Free vibrations of circular cylindrical shells
Armenàkas, Anthony E; Herrmann, George
2013-01-01
Free Vibrations of Circular Cylindrical Shells deals with thin-walled structures that undergo dynamic loads application, thereby resulting in some vibrations. Part I discusses the treatment of problems associated with the propagation of plane harmonic waves in a hollow circular cylinder. In such search for solutions, the text employs the framework of the three-dimensional theory of elasticity. The text explains the use of tables of natural frequencies and graphs of representative mode shapes of harmonic elastic waves bounding in an infinitely long isotropic hollow cylinder. The tables are
Natural frequency of a circular cylindrical shell filled with fluid
Jeong, Kyeong Hoon; Kim, Tae Wan; Kim, Kang Soo; Park, Keun Bae [Korea Atomic Energy Research Institute, Taejon (Korea)
1998-08-01
This report presents an analytical method for evaluating the free vibration of a circular cylindrical shell filled with bounded compressible fluid. The analytical method was developed by means of the finite Fourier series expansion method. The compressible fluid motion was determined by means of the linear velocity potential theory. To clarify the validity of the analytical method, the natural frequencies of a circular cylindrical shell with the clamped-clamped boundary condition, and filled with water, were obtained by the analytical method and the finite element method using a commercial ANSYS 5.2 software. Excellent agreement on the natural frequencies of the fluid-filled shell structure was found. The compressibility and density of fluid effects the normalized coupled natural frequencies were investigated. The density of fluid affects on all coupled natural frequencies of the shell,, whereas the compressibility and bounding of fluid affects mainly on the natural frequencies of lower circumferential modes. The theory developed in this report will be applicable to the dynamic analysis of a core support barrel in SMART integral reactor filled with coolant. (author). 15 refs., 14 figs., 1 tab.
Vibrations of cantilevered circular cylindrical shells Shallow versus deep shell theory
Lee, J. K.; Leissa, A. W.; Wang, A. J.
1983-01-01
Free vibrations of cantilevered circular cylindrical shells having rectangular planforms are studied in this paper by means of the Ritz method. The deep shell theory of Novozhilov and Goldenveizer is used and compared with the usual shallow shell theory for a wide range of shell parameters. A thorough convergence study is presented along with comparisons to previously published finite element solutions and experimental results. Accurately computed frequency parameters and mode shapes for various shell configurations are presented. The present paper appears to be the first comprehensive study presenting rigorous comparisons between the two shell theories in dealing with free vibrations of cantilevered cylindrical shells.
Internal resonance of axially moving laminated circular cylindrical shells
Wang, Yan Qing; Liang, Li; Guo, Xing Hui
2013-11-01
The nonlinear vibrations of a thin, elastic, laminated composite circular cylindrical shell, moving in axial direction and having an internal resonance, are investigated in this study. Nonlinearities due to large-amplitude shell motion are considered by using Donnell's nonlinear shallow-shell theory, with consideration of the effect of viscous structure damping. Differently from conventional Donnell's nonlinear shallow-shell equations, an improved nonlinear model without employing Airy stress function is developed to study the nonlinear dynamics of thin shells. The system is discretized by Galerkin's method while a model involving four degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the nonlinear dynamic responses of the multi-degrees-of-freedom system. When the structure is excited close to a resonant frequency, very intricate frequency-response curves are obtained, which show strong modal interactions and one-to-one-to-one-to-one internal resonance phenomenon. The effects of different parameters on the complex dynamic response are investigated in this study. The stability of steady-state solutions is also analyzed in detail.
Simplified dispersion curves for circular cylindrical shells using shallow shell theory
Sarkar, Abhijit; Sonti, Venkata R.
2009-04-01
An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.
Nonlinear vibrations of fluid-filled clamped circular cylindrical shells
Karagiozis, K. N.; Amabili, M.; Païdoussis, M. P.; Misra, A. K.
2005-12-01
In this study, the nonlinear vibrations are investigated of circular cylindrical shells, empty or fluid-filled, clamped at both ends and subjected to a radial harmonic force excitation. Two different theoretical models are developed. In the first model, the standard form of the Donnell's nonlinear shallow-shell equations is used; in the second, the equations of motion are derived by a variational approach which permits the inclusion of constraining springs at the shell extremities and taking in-plane inertial terms into account. In both cases, the solution includes both driven and companion modes, thus allowing for a travelling wave in the circumferential direction; they also include axisymmetric modes to capture the nonlinear inward shell contraction and the correct type (softening) nonlinear behaviour observed in experiments. In the first model, the clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions, leading to a 7 degree-of-freedom (dof) expansion for the solution. In the second model, rotational springs are used at the ends of the shell, which when large enough reproduce a clamped end; the solution involves a sine series for axial variations of the shell deformation, leading to a 54 dof expansion for the solution. In both cases the modal expansions satisfy the boundary conditions and the circumferential continuity condition exactly. The Galerkin method is used to discretize the equations of motion, and AUTO to integrate the discretized equations numerically. When the shells are fluid-filled, the fluid is assumed to be incompressible and inviscid, and the fluid structure interaction is described by linear potential flow theory. The results from the two theoretical models are compared with existing experimental data, and in all cases good qualitative and quantitative agreement is observed.
Crack detection in circular cylindrical shells using differential quadrature method
The differential quadrature method combined with an evolutionary optimization algorithm has been proposed for crack detection in cylindrical shell structures. The circumferential crack, which is assumed to be open, is modeled by the extended rotational spring. A crack with finite length divides the shell into four segments. The governing differential equations of motion of the shell are formulated based on Flugge's shell theory. Applying differential quadrature to the differential equations of each segment and the corresponding boundary and continuity conditions results in an algebraic system of equations. Then, an eigenvalue analysis is performed to obtain the natural frequencies of the cracked shell. To identify the crack parameters, an optimization problem is defined and minimized by Bees algorithm, a swarm-based evolutionary optimization technique. The integrity and applicability of the proposed method is confirmed by some experimental case studies. The results show that the crack statuses are predicted well. -- Highlights: • The problem of crack detection in cylindrical shell structures is investigated. • To do this, the differential quadrature method and bees algorithm has been used. • Numerical and experimental studies on the cracked free–free shells were conducted. • The results showed that the crack locations, sizes and depths were predicted well
Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells
Nemeth, Michael P.; Smeltzer, Stanley S., III
2000-01-01
A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.
