 300 h and then the voltage was kept constant after 300 h.

Heat transfer effects on a viscous dissipative fluid flow past a vertical plate in the presence of induced magnetic field

Directory of Open Access Journals (Sweden)

M.C. Raju

2015-03-01

Full Text Available A theoretical analysis is performed to study induced magnetic field effects on free convection flow past a vertical plate. The x¯-axis is taken vertically upwards along the plate, y¯-axis normal to the plate into the fluid region. It is assumed that the plate is electrically non-conducting and the applied magnetic field is of uniform strength (H0 and perpendicular to the plate. The magnetic Reynolds number of the flow is not taken to be small enough so that the induced magnetic field is taken into account. The coupled nonlinear partial differential equations are solved by Perturbation technique and the effects of various physical parameters on velocity, temperature, and induced magnetic fields are studied through graphs and tables. Variations in Skin friction and rate of heat transfer are also studied. It is observed that an increase in magnetic parameter decreases the velocity for both water and air. It is also seen that there is a fall in induced magnetic field as magnetic Prandtl number, and magnetic field parameter increase.

Investigation of one-dimensional heat flow in a solarflat plate collector with sun tracing system

Directory of Open Access Journals (Sweden)

H Samimi Akhijahani

2016-09-01

Full Text Available Introduction Drying is one of the most common methods for storing food and agricultural products. During drying process, free water that causes the growth of microorganisms and spoilage of products is removed from the product. There are several methods for drying of agricultural products. one of the most important methods of investment is drying by using sunlight. Iran is situated at 25- 43oE longitude and mean solar radiation is about 4.9 kwh.m-2.d-1. Because of the proper solar radiations in 95% of the agricultural areas in Iran, solar drying is widely used for drying of fruits and vegetables. The use of solar dryer causes saving in energy consumption and processing costs for drying of products in farms and gardens. Several researchers investigated heat transfer and heat flow in dryers. Selection of appropriate method was carried out for drying of agricultural products using heat pump. Experiments were done and mathematical relationships were estimated to obtain correlation parameters between Reynolds number and Nusselt number for the three cases of solar dryer (cabinet, indirect and combination.The best working conditions were determined for three types of solar collectors (flat, finned and corrugated. In this study, the process of heat transfer and heat transfer coefficient of a solar dryer with and without rotation of absorber plate was compared. Materials and Methods The experiments were conducted in Azarshahr, East Azarbayjan province, Iran in September 2014. Newton's law of thermodynamic was used to analyze the working condition of solar absorber. For this purpose the absorber plate was divided into four equal parts. According to the thermal equations and related boundary conditions as well as the relationship between heat transfer coefficient and the temperature gradient, equation 1 for the Nusselet number obtained: 1 Beside the relationship between Nusselt number and heat transfer coefficient is defined as equation 2: 2 Finally

Study the effect of chemical reaction and variable viscosity on free convection MHD radiating flow over an inclined plate bounded by porous medium

Energy Technology Data Exchange (ETDEWEB)

Ali, M., E-mail: ali.mehidi93@gmail.com [Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000 (Bangladesh); Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong-4349 (Bangladesh); Alim, M. A., E-mail: maalim@math.buet.ac.bd; Nasrin, R., E-mail: rehena@math.buet.ac.bd [Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000 (Bangladesh); Alam, M. S., E-mail: shahalammaths@gmail.com [Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong-4349 (Bangladesh)

2016-07-12

An analysis is performed to study the free convection heat and mass transfer flow of an electrically conducting incompressible viscous fluid about a semi-infinite inclined porous plate under the action of radiation, chemical reaction in presence of magnetic field with variable viscosity. The dimensionless governing equations are steady, two-dimensional coupled and non-linear ordinary differential equation. Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme is used to solve the non-dimensional governing equations. The effects of magnetic parameter, viscosity parameter and chemical reaction parameter on velocity, temperature and concentration profiles are discussed numerically and shown graphically. Therefore, the results of velocity profile decreases for increasing values of magnetic parameter and viscosity parameter but there is no effect for reaction parameter. The temperature profile decreases in presence of magnetic parameter, viscosity parameter and Prandtl number but increases for radiation parameter. Also, concentration profile decreases for the increasing values of magnetic parameter, viscosity parameter and reaction parameter. All numerical calculations are done with respect to salt water and fixed angle of inclination of the plate.

Study the effect of chemical reaction and variable viscosity on free convection MHD radiating flow over an inclined plate bounded by porous medium

International Nuclear Information System (INIS)

Ali, M.; Alim, M. A.; Nasrin, R.; Alam, M. S.

2016-01-01

An analysis is performed to study the free convection heat and mass transfer flow of an electrically conducting incompressible viscous fluid about a semi-infinite inclined porous plate under the action of radiation, chemical reaction in presence of magnetic field with variable viscosity. The dimensionless governing equations are steady, two-dimensional coupled and non-linear ordinary differential equation. Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme is used to solve the non-dimensional governing equations. The effects of magnetic parameter, viscosity parameter and chemical reaction parameter on velocity, temperature and concentration profiles are discussed numerically and shown graphically. Therefore, the results of velocity profile decreases for increasing values of magnetic parameter and viscosity parameter but there is no effect for reaction parameter. The temperature profile decreases in presence of magnetic parameter, viscosity parameter and Prandtl number but increases for radiation parameter. Also, concentration profile decreases for the increasing values of magnetic parameter, viscosity parameter and reaction parameter. All numerical calculations are done with respect to salt water and fixed angle of inclination of the plate.

A feedback control system for vibration of magnetostrictive plate subjected to follower force using sinusoidal shear

Directory of Open Access Journals (Sweden)

A. Ghorbanpour Arani

2016-03-01

Full Text Available In this research, the vibrational behavior of magnetostrictive plate (MsP as a smart component is studied. The plate is subjected to an external follower force and a magnetic field in which the vibration response of MsP has been investigated for both loading combinations. The velocity feedback gain parameter is evaluated to study the effect of magnetic field which is generated by the coil. Sinusoidal shear deformation theory is utilized due to its accuracy of polynomial function with respect to other plate theories. Equations of motion are derived using Hamilton’s principle and solved by differential quadrature method (DQM considering general boundary conditions. The effects of aspect ratio, thickness ratio, follower force and velocity feedback gain are investigated on the frequency response of MsP. Results indicate that magneto-mechanical coupling in MsM helps to control vibrational behaviors of systems such as electro-hydraulic actuator, wireless linear Motors and sensors.