2008-01-01
The effect of matrix cracking on the bifurcation creep buckling of viscoelastic laminated circular cylindrical shells is investigated.The viscoelastic behavior of laminas is modeled by Schapery’s integral constitutive equation with growing matrix cracks.The values of damage variables are correlated to non-dimensional density of matrix cracks relying on the formulas from mesomechanics approach,and the evolution equation predicting the growth rate of density of matrix cracks is assumed to follow a power type relation with transverse tensile stress.The governing equations for prebuckling creep deformation and bifurcation buckling of laminated circular cylindrical shells under axial compression are obtained on the basis of the Donnell type shallow shell theory and Kármán-Donnell geometrically nonlinear relationship.Corresponding solution strategy is constructed by integrating finite-difference technique,trigonometric series expansion method and Taylor’s numerical recursive scheme for convolution integration.The bifurcation creep buckling of symmetrically laminated glass-epoxy circular cylindrical shells with matrix creep cracking coupled are examined for various geometrical parameters and parameters of damage evolution as well as boundary conditions.The numerical results show that matrix creep cracking remarkably shortens the critic time of bifurcation buckling and reduces the durable critic loads,and its effects become weak and finally vanish with the increase of the ratio of radius to thickness in the case of short laminated circular cylindrical shells,also the influence of the matrix creep cracking is mainly dependent on the boundary conditions at two ends for moderately long circular cylindrical shells.
PENG Fan; FU YiMing; CHEN YaoJun
2008-01-01
The effect of matrix cracking on the bifurcation creep buckling of viscoelastic laminated circular cylindrical shells is investigated. The viscoelastic behavior of laminas is modeled by Schapery's integral constitutive equation with growing ma-trix cracks. The values of damage variables are correlated to non-dimensional density of matrix cracks relying on the formulas from meso-mechanics approach, and the evolution equation predicting the growth rate of density of matrix cracks is assumed to follow a power type relation with transverse tensile stress. The gov-erning equations for pre-buckling creep deformation and bifurcation buckling of laminated circular cylindrical shells under axial compression are obtained on the basis of the Donnell type shallow shell theory and Karman-Donnell geometrically nonlinear relationship. Corresponding solution strategy is constructed by inte-grating finite-difference technique, trigonometric series expansion method and Taylor's numerical recursive scheme for convolution integration. The bifurcation creep buckling of symmetrically laminated glass-epoxy circular cylindrical shells with matrix creep cracking coupled are examined for various geometrical parame-ters and parameters of damage evolution as well as boundary conditions. The nu-merical results show that matrix creep cracking remarkably shortens the critic time of bifurcation buckling and reduces the durable critic loads, and its effects become weak and finally vanish with the increase of the ratio of radius to thickness in the case of short laminated circular cylindrical shells, also the influence of the matrix creep cracking is mainly dependent on the boundary conditions at two ends for moderately long circular cylindrical shells.
无
2007-01-01
The present work discusses the problem of dynamic stability of a viscoelastic circular cylindrical shell, according to revised Timoshenko theory, with an account of shear deformation and rotatory inertia in the geometrically nonlinear statement. Proceeding by Bubnov-Galerkin method in combination with a numerical method based on the quadrature formula the problem is reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation. For a wide range of variation of physical mechanical and geometrical parameters, the dynamic behavior of the shell is studied. The influence of viscoelastic properties of the material on the dynamical stability of the circular cylindrical shell is shown. Results obtained using different theories are compared.
Free-vibration Characteristics of Laminated Angle-ply Non-circular Cylindrical Shells
M. Ganapathi
2004-10-01
Full Text Available This paper deals with the free-vibration behaviour of anisotropic laminated angle-ply noncircular cylindrical shells using finite element approach. The formulation is based on first-ordershear deformation theory. The present model accounts for in-plane and rotary inertia effects. A detailed study has been carried out to highlight the effects of shell geometry, cross-sectionalproperties, lay-up and ply-angles on the natural frequencies of different types of modes of vibration of non-circular elliptical shell structures.
Free vibrations of finite circular cylindrical shells and tubes with and without a surrounding fluid
Numerical models are evaluated for determining the natural frequencies of thin-walled closed circular cylindrical shells and straight tube bundles in a fluid or without a fluid. Experiments are described to check the reliability of the numerical models. Some of the models are applied for the vibration analysis of some parts of the sodium-steam heat exchangers of the SNR-300 reactor in Kalkar (West Germany). (Auth.)
Free vibration of symmetric angle-ply laminated circular cylindrical shells
Free vibration of symmetric angle-ply laminated circular cylindrical shells is studied using Spline approximation. The equations of motions in longitudinal, circumferential and transverse displacement components, are derived using Love's first approximation theory. The coupled differential equations are solved using Spline approximation to obtain the generalized eigenvalue problem. Parametric studies are performed to analyse the frequency response of the shell with reference to the material properties, number of layers, ply orientation, length and circumferential node number and different boundary conditions
Yuan, Li-Yun; Xiang, Yu; Lu, Jing; Jiang, Hong-Hua
2015-12-01
Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping (i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic. Project supported by the National Natural Science Foundation of China (Grant Nos. 11162001, 11502056, and 51105083), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2012GXNSFAA053207), the Doctor Foundation of Guangxi
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
Wang, Y. Q.; Guo, X. H.; Li, Y. G.; Li, J.