Phase formation kinetics, hardness and magnetocaloric effect of sub-rapidly solidified LaFe11.6Si1.4 plates during isothermal annealing

Science.gov (United States)

Dai, Yuting; Xu, Zhishuai; Luo, Zhiping; Han, Ke; Zhai, Qijie; Zheng, Hongxing

2018-05-01

High-temperature phase transition behavior and intrinsic brittleness of NaZn13-type τ1 phase in La-Fe-Si magnetocaloric materials are two key problems from the viewpoint of materials production and practical applications. In the present work, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation was introduced to quantitatively characterize the formation kinetics of τ1 phase in sub-rapidly solidified LaFe11.6Si1.4 plates during the isothermal annealing process. Avrami index was estimated to be 0.43 (∼0.5), which suggests that the formation of τ1 phase is in a diffusion-controlled one-dimensional growth mode. Meanwhile, it is found that the Vickers hardness as a function of annealing time for sub-rapidly solidified plates also agrees well with the JMAK equation. The Vickers hardness of τ1 phase was estimated to be about 754. Under a magnetic field change of 30 kOe, the maximum magnetic entropy change was about 22.31 J/(kg·K) for plates annealed at 1323 K for 48 h, and the effective magnetic refrigeration capacity reached 191 J/kg.

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Full Text Available ... foods you want, but changes the portion sizes so you are getting larger portions of non-starchy ... plate. Then on one side, cut it again so you will have three sections on your plate. ...

Elastic stability of thick auxetic plates

International Nuclear Information System (INIS)

Lim, Teik-Cheng

2014-01-01

Auxetic materials and structures exhibit a negative Poisson’s ratio while thick plates encounter shear deformation, which is not accounted for in classical plate theory. This paper investigates the effect of a negative Poisson’s ratio on thick plates that are subjected to buckling loads, taking into consideration the shear deformation using Mindlin plate theory. Using a highly accurate shear correction factor that allows for the effect of Poisson’s ratio, the elastic stability of circular and square plates are evaluated in terms of dimensionless parameters, namely the Mindlin-to-Kirchhoff critical buckling load ratio and Mindlin critical buckling load factors. Results for thick square plates reveal that both parameters increase as the Poisson’s ratio becomes more negative. In the case of thick circular plates, the Mindlin-to-Kirchhoff critical buckling load ratios and the Mindlin critical buckling load factors increase and decrease, respectively, as the Poisson’s ratio becomes more negative. The results obtained herein show that thick auxetic plates behave as thin conventional plates, and therefore suggest that the classical plate theory can be used to evaluate the elastic stability of thick plates if the Poisson’s ratio of the plate material is sufficiently negative. The results also suggest that materials with highly negative Poisson’s ratios are recommended for square plates, but not circular plates, that are subjected to buckling loads. (paper)

Neutron imaging plates

International Nuclear Information System (INIS)

Niimura, Nobuo

1995-01-01

Imaging plates have been used in the field of medical diagnosis since long ago, but their usefulness was verified as the two-dimensional detector for analyzing the X-ray crystalline structure of high bio molecules like protein, and they have contributed to the remarkable progress in this field. The great contribution is due to the excellent features, such as the detection efficiency of about 100%, the positional resolution smaller than 0.2 mm, the dynamic range of five digits, and the area of several hundreds mm square. The neutron imaging plates have not yet obtained the sufficient results. It was planned to construct the neutron diffractometer for biological matters, and to put imaging plate neutron detectors (IP-ND) to practical use as the detector. The research on the development of IP-NDs was carried out, and the IPp-NDs having the performance comparable with that for X-ray were able to be produced. Imaging plates are the integral type two-dimensional radiation detector using photostimulated luminescence matters, and their principle is explained. As to neutron imaging plates, the converter, neutron detection efficiency and the flight of secondary particles in photo-stimulated luminescence matters are described. As for the present state of development of neutron imaging plates, the IP-NDs made for trial, the dynamic range, the positional resolution, the detection efficiency and the kinds of converters, and the application of IP-NDs are reported. (K.I.)

Towards stacked zone plates

International Nuclear Information System (INIS)

Werner, S; Rehbein, S; Guttman, P; Heim, S; Schneider, G

2009-01-01

Fresnel zone plates are the key optical elements for soft and hard x-ray microscopy. For short exposure times and minimum radiation load of the specimen the diffraction efficiency of the zone plate objectives has to be maximized. As the efficiency strongly depends on the height of the diffracting zone structures the achievable aspect ratio of the nanostructures determines these limits. To reach aspect ratios ≥ 20:1 for high efficient optics we propose to superimpose zone plates on top of each other. With this multiplication approach the final aspect ratio is only limited by the number of stacked zone plate layers. For the stack process several nanostructuring process steps have to be developed and/or improved. Our results show for the first time two layers of zone plates stacked on top of each other.

Anisotropic elastic plates

CERN Document Server

Hwu, Chyanbin

2010-01-01

As structural elements, anisotropic elastic plates find wide applications in modern technology. The plates here are considered to be subjected to not only in plane load but also transverse load. In other words, both plane and plate bending problems as well as the stretching-bending coupling problems are all explained in this book. In addition to the introduction of the theory of anisotropic elasticity, several important subjects have are discussed in this book such as interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermoelastic problems and boundary element a

Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions

Directory of Open Access Journals (Sweden)

Hamid Khan

2012-01-01

Full Text Available We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions ur(r,z,t=(1/r(∂ψ/∂z and uz(r,z,t=−(1/r(∂ψ/∂r and a transformation ψ(r,z=r2F(z. The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.

Buckling analysis for axially compressed flat plates, structural sections, and stiffened plates reinforced with laminated composites

Science.gov (United States)

Viswanathan, A. V.; Soong, T.; Miller, R. E., Jr.

1971-01-01

A classical buckling analysis is developed for stiffened, flat plates composed of a series of linked plate and beam elements. Plates are idealized as multilayered orthotropic elements. Structural beads and lips are idealized as beams. The loaded edges of the stiffened plate are simply-supported and the conditions at the unloaded edges can be prescribed arbitrarily. The plate and beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Offsets between elements are considered in the analysis. Buckling under uniaxial compressive load for plates, sections, and stiffened plates is investigated. Buckling loads are the lowest of all possible general and local failure modes, and the mode shape is used to determine whether buckling is a local or general instability. Numerical correlations with existing analysis and test data for plates, sections, and stiffened plates including boron-reinforced structures are discussed. In general correlations are reasonably good.

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BAO Plate Archive Project

Science.gov (United States)

Mickaelian, A. M.; Gigoyan, K. S.; Gyulzadyan, M. V.; Paronyan, G. M.; Abrahamyan, H. V.; Andreasyan, H. R.; Azatyan, N. M.; Kostandyan, G. R.; Samsonyan, A. L.; Mikayelyan, G. A.; Farmanyan, S. V.; Harutyunyan, V. L.

2017-12-01

We present the Byurakan Astrophysical Observatory (BAO) Plate Archive Project that is aimed at digitization, extraction and analysis of archival data and building an electronic database and interactive sky map. BAO Plate Archive consists of 37,500 photographic plates and films, obtained with 2.6m telescope, 1m and 0.5m Schmidt telescopes and other smaller ones during 1947-1991. The famous Markarian Survey (or the First Byurakan Survey, FBS) 2000 plates were digitized in 2002-2005 and the Digitized FBS (DFBS, www.aras.am/Dfbs/dfbs.html) was created. New science projects have been conducted based on this low-dispersion spectroscopic material. Several other smaller digitization projects have been carried out as well, such as part of Second Byurakan Survey (SBS) plates, photographic chain plates in Coma, where the blazar ON 231 is located and 2.6m film spectra of FBS Blue Stellar Objects. However, most of the plates and films are not digitized. In 2015, we have started a project on the whole BAO Plate Archive digitization, creation of electronic database and its scientific usage. Armenian Virtual Observatory (ArVO, www.aras.am/Arvo/arvo.htm) database will accommodate all new data. The project runs in collaboration with the Armenian Institute of Informatics and Automation Problems (IIAP) and will continues during 4 years in 2015-2018. The final result will be an Electronic Database and online Interactive Sky map to be used for further research projects. ArVO will provide all standards and tools for efficient usage of the scientific output and its integration in international databases.

MHD Heat and Mass Transfer of Chemical Reaction Fluid Flow over a Moving Vertical Plate in Presence of Heat Source with Convective Surface Boundary Condition

Directory of Open Access Journals (Sweden)

B. R. Rout

2013-01-01

Full Text Available This paper aims to investigate the influence of chemical reaction and the combined effects of internal heat generation and a convective boundary condition on the laminar boundary layer MHD heat and mass transfer flow over a moving vertical flat plate. The lower surface of the plate is in contact with a hot fluid while the stream of cold fluid flows over the upper surface with heat source and chemical reaction. The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. The effects of physical parameters on the velocity, temperature, and concentration profiles are illustrated graphically. A table recording the values of skin friction, heat transfer, and mass transfer at the plate is also presented. The discussion focuses on the physical interpretation of the results as well as their comparison with previous studies which shows good agreement as a special case of the problem.

Modification of the Hottel-Whillier-Bliss equation for cover absorption effects in solar collectors

Energy Technology Data Exchange (ETDEWEB)

Wijeysundera, N E

1981-01-01

The effects of solar radiation absorption and the thermal resistance of a solar collector cover system on the various factors which occur in the Hottel-Whillier-Bliss (HWB) equation are considered. It is shown that by extending the thermal network analogy to systems with distributed heat sources, the heat transfer analysis of the collector can be done with little computational effort. The analysis also leads to a simple form of the HWB equation, with additional factors to account for the source distribution and the thermal resistance of the cover system, and it is applicable to conventional flat plate collectors and to other thermal trap collectors. A series of calculations for multilayer systems is presented to show the relative importance of the various factors in the modified HWB equation for different cover configurations.

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

KAUST Repository

Saghir, S.

2016-06-16

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

KAUST Repository

Saghir, Shahid; Younis, Mohammad I.

2016-01-01

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.

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Gain stabilized microchannel plates and a treatment method for microchannel plates

International Nuclear Information System (INIS)

1979-01-01

Microchannel plates having increased gain and significantly improved aging characteristics are provided by forming a thin film of a cesium compound on the channel walls. In an exemplary embodiment, a suface film of cesium hydroxide is applied to the interior wall surfaces of an MCP by saturating the plate with a solution of the compound, then allowing the solvent to evaporate. The cesium hydroxide residue on the walls subsequently is converted to cesium oxide by a high temperature bake. Microchannel plates are used in image amplifiers, radiation detectors and such like equipment. (Auth.)

Bottom nozzle for nuclear reactor fuel assembly having an adaptor plate and a coupled filtration plate

International Nuclear Information System (INIS)

Verdier, M.; Mortgat, R.

1992-01-01

The bottom nozzle includes an adaptor plate with openings to allow the passage of water and a filtration plate with small holes. The openings in the adaptor plate are symmetrical with regard to medians and diagonals. Within each zone, some of the openings are rectangular and some may be circular. The small holes in the filtration plate coincide with the rectangular openings in the adaptor plate

Determination of group velocity of propagation of Lamb waves in aluminium plate using piezoelectric transducers

Directory of Open Access Journals (Sweden)

Lašová Z.

2017-06-01

Full Text Available A prior knowledge of group velocities of Lamb wave modes is a key for analysis of time signals in guidedwave based structural health monitoring. The identification of multiple wave modes may be complicated due to dependency of group velocity on frequency (dispersion. These dependencies for infinite plate of constant thickness can be calculated by a numerical solution of analytic equation. Two alternative approaches to determine group velocities of zero-order Lamb wave modes in aluminum plate were used in this work: Two-dimensional Fast Fourier Transform (2D-FFT and methods of time-frequency processing. 2D-FFT requires a high number of time signals in equidistant points, therefore it was applied on data from finite element analysis of wave propagation in the plate. Group velocities for chosen frequencies were also determined using wavelet transform (WT of signals as differencies of times of arrival measured by a pair of piezoelectric transducers. The results from 2D-FFT and wavelet transform were compared to the analytic solution.

Scintillating plate calorimeter optical design

International Nuclear Information System (INIS)

McNeil, R.; Fazely, A.; Gunasingha, R.; Imlay, R.; Lim, J.

1990-01-01

A major technical challenge facing the builder of a general purpose detector for the SSC is to achieve an optimum design for the calorimeter. Because of its fast response and good energy resolution, scintillating plate sampling calorimeters should be considered as a possible technology option. The work of the Scintillating Plate Calorimeter Collaboration is focused on compensating plate calorimeters. Based on experimental and simulation studies, it is expected that a sampling calorimeter with alternating layers of high-Z absorber (Pb, W, DU, etc.) and plastic scintillator can be made compensating (e/h = 1.00) by suitable choice of the ratio of absorber/scintillator thickness. Two conceptual designs have been pursued by this subsystem collaboration. One is based on lead as the absorber, with read/out of the scintillator plates via wavelength shifter fibers. The other design is based on depleted uranium as the absorber with wavelength shifter (WLS) plate readout. Progress on designs for the optical readout of a compensating scintillator plate calorimeter are presented. These designs include readout of the scintillator plates via wavelength shifter plates or fiber readout. Results from radiation damage studies of the optical components are presented

HEAT AND MASS TRANSFER EFFECTS ON FLOW PAST PARABOLIC STARTING MOTION OF ISOTHERMAL VERTICAL PLATE IN THE PRESENCE OF FIRST ORDER CHEMICAL REACTION

Directory of Open Access Journals (Sweden)

R. Muthucumaraswamy

2013-06-01

Full Text Available An exact solution of unsteady flow past a parabolic starting motion of the infinite isothermal vertical plate with uniform mass diffusion, in the presence of a homogeneous chemical reaction of the first order, has been studied. The plate temperature and the concentration level near the plate are raised uniformly. The dimensionless governing equations are solved using the Laplace transform technique. The effect of velocity profiles are studied for different physical parameters, such as chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, and time. It is observed that velocity increases with increasing values of thermal Grashof number or mass Grashof number. The trend is reversed with respect to the chemical reaction parameter.