2010-03-01
This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.
ANALYSIS OF THE DYNAMIC STABILITY OF ELECTRICAL GRADED PIEZOELECTRIC CIRCULAR CYLINDRICAL SHELLS
ZhuJunqiang; ShenYapeng; ChenChangqing
2004-01-01
A system of Mathieu Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric field. Bolotin's method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric effect, the piezoelectric graded effect and the electric field only have minor effect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.
2008-01-01
Based on the first order shear deformation theory and classic buckling theory, the paper investigates the creep buckling behavior of viscoelastic laminated plates and laminated circular cylindrical shells. The analysis and elaboration of both instantaneous elastic critic load and durable critic load are emphasized. The buckling load in phase domain is obtained from governing equations by applying Laplace transform, and the instantaneous elastic critic load and durable critic load are determined according to the extreme value theorem for inverse Laplace transform. It is shown that viscoelastic approach and quasi-elastic approach yield identical solutions for these two types of critic load respectively. A transverse disturbance model is developed to give the same mechanics significance of durable critic load as that of elastic critic load. Two types of critic loads of boron/epoxy composite laminated plates and circular cylindrical shells are discussed in detail individually, and the influencing factors to induce creep buckling are revealed by examining the viscoelasticity incorporated in transverse shear deformation and in-plane flexibility.
Free flexural radial vibrations of a thin circular cylindrical shell bearing added mass
Seregin Sergey Valer’evich
2014-12-01
Full Text Available The author comes up with a refined mathematical model contemplating that added mass facilitates interaction between coupled flexural and radial vibrations in the linear setting. The author has identified a higher splitting of the flexural frequency spectrum due to the presence of the added mass and the wave generation parameters that characterize the relative length and thickness of the shell. Within the framework of the shallow-shell theory, the influence of the small concentrated mass onto natural dynamic properties of the shell is exposed to research. The refined mathematical model was employed to identify that the added mass binds the coupled flexural shape of the circular cylindrical shell and facilitates interaction between low-frequency flexural vibrations and high-frequency radial vibrations. Moreover, radial vibrations act as a supplementary inertial link between coupled flexural shapes. Due to the availability of the exciting load, non-resonant areas, identified through the application of the traditional mathematical model, can be resonant in essence. The findings of this research must be considered in the course of the assessment of the dynamic strength of any shell structures designed. This refined finite-dimensional model, capable of recognizing radial vibrations, has generated the results that comply with numerical analyses and experimental data both quantitatively and qualitatively. Therefore, dynamic problems that have already been resolved may need refinement.
Finite element analysis of cylindrical shells with circular and elliptical holes
A finite element solution to the problem of stress distribution in cylindrical shells with circular and elliptical holes is given in the present paper. Quadrilateral and triangular curved finite elements are used in the analysis. The elements of a new class, based on simple independent generalized strain functions insofar as this is allowed by the compatibility equations. The elements also satisfy exactly the requirements of strain-free-rigid body displacements and uses only the external open-quotes geometricclose quotes nodal degrees of freedom to avoid the difficulties associated with unnecessary internal degree of freedom. A rectangular curved element was first developed and applied to the analysis of the familiar pinched cylinder and barrel vault problems Ashwell and Sabir. The results converge rapidly for displacements as well as for stresses. Further tests were carried out to investigate the ability of this element in predicting the high stresses in the neighborhood of applied concentrated loads Sabir and Ashwell. The loads considered were either radial or axial forces as well as moments about tangents to the circular cross section. The results obtained were not only in agreement with those of Forsberg and Flagge but when plotted for the complex parameters defining proportions of the shell and flexibility as suggested by Calladine, their general forms corresponded closely with theoretical predications. In the present paper we first develop strain based quadrilateral and triangular elements and apply them to the solution of the problem of stress concentrations in the neighborhood of small and large circular and elliptical holes when the cylinders are subjected to a uniform axial tension. These results are compared with analytical solutions based on shallow sheel approximations and show that the use of these strain based elements obviates the need for using an inordinately large number of elements
Dong Tang
2016-01-01
Full Text Available An analytical procedure for free vibration analysis of circular cylindrical shells with arbitrary boundary conditions is developed with the employment of the method of reverberation-ray matrix. Based on the Flügge thin shell theory, the equations of motion are solved and exact solutions of the traveling wave form along the axial direction and the standing wave form along the circumferential direction are obtained. With such a unidirectional traveling wave form solution, the method of reverberation-ray matrix is introduced to derive a unified and compact form of equation for natural frequencies of circular cylindrical shells with arbitrary boundary conditions. The exact frequency parameters obtained in this paper are validated by comparing with those given by other researchers. The effects of the elastic restraints on the frequency parameters are examined in detail and some novel and useful conclusions are achieved.
Bich, Dao Huy; Xuan Nguyen, Nguyen
2012-12-01
In the present work, the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented. Material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents. Governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration. One-term approximate solution is assumed to satisfy simply supported boundary conditions. The Galerkin method, the Volmir's assumption and fourth-order Runge-Kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies, nonlinear frequency-amplitude relation and nonlinear dynamic responses. Numerical results show the effects of characteristics of functionally graded materials, pre-loaded axial compression and dimensional ratios on the dynamical behavior of shells. The proposed results are validated by comparing with those in the literature.
Liu, Y. Z.; Hao, Y. X.; Zhang, W.; Chen, J.; Li, S. B.