A similar solution for an unsteady free convection flow past an impulsively started vertical plate with mass transfer and suction or injection

International Nuclear Information System (INIS)

Sattar, M.A.

1990-12-01

A similar solution for the flow past a vertical plate started impulsively in its own plane in a viscous incompressible fluid is presented on taking into account the effects of variable suction and/or injection and mass transfer. To solve the momentum, energy and concentration equations, a time dependent length scale is introduced, which leads to the driving parameters γ(=G r /R σ 2 ) and γ*(=G r */R σ 2 ), where G r and G r * are respectively the Grashof and modified Grashof numbers while R σ is the Reynolds number. The resulting locally similar momentum equation is then solved by the method of superposition. The effects of the parameters and that of suction/injection on the flow and on the wall shear-stress of the plate are shown graphically for different values of Schmidt number and transpiration parameter. (author). 24 refs, 11 figs

Study of uranium plating measurement

International Nuclear Information System (INIS)

Lin Jufang; Wen Zhongwei; Wang Mei; Wang Dalun; Liu Rong; Jiang Li; Lu Xinxin

2007-06-01

In neutron physics experiments, the measurement for plate-thickness of uranium can directly affect uncertainties of experiment results. To measure the plate-thickness of transform target (enriched uranium plating and depleted uranium plating), the back to back ionization chamber, small solid angle device and Au-Si surface barrier semi-conductor, were used in the experiment study. Also, the uncertainties in the experiment were analyzed. Because the inhomo-geneous of uranium lay of plate can quantitively affect the result, the homogeneity of uranium lay is checked, the experiment result reflects the homogeneity of uranium lay is good. (authors)

Countercurrent air/water and steam/water flow above a perforated plate. Report for October 1978-October 1979

International Nuclear Information System (INIS)

Hsieh, C.; Bankoff, S.G.; Tankin, R.S.; Yuen, M.C.

1980-11-01

The perforated plate weeping phenomena have been studied in both air/water and steam/cold water systems. The air/water experiment is designed to investigate the effect of geometric factors of the perforated plate on the rate of weeping. A new dimensionless flow rate in the form of H star is suggested. The data obtained are successfully correlated by this H star scaling in the conventional flooding equation. The steam/cold water experiment is concentrated on locating the boundary between weeping and no weeping. The effects of water subcooling, water inlet flow rate, and position of water spray are investigated. Depending on the combination of these factors, several types of weeping were observed. The data obtained at high water spray position can be related to the air/water flooding correlation by replacing the stream flow rate to an effective stream flow rate, which is determined by the mixing efficiency above the plate

Comparison of Thermal Performances between Low Porosity Perforate Plate and Flat Plate Solar Air Collector

Science.gov (United States)

Chan, Hoy-Yen; Vinson, A. A.; Baljit, S. S. S.; Ruslan, M. H.

2018-04-01

Flat plate solar air collector is the most common collector design, which is relatively simpler to fabricate and lower cost. In the present study, perforated plate solar collector was developed to improve the system thermal performance. A glazed perforated plate of 6mm holes diameter with square geometry was designed and installed as the absorber of the collector. The influences of solar radiation intensity and mass flow rate on the thermal performance were investigated. The perforated collector was compared with the flat plate solar collector under the same operating conditions. The highest values of thermal efficiency in this study for the perforated plate (PP) and the flat plate (FP) solar collectors were 59% and 36% respectively, at solar radiation intensity of 846 Wm-2 and mass flow rate of 0.02 kgs-1. Furthermore, PP collector gave better thermal performance compared to FP collector; and compared to previous studies, the present perforated design was compatible with the flat plate with double pass designs.

Assessment of Real Heat Transfer Coefficients through Shell and Tube and Plate Heat Exchangers

Directory of Open Access Journals (Sweden)

Dan CONSTANTINESCU

2011-07-01

Full Text Available The purpose of this paper is to present a procedure used in the assessment of the real heat transfer characteristic of shell and tube and plate heat exchangers. The theoretical fundamentals of the procedure are introduced as well as the measured data collection and processing. The theoretical analysis is focused on the adoption of criterial equations which, subjected to certain verification criteria presented in the paper, provide the most credible value of the convection heat transfer coefficients inside the circular and flat tubes. In the end two case studies are presented, one concerning a shell and tube heat exchanger operational at INCERC Thermal Substation and the other concerning a plate heat exchanger tested on the Laboratory Stand of the Department of Building Services and Efficient Use of Energy in Buildings of INCERC Bucharest.

Control design and robustness analysis of a ball and plate system by using polynomial chaos

Energy Technology Data Exchange (ETDEWEB)

Colón, Diego [University of São Paulo, Polytechnic School, LAC -PTC, São Paulo (Brazil); Balthazar, José M. [São Paulo State University - Rio Claro Campus, Rio Claro (Brazil); Reis, Célia A. dos [São Paulo State University - Bauru Campus, Bauru (Brazil); Bueno, Átila M.; Diniz, Ivando S. [São Paulo State University - Sorocaba Campus, Sorocaba (Brazil); Rosa, Suelia de S. R. F. [University of Brasilia, Brasilia (Brazil)

2014-12-10

In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.

A numerical and analytical investigation of Rayleigh-Taylor instability in a solid tungsten plate

International Nuclear Information System (INIS)

Robinson, A.C.; Swegle, J.W.

1987-07-01

The Rayleigh-Taylor instability response of an elastic-plastic tungsten plate is investigated by numerical experiments and an approximate modal analysis. The so-called ''minimum amplitude'' instability criteria derived from plasticity analyses is shown to be incomplete as a general indicator of instability or stability at very large driving pressures. Model equations are derived which are able to reproduce the basic qualitative features of the observed instability response given by the numerical calculations. 11 refs., 29 figs

Theoretical and experimental investigation of wickless heat pipes flat plate solar collector with cross flow heat exchanger

International Nuclear Information System (INIS)

Hussein, H.M.S.

2007-01-01

In this work, a wickless heat pipes flat plate solar collector with a cross flow heat exchanger was investigated theoretically and experimentally under the meteorological conditions of Cairo, Egypt. The author's earlier simulation program of wickless heat pipes flat plate solar water heaters was modified to be valid for the present type of wickless heat pipes solar collector by including the solution of the dimensionless governing equations of the present analysis. For verifying the modified simulation program, a wickless heat pipes flat plate solar collector with a cross flow heat exchanger was designed, constructed, and tested at different meteorological conditions and operating parameters. These parameters include different cooling water mass flow rates and different inlet cooling water temperatures. The comparison between the experimental results and their corresponding simulated ones showed considerable agreement. Under different climatic conditions, the experimental and theoretical results showed that the optimal mass flow rate is very close to the ASHRAE standard mass flow rate for testing conventional flat plate solar collectors. Also, the experimental and theoretical results indicated that the number of wickless heat pipes has a significant effect on the collector efficiency

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.

Science.gov (United States)

Tuan, P H; Wen, C P; Chiang, P Y; Yu, Y T; Liang, H C; Huang, K F; Chen, Y F

2015-04-01

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

Earth's Decelerating Tectonic Plates

Energy Technology Data Exchange (ETDEWEB)

Forte, A M; Moucha, R; Rowley, D B; Quere, S; Mitrovica, J X; Simmons, N A; Grand, S P

2008-08-22

Space geodetic and oceanic magnetic anomaly constraints on tectonic plate motions are employed to determine a new global map of present-day rates of change of plate velocities. This map shows that Earth's largest plate, the Pacific, is presently decelerating along with several other plates in the Pacific and Indo-Atlantic hemispheres. These plate decelerations contribute to an overall, globally averaged slowdown in tectonic plate speeds. The map of plate decelerations provides new and unique constraints on the dynamics of time-dependent convection in Earth's mantle. We employ a recently developed convection model constrained by seismic, geodynamic and mineral physics data to show that time-dependent changes in mantle buoyancy forces can explain the deceleration of the major plates in the Pacific and Indo-Atlantic hemispheres.

Interpretation of moving EM dipole-dipole measurements using thin plate models

International Nuclear Information System (INIS)

Oksama, M.; Suppala, I.

1998-01-01

The three dimensional inversion of electromagnetic data is still rather problematic, because forward modelling programs are usually time consuming. They are based on numerical methods like finite element or integral equation methods. In the study a specific model for interpretation: two thin plates, which are located in a horizontally layered earth with two layers has been chosen. The model is rather limited, but in a few geological cases it is relevant. This interpretation method has been applied for two geophysical EM-systems, the slingram-system and the airborne electromagnetic system of the Geological Survey of Finland (GTK)

Interpretation of moving EM dipole-dipole measurements using thin plate models

Energy Technology Data Exchange (ETDEWEB)

Oksama, M.; Suppala, I. [Geological Survey of Finland, Espoo (Finland)

1998-09-01

The three dimensional inversion of electromagnetic data is still rather problematic, because forward modelling programs are usually time consuming. They are based on numerical methods like finite element or integral equation methods. In the study a specific model for interpretation: two thin plates, which are located in a horizontally layered earth with two layers has been chosen. The model is rather limited, but in a few geological cases it is relevant. This interpretation method has been applied for two geophysical EM-systems, the slingram-system and the airborne electromagnetic system of the Geological Survey of Finland (GTK) 5 refs.

Aerodynamics of the cable of cable-stayed bridges; Shachokyo cable no kuriki shindo tokusei no rikai to soreni motozuku kuriki seishinho no teian

Energy Technology Data Exchange (ETDEWEB)

Matsumoto, M. [Kyoto University, Kyoto (Japan). Faculty of Engineering; Aoki, J.; Fuji, D. [West Japan Railway Company, Osaka (Japan); Kitayama, N. [Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo (Japan); Daito, Y. [Kyoto University, Kyoto (Japan)

1996-07-21

Wind tunnel tests were conducted assuming the aerodynamics of the cable of cable-stayed bridges especially in the case of strong wind with rain. Based on the results, an aerodynamic damping method was proposed. Factors of the rain vibration generation include the three-dimensional axial flow behind the cable, which is formed by the wind direction deviation angle, the upper side water flow on the cable surface formed by the rain, and the Karman vortex shedding, which are not uniform in the span direction. Newly proposed cable with elliptical plates showed an effective dumping performance. It restrains the formation of water flow due to its profile, and is effective for unstableness due to water flow formation. Distribution of the axial flow in the cable span direction was made clear. Three-dimensionality of the vortex shedding was greatly affected by this axial flow. Frequency of the Karman vortex shedding changed in the wide band by the axial flow. It was suggested that three-dimensionality of the flow field is enhanced by the rolling vibration, resulting in the unstableness of heaving vibration. 5 refs., 15 figs.

THERMAL PERFORMANCE OF FLAT PLATE SOLAR COLLECTOR

Directory of Open Access Journals (Sweden)

TABET I.

2017-06-01

Full Text Available In this paper, a theoretical and experimental studyof flat platesolar water collector with reflectors.A mathematical model based on energy balance equations saw the thermal behavior of the collector is investigated. The experimental test was made at the unit research applies in renewable energy (URAER located in southern Algeria.An increase of 23% for solar radiation incident on the collector surface with the addition of the planers reflectors in the day of May, this increase causes an improvement of the performance of the collector,the fluid temperature increases with an average of 5%. Thetests conducted on the flat plate solar water collector in open circuit enabled the determination of thermal performance of the collector by estimating the daily output The thermal efficiency of the collector ranges from 1% -63% during the day, a mean value of 36%obtained.

Comparison of skeletal stability after sagittal split ramus osteotomy among mono-cortical plate fixation, bi-cortical plate fixation, and hybrid fixation using absorbable plates and screws.