2015-07-01
The nonlinear vibration of a simply supported FGM cylindrical shell with small initial geometric imperfection under complex loads is studied. The effects of radial harmonic excitation, compressive in-plane force combined with supersonic aerodynamic and thermal loads are considered. The small initial geometric imperfection of the cylindrical shell is characterized in the form of the sine-type trigonometric functions. The effective material properties of this FGM cylindrical shell are graded in the radial direction according to a simple power law in terms of the volume fractions. Based on Reddy's third-order shear deformation theory, von Karman-type nonlinear kinematics and Hamilton's principle, the nonlinear partial differential equation that controls the shell dynamics is derived. Both axial symmetric and driven modes of the cylindrical shell deflection pattern are included. Furthermore, the equations of motion can be reduced into a set of coupled nonlinear ordinary differential equations by applying Galerkin's method. In the study of the nonlinear dynamics responses of small initial geometric imperfect FGM cylindrical shell under complex loads, the 4th order Runge-Kutta method is used to obtain time history, phase portraits, bifurcation diagrams and Poincare maps with different parameters. The effects of external loads, geometric imperfections and volume fractions on the nonlinear dynamics of the system are discussed.
Khalifa, Ahmed Mousa
2011-11-01
The combination of Flügge's shell theory, the transfer matrix approach and the Romberg integration method are used to investigate the free vibration behaviour of stepped orthotropic cylindrical shells. The hoop step on the shell surface is described by a reduced thickness over part of its circumference. Modal displacements of the shell can be described by trigonometric functions and Fourier's approach is used to separate the variables. The vibration equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells by introducing the trigonometric functions in the longitudinal direction and applying the numerical integration in the circumferential direction. The proposed model is used to get the vibration frequencies and the corresponding mode shapes for symmetrical and antisymmetrical type-modes. Computed results indicate the sensitivity of the frequency parameters and the bending deformations to the geometry of stepped shell, and also to the axial and circumferential rigidities of the shell.
无
2008-01-01
Based on the linear theories of thin cylindrical shells and viscoelastic materi-als, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then pre-sented with an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary, conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.
Pellicano, F.; Amabili, M.
2006-05-01
In the present paper the dynamic stability of circular cylindrical shells subjected to static and dynamic axial loads is investigated. Both Donnell's nonlinear shallow shell and Sanders-Koiter shell theories have been applied to model finite-amplitude static and dynamic deformations. Results are compared in order to evaluate the accuracy of these theories in predicting instability onset and post-critical nonlinear response. The effect of a contained fluid on the stability and the post-critical behaviour is analyzed in detail. Geometric imperfections are considered and their influence on the dynamic instability and post-critical behaviour is investigated. Chaotic dynamics of pre-compressed shells is investigated by means of nonlinear time-series techniques, extracting correlation dimension and Lyapunov exponents.
Cylindrical shells are utilized as structural elements of nuclear power plans, heat exchangers or pressure vessels, which are operated under elevated temperature. Creep buckling is one of the failure modes of structures at elevated temperature. In some experiments conducted by other authors, axially compressive cylindrical shells with a large ratio of radius to thickness were observed to buckle with circumferential waves. We reported that the circumferential weaves occur due to bifurcation buckling. But, the citrical time and the minimum loading for bifurcation buckling obtained from calculations of finite element analyses are not very good agreement with those of the experiments. One of the reasons for the disagreement is considered to be that the creep constitutive equations employed in many previous analyses represent steady creep. The creep phenomena usually have primary creep period, steady creep one and tertiary creep one. A creep strain-time relation through the three periods can be simulated by using a constitutive equation based on creep damage mechanics. In the present paper, we analyze bifurcation creep buckling of circular cylindrical shells subjected to axial compression by the use of the finite element method taking account of the creep damage mechanics of Kachanov-Rabotnov. (author)
Rahmani, Omid; Khalili, S.M.R.; Thomsen, Ole Thybo
2012-01-01
A new model based on the high order sandwich panel theory is proposed to study the effect of external loads on the free vibration of circular cylindrical composite sandwich shells with transversely compliant core, including also the calculation of the buckling loads. In the present model, in...... contrast to most of the available sandwich plate and shell theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core material are determined through a 3D elasticity solution. The performance of the present theory is......, which is based on a 3D elasticity solution for the core material, can be used as a benchmark in future studies of the free vibration and buckling of circular cylindrical composite sandwich shells with a transversely compliant core....
Free flexural radial vibrations of a thin circular cylindrical shell bearing added mass
Seregin Sergey Valer’evich
2014-01-01
The author comes up with a refined mathematical model contemplating that added mass facilitates interaction between coupled flexural and radial vibrations in the linear setting. The author has identified a higher splitting of the flexural frequency spectrum due to the presence of the added mass and the wave generation parameters that characterize the relative length and thickness of the shell. Within the framework of the shallow-shell theory, the influence of the small concentrated mass onto ...
A semi-analytical approach eccentrically stiffened functionally graded circular cylindrical shells surrounded by an elastic medium subjected to external pressure is presented. The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffeners technique and Galerkin method, this paper deals the nonlinear dynamic problem. The approximate three-term solution of deflection shape is chosen and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form. The nonlinear dynamic responses are analyzed by using fourth order Runge-Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells is investigated according to Budiansky-Roth criterion. Results are given to evaluate effects of stiffener, elastic foundation and input factors on the frequency-amplitude curves, natural frequencies, nonlinear responses and nonlinear dynamic buckling loads of functionally graded cylindrical shells. (authors)
Amabili, M.; Sarkar, A.; Païdoussis, M. P.
2006-03-01
The geometric nonlinear response of a water-filled, simply supported circular cylindrical shell to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency is investigated. The response is investigated for a fixed excitation frequency by using the excitation amplitude as bifurcation parameter for a wide range of variation. Bifurcation diagrams of Poincaré maps obtained from direct time integration and calculation of the Lyapunov exponents and Lyapunov dimension have been used to study the system. By increasing the excitation amplitude, the response undergoes (i) a period-doubling bifurcation, (ii) subharmonic response, (iii) quasi-periodic response and (iv) chaotic behaviour with up to 16 positive Lyapunov exponents (hyperchaos). The model is based on Donnell's nonlinear shallow-shell theory, and the reference solution is obtained by the Galerkin method. The proper orthogonal decomposition (POD) method is used to extract proper orthogonal modes that describe the system behaviour from time-series response data. These time-series have been obtained via the conventional Galerkin approach (using normal modes as a projection basis) with an accurate model involving 16 degrees of freedom (dofs), validated in previous studies. The POD method, in conjunction with the Galerkin approach, permits to build a lower-dimensional model as compared to those obtainable via the conventional Galerkin approach. Periodic and quasi-periodic response around the fundamental resonance for fixed excitation amplitude, can be very successfully simulated with a 3-dof reduced-order model. However, in the case of large variation of the excitation, even a 5-dof reduced-order model is not fully accurate. Results show that the POD methodology is not as "robust" as the Galerkin method.