Science.gov (United States)

Ueki, Koichiro; Moroi, Akinori; Yoshizawa, Kunio; Hotta, Asami; Tsutsui, Takamitsu; Fukaya, Kenichi; Hiraide, Ryota; Takayama, Akihiro; Tsunoda, Tatsuta; Saito, Yuki

2017-02-01

The purpose of this study was to examine skeletal stability and plate breakage after sagittal split ramus osteotomy (SSRO) with the mono-cortical plate fixation, bi-cortical plate fixation, and hybrid fixation techniques using absorbable plates and screws. A total of 76 Japanese patients diagnosed with mandibular prognathism with and without maxillary deformity were divided into 3 groups randomly. A total of 28 patients underwent SSRO with mono-cortical plate fixation, 23 underwent SSRO with bi-cortical plate fixation, and 25 underwent SSRO with hybrid fixation. Skeletal stability and horizontal condylar angle were analyzed by axial, frontal, and lateral cephalograms from before the operation to 1 year postoperatively. Breakage of the plate and screws was observed by 3-dimensional computed tomography (3DCT) immediately after surgery and after 1 year. Although there was a significant difference between the mono-cortical plate fixation group and hybrid fixation group regarding right MeAg in T1 (P = 0.0488) and occlusal plane in T1 (P = 0.0346), there were no significant differences between the groups for the other measurements in each time interval. In 2 cases, namely, 6 sides in the mono-cortical plate fixation group, breakage of the absorbable plate was found by 3DCT. However, there was no breakage in the bi-cortical plate fixation group and hybrid fixation group. This study results suggested that there were no significant differences in the postoperative skeletal stability among the 3 groups, and bi-cortical fixation as well as hybrid fixation was a reliable and useful method to prevent plate breakage even if an absorbable material was used. Copyright © 2016 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

Limit load and fully plastic stress analysis for circular notched plates and bars using fully plastic analysis

International Nuclear Information System (INIS)

Oh, Chang Kyun; Myung, Man Sik; Kim, Yun Jae; Park, Jin Moo

2005-01-01

For the last four decades, tension test of notched bars has been performed to investigate the effect of stress triaxiality on ductile fracture. To quantify the effect of the notch radius on stress triaxiality, the Bridgman equation is typically used. However, recent works based on detailed finite element analysis have shown that the Bridgman equation is not correct, possibly due to his assumption that strain is constant in the necked ligament. Up to present, no systematic work has been performed on fully plastic stress fields for notched bars in tension. This paper presents fully plastic results for tension of notched bars and plates in plane strain, via finite element limit analysis. The notch radius is systematically varied, covering both un-cracked and cracked cases. Comparison of plastic limit loads with existing solutions shows that existing solutions are accurate for notched plates, but not for notched bars. Accordingly new limit load solutions are given for notched bars. Variations of stress triaxiality with the notch radius and depth are also given, which again indicates that the Bridgman solution for notched bars is not correct and inaccuracy depends on the notch radius and depth

Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating.

Science.gov (United States)

Hussanan, Abid; Zuki Salleh, Mohd; Tahar, Razman Mat; Khan, Ilyas

2014-01-01

In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.

Create Your Plate

Medline Plus

Full Text Available ... ready, you can try new foods within each food category. Try these seven steps to get started: Using your dinner plate, put a line down the middle of the plate. Then on one side, cut it ... and starchy foods. See this list of grains and starchy foods . ...

Development of a finite-element-based design sensitivity analysis for buckling and postbuckling of composite plates

Directory of Open Access Journals (Sweden)

Guo Ruijiang

1995-01-01

Full Text Available A finite element based sensitivity analysis procedure is developed for buckling and postbuckling of composite plates. This procedure is based on the direct differentiation approach combined with the reference volume concept. Linear elastic material model and nonlinear geometric relations are used. The sensitivity analysis technique results in a set of linear algebraic equations which are easy to solve. The procedure developed provides the sensitivity derivatives directly from the current load and responses by solving the set of linear equations. Numerical results are presented and are compared with those obtained using finite difference technique. The results show good agreement except at points near critical buckling load where discontinuities occur. The procedure is very efficient computationally.

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

Indonesian Landforms and Plate Tectonics

Directory of Open Access Journals (Sweden)

Herman Th. Verstappen

2014-06-01

Full Text Available DOI: 10.17014/ijog.v5i3.103The horizontal configuration and vertical dimension of the landforms occurring in the tectonically unstable parts of Indonesia were resulted in the first place from plate tectonics. Most of them date from the Quaternary and endogenous forces are ongoing. Three major plates – the northward moving Indo-Australian Plate, the south-eastward moving SE-Asian Plate and the westward moving Pacific Plate - meet at a plate triple-junction situated in the south of New Guinea’s Bird’s Head. The narrow North-Moluccan plate is interposed between the Asia and Pacific. It tapers out northward in the Philippine Mobile Belt and is gradually disappearing. The greatest relief amplitudes occur near the plate boundaries: deep ocean trenches are associated with subduction zones and mountain ranges with collision belts. The landforms of the more stable areas of the plates date back to a more remote past and, where emerged, have a more subdued relief that is in the first place related to the resistance of the rocks to humid tropical weathering Rising mountain ranges and emerging island arcs are subjected to rapid humid-tropical river erosions and mass movements. The erosion products accumulate in adjacent sedimentary basins where their increasing weight causes subsidence by gravity and isostatic compensations. Living and raised coral reefs, volcanoes, and fault scarps are important geomorphic indicators of active plate tectonics. Compartmental faults may strongly affect island arcs stretching perpendicular to the plate movement. This is the case on Java. Transcurrent faults and related pull-apart basins are a leading factor where plates meet at an angle, such as on Sumatra. The most complicated situation exists near the triple-junction and in the Moluccas. Modern research methods, such as GPS measurements of plate movements and absolute dating of volcanic outbursts and raised coral reefs are important tools. The mega-landforms resulting

Application of a Brittle Damage Model to Normal Plate-on-Plate Impact

National Research Council Canada - National Science Library

Raftenberg, Martin N

2005-01-01

A brittle damage model presented by Grinfeld and Wright of the U.S. Army Research Laboratory was implemented in the LS-DYNA finite element code and applied to the simulation of normal plate-on-plate impact...

Heat and Mass Transfer on Squeezing Unsteady MHD Nano fluid Flow between Parallel Plates with Slip Velocity Effect

International Nuclear Information System (INIS)

Singh, K.; Rawat, S. K.; Kumar, M.

2016-01-01

Heat and mass transfer behavior of unsteady flow of squeezing between two parallel plates in the sight of uniform magnetic field with slip velocity effect is investigated. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformation. The equations thus obtained have been solved numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity, temperature, and concentration for various values of relevant parameters are illustrated graphically. The skin-friction coefficient and heat and mass transfer rate are also tabulated for various governing parameters. The results indicate that, for nano fluid flow, the rates of heat and mass transfer are inversely proportional to nanoparticle volume fraction and magnetic parameter. The rate of mass transfer increases with increasing values of Schmidt number and squeeze number.

[Experimental study on carbon fiber reinforced plastic plate--analysis of stabilizing force required for plate].

Science.gov (United States)

Iizuka, H

1990-11-01

Plates currently in use for the management of bone fracture made of metal present with various problems. We manufactured carbon fiber reinforced plastic (CFRP) plates from Pyrofil T/530 puriplegs overlaid at cross angles of +/- 10 degrees, +/- 20 degrees, and +/- 30 degrees for trial and carried out an experimental study on rabbit tibiofibular bones using 316L stainless steel plates of comparable shape and size as controls. The results indicate the influence of CFRP plate upon cortical bone was milder than that of stainless steel plate, with an adequate stabilizing force for the repair of fractured rabbit tibiofibular bones. CFRP has the advantages over metals of being virtually free from corrosion and fatigue, reasonably radiolucent and able to meet a wide range of mechanical requirements. This would make CFRP plate quite promising as a new devices of treating fracture of bones.

Derivation of finite element formulation for electrochemical governing equations of ionic polymer actuators

International Nuclear Information System (INIS)

Kang, Sung Soo

2013-01-01

Ionic polymer actuators have recently attracted a great deal of interest as electroactive materials with potentials as soft actuators, sensors, artificial muscles, robotics, and microelectromechanical systems because of their numerous advantages, including low voltage requirement, high compliance, lightness, and flexibility. The platinum-plated Nafion, a perfluorosulfonic acid membrane made by Dupont, is commonly used as a polyelectrolyte in actuator applications. The bending of the ionic polymer actuators in an electric field is dominated by the electro-osmosis of hydrated ions and slow diffusion of free water molecules. The changes in hydration cause a local volumetric strain resulting in bending deformation, such as expansion and contraction. In this study, a two-dimensional finite element (FE) formulation based on the Galerkin method is derived for the governing equations describing these electrochemical responses. In addition, a three-dimensional FE deformation analysis is conducted on the bending behaviors of the platinum-plated ionic polymer actuators. Several numerical studies for ionic polymer actuators, such as plates with various electrode arrangements and disk models in electric field, are performed to confirm the validity of the proposed formulation.

Calibrated expressions for welding and their application to isotherm width in a thick plate

Directory of Open Access Journals (Sweden)

Gentry Wood

2014-09-01

Full Text Available The present paper introduces a possible solution to the limitations of modern trial and error solutions to welding procedure development. The difficulties of finding generalized solutions to Rosenthal´s equation are discussed and the Minimal Representation and Calibration approach is introduced as a promising procedure for developing these solutions. Dominant factors are identified, with effects from secondary phenomena being taken into account by correction factors. These correction factors are then calibrated and presented in a form that can be easily computed, and therefore be amendable to industry. The approach is then demonstrated by determining the isotherm width from Rosenthal´s thick plate solution. Comparison of the calibrated scaling equations to Rosenthal´s exact solution showed a maximum error of less than 0.8% for any isotherm.

Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

Science.gov (United States)

Viswanathan, K. K.; Karthik, K.; Sanyasiraju, Y. V. S. S.; Aziz, Z. A.

2016-11-01

Two type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

Evaluation of Using Triangular Plates as Continuity Plates in Box Column Section in Prequalified Welded Connections under Cyclic Loading

Directory of Open Access Journals (Sweden)

Mohammad Ali Kafi

2017-02-01

Full Text Available Welding of Continuity plates in box columns are not easily possible, therefore some researches has been done for substitution of external continuity plates.In this study first discussed about effects of continuity plate in I beam to Box column with top and bottom plate (WFP and welded unreinforced flange-welded web connection (WUF-W and reduced beam section connection (RBS. Then, triangular plates use to in connection beam to box column as continuity plates and to consider under cyclic loading. Studies have shown that existence of continuity plates in connections mentioned above have averagely increased loading capacity, rigidity and energy absorption 63, 86 and 75 percent respectively. The results also showed that using of triangular plates as continuity plates of box columns causing plastic strain in column flange in the area that concentration of materials is not much in triangular plates and increased the probability of failure in weld of plates to the column flange. Also using of triangular plates as continuity plates have not affected on plastic hinge location.

Fundamental processes in ion plating

International Nuclear Information System (INIS)

Mattox, D.M.

1980-01-01

Ion plating is a generic term applied to film deposition processes in which the substrate surface and/or the depositing film is subjected to a flux of high energy particles sufficient to cause changes in the interfacial region of film properties compared to a nonbombarded deposition. Ion plating is being accepted as an alternative coating technique to sputter deposition, vacuum evaporation and electroplating. In order to intelligently choose between the various deposition techniques, the fundamental mechanisms, relating to ion plating, must be understood. This paper reviews the effects of low energy ion bombardment on surfaces, interface formation and film development as they apply to ion plating and the implementation and applications of the ion plating process

Development of neutronics and thermal hydraulics coupled code – SAC-RIT for plate type fuel and its application to reactivity initiated transient analysis

International Nuclear Information System (INIS)

Singh, Tej; Kumar, Jainendra; Mazumdar, Tanay; Raina, V.K.

2013-01-01

Highlights: • A point reactor kinetics code coupled with thermal hydraulics of plate type fuel is developed. • This code is applicable for two phase flow of coolant. • Safety analysis of IAEA benchmark reactor core is carried out. • Results agree well with the results available in literature. - Abstract: A point reactor kinetics code SAC-RIT, acronym of Safety Analysis Code for Reactivity Initiated Transient, coupled with thermal hydraulics of two phase coolant flow for plate type fuel, is developed to calculate reactivity initiated transient analysis of nuclear research and test reactors. Point kinetics equations are solved by fourth order Runge Kutta method. Reactivity feedback effect is included into the code. Solution of kinetics equations gives neutronic power and it is then fed into a thermal hydraulic code where mass, momentum and thermal energy conservation equations are solved by explicit finite difference method to find out fuel, clad and coolant temperatures during transients. In this code, all possible flow regimes including laminar flow, transient flow and turbulent flow have been covered. Various heat transfer coefficients suitable for single liquid, sub-cooled boiling, saturation boiling, film boiling and single vapor phases are incorporated in the thermal hydraulic code

Ultraviolet-light-induced multi-physics behaviors of 0–3 polarized transparent PLZT plates: II. Finite element analysis and validation

International Nuclear Information System (INIS)

Luo, Quantian; Tong, Liyong

2011-01-01

This paper presents a novel finite element formulation for 0–3 polarized PbLaZrTi (PLZT) plates and a comparison of the predicted and measured bending displacements. The coupled multi-physics fields and Hamilton's principle for piezoelectric (PZT) materials are first extended to PLZT ceramics by including the anomalous photovoltaic and photo-thermal effects. The photo-induced non-uniform electrical field and mechanical strains across the thickness are modeled in the present finite element formulation for 0–3 polarized PLZT plates, and the associated actuator and sensor equations are derived. The transverse displacements of a 0–3 polarized PLZT plate are predicted using the present finite element formulation and compared with the measured data given in part I. A reasonably good correlation is noted for the transverse displacements at the ten measurement points

Free Vibration Analysis of a Spinning Flexible DISK-SPINDLE System Supported by Ball Bearing and Flexible Shaft Using the Finite Element Method and Substructure Synthesis

Science.gov (United States)

JANG, G. H.; LEE, S. H.; JUNG, M. S.