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
Several experimental investigations indicate the necessity to take into account the material anisotropy as well as different creep strengths in uniaxial tension and compression (CSD-effect) in descriptions of deformation behaviour of such materials which are used in the design of pressure vessels and pipings of the chemical industry and power plants. Within the frame of the representation theory of tensor functions a suitable constitutive equation is proposed and used in connection with the Norton-Bailey power creep law for the numerical analysis of the steady state creep of thin-walled circular cylindrical shells, subjected to an axially symmetric load. Thereby the investigations are not performed with the assumption of a sandwich shell but start from an actual solid wall shell whose creep deformations are analysed by using the extended Newton-method combined with the method of finite differences. As numerical example a circular cylindrical shell with open ends subjected to internal pressure is investigated. Thereby the shell is assumed to be clamped at both ends in supports that are free to move in the axial direction. The results of calculation indicate that material anisotropy as well as the CSD-effect have great influence on the components of displacement and bending moment. (orig.)
Torsion of Elliptical Composite Cylindrical Shells
Haynie, Waddy
2007-01-01
The response of elliptical composite cylindrical shells under torsion is studied. The torsional condition is developed by rotating one end of the cylinder relative to the other. Prebuckling, buckling, and postbuckling responses are examined, and material failure is considered. Four elliptical cross sections, defined by their aspect ratio, the ratio of minor to major radii, are considered: 1.00 (circular), 0.85, 0.70, and 0.55. Two overall cylinder sizes are studied; a small size with a radius...
Plastic buckling of cylindrical shells
Cylindrical shells exhibit buckling under axial loads at stresses much less than the respective theoretical critical stresses. This is due primarily to the presence of geometrical imperfections even though such imperfections could be very small (e.g., comparable to thickness). Under internal pressure, the shell regains some of its buckling strength. For a relatively large radius-to-thickness ratio and low internal pressure, the effect can be reasonably estimated by an elastic analysis. However, for low radius-to-thickness ratios and greater pressures, the elastic-plastic collapse controls the failure load. in order to quantify the elastic-plastic buckling capacity of cylindrical shells, an analysis program was carried out by use of the computer code BOSOR5 developed by Bushnell of Lockheed Missiles and Space Company. The analysis was performed for various radius-to-thickness ratios and imperfection amplitudes. The purpose of the analytical program was to compute the buckling strength of underground cylindrical tanks, that are used for storage of nuclear wastes, for realistic geometric imperfections and internal pressure loads. This paper presents the results of the elastic-plastic analyses and compares them with other available information for various pressure loads
Vibration of cylindrical shells of bimodulus composite materials
Bert, C. W.; Kumar, M.
1982-03-01
A theory is formulated for the small amplitude free vibration of thick, circular cylindrical shells laminated of bimodulus composite materials, which have different elastic properties depending upon whether the fiber-direction strain is tensile or compressive. The theory used is the dynamic, shear deformable (moderately thick shell) analog of the Sanders best first approximation thin shell theory. By means of tracers, the analysis can be reduced to that of various simpler shell theories, namely Love's first approximation, and Donnell's shallow shell theory. As an example of the application of the theory, a closed form solution is presented for a freely supported panel or complete shell. To validate the analysis, numerical results are compared with existing results for various special cases. Also, the effects of the various shell theories, thickness shear flexibility, and bimodulus action are investigated.
Omnidirectional, circularly polarized, cylindrical microstrip antenna
Stanton, Philip H. (Inventor)
1985-01-01
A microstrip cylindrical antenna comprised of two concentric subelements on a ground cylinder, a vertically polarized (E-field parallel to the axis of the antenna cylinder) subelement on the inside and a horizontally polarized (E-field perpendicular to the axis) subelement on the outside. The vertical subelement is a wraparound microstrip radiator. A Y-shaped microstrip patch configuration is used for the horizontally polarized radiator that is wrapped 1.5 times to provide radiating edges on opposite sides of the cylindrical antenna for improved azimuthal pattern uniformity. When these subelements are so fed that their far fields are equal in amplitude and phased 90.degree. from each other, a circularly polarized EM wave results. By stacking a plurality of like antenna elements on the ground cylinder, a linear phased array antenna is provided that can be beam steered to the desired elevation angle.
RESONANCE RADIATION OF SUBMERGED INFINITE CYLINDRICAL SHELL
无
2002-01-01
The resonance sound radiation from submerged infinite elastic cylindrical shell, excited by internal harmonic line force, is investigated. The shell radiation power is presented in terms of resonant modal radiation derived from resonance radiation theory (RRT). The resonance radiation formulae are derived from classical Rayleigh normal mode solution, which are useful for understanding the mechanism of sound radiation from submerged shells. As an example, numerical calculation of a thin steel cylindrical shell is done by using these two methods. It seems that the results of RRT solutions are in good agreement with that of Rayleigh normal mode solutions.
Multimode interaction in axially excited cylindrical shells
Silva F. M. A.; Rodrigues L.; Gonçalves P. B.; Del Prado Z. J. G. N
2014-01-01
Cylindrical shells exhibit a dense frequency spectrum, especially near the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to a complex dynamic behavior. So, the aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under axial forcing with multiple equal or nearly equal natural fr...