2002-03-01

Free vibration of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft is analyzed by using Hamilton's principle, FEM and substructure synthesis. The spinning disk is described by using the Kirchhoff plate theory and von Karman non-linear strain. The rotating spindle and stationary shaft are modelled by Rayleigh beam and Euler beam respectively. Using Hamilton's principle and including the rigid body translation and tilting motion, partial differential equations of motion of the spinning flexible disk and spindle are derived consistently to satisfy the geometric compatibility in the internal boundary between substructures. FEM is used to discretize the derived governing equations, and substructure synthesis is introduced to assemble each component of the disk-spindle-bearing-shaft system. The developed method is applied to the spindle system of a computer hard disk drive with three disks, and modal testing is performed to verify the simulation results. The simulation result agrees very well with the experimental one. This research investigates critical design parameters in an HDD spindle system, i.e., the non-linearity of a spinning disk and the flexibility and boundary condition of a stationary shaft, to predict the free vibration characteristics accurately. The proposed method may be effectively applied to predict the vibration characteristics of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft in the various forms of computer storage device, i.e., FDD, CD, HDD and DVD.

Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

Science.gov (United States)

Shamshuddin, MD.; Anwar Bég, O.; Sunder Ram, M.; Kadir, A.

2018-02-01

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic, incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted.

Effect of Surface Texturing Parameters on the Lubrication Characteristics of an Axial Piston Pump Valve Plate

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Zhaoqiang Wang

2018-05-01

Full Text Available In this article, a geometrical model of different microtextures is established for an axial piston pump valve plate. A finite differential method was used to solve the Reynolds equation for the oil film thickness and pressure, which were simulated under different microtextures. The influence of microtexture shape and structure on performance was studied and optimal parameters sought. Different convergence gaps are formed by different microtexture radii, and they produce different hydrodynamic effects. The lubrication characteristics of the valve plate are better when a microtexture is used and are influenced by the type of microtexture. We reached the following conclusions: (1 The lubrication characteristics of the valve plate are influenced by different microtexture parameters and can be improved by optimizing the microtexture parameters; (2 There is an optimal parameter combination when adding microtexture with three shapes (spherical, cylindrical and square and the optimal dimensionless oil film pressure lubrication characteristics can be obtained; (3 The degree of improvement in the dimensionless oil film pressure lubrication characteristics was (listed from highest to lowest: micro-hemispherical texture > micro-cylindrical texture > micro-square texture.

Mandibular reconstruction using a titanium plate: the impact of radiation therapy on plate preservation

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Ryu, Janice K; Stern, Robin L; Robinson, Marilyn G; Bowers, Michael K; Kubo, Hideo D; Donald, Paul J; Rosenthal, Seth A; Fu, Karen K

1995-06-15

Purpose: To evaluate the soft tissue and bone tolerance of radiation therapy (RT) in patients undergoing radical composite resection and mandibular reconstruction using a bridging titanium plate with myocutaneous flap closure. Methods and Materials: From 1990 to 1994, 47 patients with primary or recurrent oral cavity or oropharyngeal carcinomas were treated with radical composite resection and mandibular reconstruction using a bridging titanium plate with myocutaneous flap closure. Eleven patients received no RT (no RT), 10 patients received RT greater than 10 months from the time of surgery (remote RT), and 26 patients received RT within 12 weeks of surgery (perioperative RT). The radiation dose to the reconstructed mandible ranged from 45 to 75 Gy (median 63 Gy). The effect of the titanium plate on the radiation dose was measured using film dosimetry and soft tissue and bone-equivalent materials. The median follow-up was 17 months (range: 3-50 months). Results: Late complications included four patients with osteomyelitis or necrosis, two plate exposures requiring flap revision, one chronic infection, two cases of chronic pain, two fistulae, and one case of trismus and malocclusion. The crude incidence of late complications by treatment was: (a) no RT: 3 of 11 patients (27%); (b) remote RT: 2 of 10 patients (20%); and (c) perioperative RT: 9 of 26 patients (35%). One patient in the no-RT group lost the plate due to chronic pain. Five patients in the perioperative RT group also had plate loss, four due to osteomyelitis and/or necrosis, and one due to pain related to a recurrent tumor. No patients in the remote RT group had plate loss. The actuarial prosthesis preservation rate at 2 years was 88% for the no RT, 100% for the remote RT, and 57% for the perioperative RT groups (p = 0.05). Phantom dose measurements showed that for parallel opposed 6 MV photon beams, there was no significant increase in the dose proximal or distal to the plate in either a soft tissue- or

[Comparison of novel infrared heating plates and conventional warm water plates for piglets' creep areas in farrowing pens].

Science.gov (United States)

Strauch-Sürken, L; Wendt, M

2015-01-01

On a conventionally managed piglet-producing farm, novel infrared (IR) heating plates for piglets in the farrowing pens were tested for their suitability and compared with common warm-water (WW) heating plates. In total, 134 litters (summer n = 82, winter n = 52) were investigated, which were housed on IR or WW heating plates, respectively, with or without an extra cover plate (groups 1-4). To determine the influence of the different heat sources, the wound healing after castration and tail docking, the umbilical regression and the weight gain of the piglets were investigated. Additionally, the lying behavior of the piglets and the position of the sows' udder at the time of farrowing were examined with regard to the heating plates. Furthermore, the energy consumption and costs were compared. The piglets housed on IR heating plates displayed better wound healing after castration and tail docking than the piglets housed on WW plates. The best results were obtained in piglets kept on IR heating plates with an extra cover plate. In addition, significant benefits were demonstrated for the usage of IR heating plates regarding umbilical regression. The piglets kept on IR heating plates had a slightly better weight gain in summer, whereas there were no differences between groups during winter. The lying behavior in the creep areas was similar in all groups. In general, with increasing age the percentage of time piglets spent in the lying position on the plates decreased. The percentage of time lying on the plates was higher in winter than in summer. At farrowing, 74.6% of all investigated sows directed their udder towards the heating plates. With the IR heating plates, this behavior occurred significantly more often. The energy consumption (kWh) per litter was significantly lower for the IR heating plates (electric power) both in winter and summer in comparison with the WW plates (gas). The energy costs were comparable in summer, but were higher for the IR heating plates