Improvement of the axial buckling capability of elliptical cylindrical shells
Paschero, Maurizio
2008-01-01
A rather thorough and novel buckling analysis of an axially-loaded orthotropic circular cylindrical shell is formulated. The analysis assumes prebuckling rotations are negligible and uses a unique re-defining of the orthotropic material properties in terms of a so-called geometric mean isotropic (GMI) material. Closed-form expressions for the buckling stress in terms of cylinder geometry and orthotropic material properties are presented, the particular closed form depending on ...
Distributed neural signals on parabolic cylindrical shells
Hu, S. D.; Li, H.; Tzou, H. S.
2013-06-01
Parabolic cylindrical shells are commonly used as key components in communication antennas, space telescopes, solar collectors, etc. This study focuses on distributed modal neural sensing signals on a flexible simply-supported parabolic cylindrical shell panel. The parabolic cylindrical shell is fully laminated with a piezoelectric layer on its outer surface and the piezoelectric layer is segmented into infinitesimal elements (neurons) to investigate the microscopic distributed neural sensing signals. Since the dominant vibration component of the shell is usually the transverse oscillation, a new transverse mode shape function is defined. Two shell cases, i.e., the ratio of the meridian height to the half span distance of a parabola at 1:4 (shallow) and 1:1 (deep), are studied to reveal the curvature effect to the neural sensing signals. Studies suggest that the membrane signal component dominates for lower natural modes and the bending signal component dominates for higher natural modes. The meridional membrane and bending signal components are mostly concentrated on the high-curvature areas, while the longitudinal bending component is mostly concentrated on the relatively flat areas. The concentration behavior becomes more prominent as the parabolic cylindrical shell deepens, primarily resulting from the enhanced membrane effect due to the increased curvature.
OPTIMAL THICKNESS OF A CYLINDRICAL SHELL
Paul Ziemann
2015-01-01
Full Text Available In this paper an optimization problem for a cylindrical shell is discussed. The aim is to look for an optimal thickness of a shell to minimize the deformation under an applied external force. As a side condition, the volume of the shell has to stay constant during the optimization process. The deflection is calculated using an approach from shell theory. The resulting control-to-state operator is investigated analytically and a corresponding optimal control problem is formulated. Moreover, necessary conditions for an optimal solution are stated and numerical solutions are presented for different examples.
Indentation of Ellipsoidal and Cylindrical Elastic Shells
Vella, Dominic
2012-10-01
Thin shells are found in nature at scales ranging from viruses to hens\\' eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus etal. [following paper, Phys. Rev. Lett. 109, 144301 (2012)PRLTAO0031-9007] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells. © 2012 American Physical Society.
Research on cylindrical shell vibration reduction systems
XING Xiao-liang; WANG Min-qing
2008-01-01
Longitudinal and horizontal vibration must both be reduced in an effective vibration isolation system. We present a cylindrical shell vibration isolator as a dynamic system composed of four springs and dampers. Vibration is directly produced by the motion of machinery, and more is subsequently generated by harmonic frequencies within their structure. To test the effectiveness of our isolator, we first determined equations for the transmission of vibration from the machine to its cylindrical shell. Damping effects produced by the vibration parameters of our system are then analyzed.
Free Vibration of Partially Supported Cylindrical Shells
Mirza, S.; Y. Alizadeh
1995-01-01
The effects of detached base length on the natural frequencies and modal shapes of cylindrical shell structures were investigated in this work. Some of the important applications for this type of problem can be found in the cracked fan and rotor blades that can be idealized as partially supported shells with varying unsupported lengths. A finite element model based on small deflection linear theory was developed to obtain numerical solutions for this class of problems. The numerical results w...
SPSM and its application in cylindrical shells
Nie, Wu; Zhou, Su-Lian; Peng, Hui
2008-03-01
In naval architectures, the structure of prismatic shell is used widely. But there is no suitable method to analyze this kind of structure. Stiffened prismatic shell method (SPSM) presented in this paper, is one of the harmonic semi-analytic methods. Theoretically, strong stiffened structure can be analyzed economically and accurately. SPSM is based on the analytical solution of the governing differential equations for orthotropic cylindrical shells. In these differential equations, the torsional stiffness, bending stiffness and the exact position of each stiffener are taken into account with the Heaviside singular function. An algorithm is introduced, in which the actions of stiffeners on shells are replaced by external loads at each stiffener position. Stiffened shells can be computed as non-stiffened shells. Eventually, the displacement solution of the equations is acquired by the introduction of Green function. The stresses in a corrugated transverse bulkhead without pier base of an oil tanker are computed by using SPSM.
Stochastic Analysis of Cylindrical Shell
Grzywiński Maksym
2014-06-01
Full Text Available The paper deals with some chosen aspects of stochastic structural analysis and its application in the engineering practice. The main aim of the study is to apply the generalized stochastic perturbation techniques based on classical Taylor expansion with a single random variable for solution of stochastic problems in structural mechanics. The study is illustrated by numerical results concerning an industrial thin shell structure modeled as a 3-D structure.
Vibrations of cantilevered shallow cylindrical shells of rectangular planform
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1981-10-01
A cantilevered, shallow shell of circular cylindrical curvature and rectangular planform exhibits free vibration behavior which differs considerably from that of a cantilevered beam or of a flat plate. Some numerical results can be found for the problem in the previously published literature, mainly obtained by using various finite element methods. The present paper is the first definitive study of the problem, presenting accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio. The analysis is based upon shallow shell theory. Numerical results are obtained by using the Ritz method, with algebraic polynomial trial functions for the displacements. Convergence is investigated, with attention being given both to the number of terms taken for each co-ordinate direction and for each of the three components of displacement. Accuracy of the results is also established by comparison with finite element results for shallow shells and with other accurate flat plate solutions.
Vibrations of cantilevered shallow cylindrical shells of rectangular planform
Leissa, A. W.; Lee, J. K.; Wang, A. J.
1981-01-01
A cantilevered, shallow shell of circular cylindrical curvature and rectangular planform exhibits free vibration behavior which differs considerably from that of a cantilevered beam or of a flat plate. Some numerical results can be found for the problem in the previously published literature, mainly obtained by using various finite element methods. The present paper is the first definitive study of the problem, presenting accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio. The analysis is based upon shallow shell theory. Numerical results are obtained by using the Ritz method, with algebraic polynomial trial functions for the displacements. Convergence is investigated, with attention being given both to the number of terms taken for each co-ordinate direction and for each of the three components of displacement. Accuracy of the results is also established by comparison with finite element results for shallow shells and with other accurate flat plate solutions.
Multimode interaction in axially excited cylindrical shells
Silva F. M. A.
2014-01-01
Full Text Available Cylindrical shells exhibit a dense frequency spectrum, especially near the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to a complex dynamic behavior. So, the aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under axial forcing with multiple equal or nearly equal natural frequencies. The shell is modelled using the Donnell nonlinear shallow shell theory and the discretized equations of motion are obtained by applying the Galerkin method. For this, a modal solution that takes into account the modal interaction among the relevant modes and the influence of their companion modes (modes with rotational symmetry, which satisfies the boundary and continuity conditions of the shell, is derived. Special attention is given to the 1:1:1:1 internal resonance (four interacting modes. Solving numerically the governing equations of motion and using several tools of nonlinear dynamics, a detailed parametric analysis is conducted to clarify the influence of the internal resonances on the bifurcations, stability boundaries, nonlinear vibration modes and basins of attraction of the structure.
Realization of cylindrical submicron shell arrays by diffraction-introduced photolithography
In this paper, we present an approach for the fabrication of cylindrical shell arrays with shell thickness of a few hundred nanometers. This approach is based on introducing diffraction into conventional ultraviolet photolithography, which is realized by deliberately leaving a gap between mask patterns and photoresist surfaces. The cylindrical shells generated from this method have external diameters from 1.5 to 4.5 µm, internal diameters from 0.5 to 3.5 µm, and heights of 10–15 µm at most, while side lengths of original square mask patterns (or diameters of circular mask patterns) are within 2–5 µm. Experimental results indicate that these cylindrical submicron shell arrays are reproducible and uniform in morphologies and dimensions. The optical principle of the fabrication is simulated based on Fresnel diffraction theory. Moreover, the cylindrical submicron shell arrays fabricated herein may find applications in bio-chemical and micro/nano-fluidic fields
Free Vibration of Partially Supported Cylindrical Shells
S. Mirza
1995-01-01
Full Text Available The effects of detached base length on the natural frequencies and modal shapes of cylindrical shell structures were investigated in this work. Some of the important applications for this type of problem can be found in the cracked fan and rotor blades that can be idealized as partially supported shells with varying unsupported lengths. A finite element model based on small deflection linear theory was developed to obtain numerical solutions for this class of problems. The numerical results were generated for shallow shells and some of the degenerate cases are compared with other results available in the literature. The computations presented here involve a wide range of variables: material properties, aspect ratios, support conditions, and radius to base ratio.
王延庆; 梁力; 郭星辉; 杨坤
2012-01-01
A composite circular cylindrical shell made from different materials is investigated. Based on Donnell＇s shallow shell theory and classical laminated shell theory, nonlinear vibrating equation is derived, in which the effects of dynamic Young＇s modulus and geometric large-amplitude are considered. Galerkin method is used to disperse the vibrating equation. The nonlinear vibrating responses of the system with the participation of two neighboring axial modes are solved by applying the multidimensional L-P method. And complex frequency-response curves indicating internal resonance are obtained, showing that the energy is transferred between the two modes which affect each other, and there is 1：1 internal resonance phenomenon in the system. Result of multiple scales method is compared with that of multidimensional L-P method, and the same conclusion is drawn.%以不同材料构成的复合材料圆柱壳作为研究模型，考虑几何非线性，动态弹性模量等因素，根据Dormell’s简化壳理论及经典层合壳理论建立其非线性振动方程。采用Galerkin方法对振动方程进行离散化，应用多元L-P法求解了系统包含两个相邻轴向模态的非线性振动响应，得到了反映复杂内共振的幅频特性曲线，表明能量在两个模态之间相互传递，彼此影响牵制，系统存在1：1内共振现象。最后利用多尺度法与多元L-P法所得结果进行比较，得到了相同的结论。
Thermalization Calculations in a Cylindrical Shell
An approximate, semi-analytical procedure for determining the distribution and energy spectrum of the thermal and epithermal neutron flux in a weakly neutron capturing, cylindrical shell medium is considered. The shell medium is taken to represent the moderator surrounding a fuel rod in a thermal reactor. The basis for calculating the flux in most of the moderator is the energy-dependent diffusion equation. Transient corrections to the diffusion approximation are added near the medium boundaries. The effects of adjoining media are taken into account through the boundary conditions imposed on the diffusion and transient fluxes. At the inner boundary these effects are calculated by collision probability methods. Activation fluxes are derived from the calculated neutron flux distributions and compared with measurements made in the D2O moderator surrounding a uranium metal rod in the ZEEP reactor. (author)
Mercan, Kadir; Demir, Çiğdem; Civalek, Ömer
2016-01-01
In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.
Mercan Kadir
2016-01-01
Full Text Available In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM is investigated. The method of discrete singular convolution (DSC is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.
Buckling of un-stiffened cylindrical shell under non-uniform axial conpressive stress
宋昌永
2002-01-01
This paper provides a review of recent research advances and trends in the area of stability of un-stiffened circular cylindrical shells subjected to general non-uniform axial compressive stresses. Only the more important and interesting aspects of the research, judged from a personal viewpoint, are discussed. They can be crudely classified into four categories: (1) shells subjected to non-uniform loads; (2) shells on discrete supports; (3) shells with intended cutouts/holes; and (4) shells with non-uniform settlements.
Study on 1∶ 1 internal resonance of thin laminated circular cylindrical shells%层合薄壁圆柱壳1:1内共振研究
王延庆; 梁力; 郭星辉; 楼玲娜
2011-01-01
针对一端固定,一端自由的层合薄壁圆柱壳模型,根据Donnell's非线性简化壳理论建立其非线性振动方程.采用Galerkin方法对非线性振动方程进行离散化,应用平均法对系统包含两个相邻轴向模态的非线性振动响应进行了解析分析,与数值模拟进行了比较,并得到了不同参数对层合薄壁圆柱壳复杂的振动响应的影响.结果表明,1)由于所选的两个相邻轴向模态频率相距较近,能量在两个模态之间相互传递,系统存在1∶1内共振现象；2)系统复杂的振动响应受激振力大小的影响比较大,而对于阻尼不敏感.%A cantilever thin laminated circular cylindrical shell was investigated. Based on Donnell's nonlinear shallow shell theory, nonlinear wave equation of the system was derived, in which the effects of dynamic Young's modulus, damping and geometric large-amplitude were considered. Galerkin method was used to disperse the wave equation. Applying averaging method, the nonlinear response of the system was solved with two neighboring axial modes participation, and the results obtained were compared with those gained by numerical method. The effects of different parameters on the complex dynamic response were also investigated. The results show that; due to the frequencies of the two modes selected are very close, there exists 1: 1 internal resonance in the system; the complex vibration response of the system is affected by exciting force evidendy, but it is not very sensitive to damping.
Forced Vibration Analysis for a FGPM Cylindrical Shell
Hong-Liang Dai
2013-01-01
Full Text Available This article presents an analytical study for forced vibration of a cylindrical shell which is composed of a functionally graded piezoelectric material (FGPM. The cylindrical shell is assumed to have two-constituent material distributions through the thickness of the structure, and material properties of the cylindrical shell are assumed to vary according to a power-law distribution in terms of the volume fractions for constituent materials, the exact solution for the forced vibration problem is presented. Numerical results are presented to show the effect of electric excitation, thermal load, mechanical load and volume exponent on the static and force vibration of the FGPM cylindrical shell. The goal of this investigation is to optimize the FGPM cylindrical shell in engineering, also the present solution can be used in the forced vibration analysis of cylindrical smart elements.
A circumferential crack in a cylindrical shell under tension.
Duncan-Fama, M. E.; Sanders, J. L., Jr.
1972-01-01
A closed cylindrical shell under uniform internal pressure has a slit around a portion of its circumference. Linear shallow shell theory predicts inverse square-root-type singularities in certain of the stresses at the crack tips. This paper reports the computed strength of these singularities for different values of a dimensionless parameter based on crack length, shell radius and shell thickness.
Plasmon modes of circular cylindrical double-layer graphene.
Zhao, Tao; Hu, Min; Zhong, Renbin; Chen, Xiaoxing; Zhang, Ping; Gong, Sen; Zhang, Chao; Liu, Shenggang
2016-09-01
In this paper, a theoretical investigation on plasmon modes in a circular cylindrical double-layer graphene structure is presented. Due to the interlayer electromagnetic interaction, there exist two branches of plasmon modes, the optical plasmon mode and the acoustic plasmon mode. The characteristics of these two modes, such as mode pattern, effective mode index and propagation loss, are analyzed. The modal behaviors can be effectively tuned by changing the distance between two graphene layers, the chemical potential of graphene and the permittivity of interlayer dielectric. Importantly, the breakup of tradeoff between mode confinement and propagation loss is discovered in the distance-dependent modal behavior, which originates from the unique dispersion properties of a double-layer graphene system. As a consequence, both strong mode confinement and longer propagation length can be achieved. Our results may provide good opportunities for developing applications based on graphene plasmonics in circular cylindrical structure. PMID:27607651
NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER
菅永军; 鄂学全; 柏威
2003-01-01
In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode bysolving potential equations of water waves in a rigid circular cylinder, which is subject to avertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid ,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubicand vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that differentfree surface standing wave patterns will be formed in different excited frequencies andamplitudes. The contours of free surface waves are agreed well with the experimental resultswhich were carried out several years ago.
On the accuracy of the asymptotic theory for cylindrical shells
Niordson, Frithiof; Niordson, Christian
1999-01-01
We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this shell theory for a cylindrical shell with clamped ends with the results of a solution to the three......-dimensional problem. The results are also compared with those of some commonly used engineering shell theories....
Gravitational collapse of a cylindrical null shell in vacuum
S. Khakshournia
2008-03-01
Full Text Available Barrabès-Israel null shell formalism is used to study the gravitational collapse of a thin cylindrical null shell in vacuum. In general the lightlike matter shell whose history coincides with a null hypersurface is characterized by a surface energy density. In addition, a gravitational impulsive wave is present on this null hypersurface whose generators admit both the shear and expansion. In the case of imposing the cylindrical flatness the surface energy-momentum tensor of the matter shell on the null hypersurface vanishes and the null hyper- surface is just the history of the gravitational wave .
The covariant electromagnetic Casimir effect for real conducting cylindrical shells
Using covariant quantization of the electromagnetic field, the Casimir force per unit area experienced by a long conducting cylindrical shell, under both Dirichlet and Neumann boundary conditions, is calculated. The renormalization procedure is based on the plasma cut-off frequency for real conductors. The real case of a gold (silver) cylindrical shell is considered and the corresponding electromagnetic Casimir pressure is computed. It is discussed that the Dirichlet and Neumann problems should be considered separately without adding their corresponding results.
NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS
周承倜; 王列东
2001-01-01
Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.
Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.
1996-01-01
Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.
Dynamic stability of simply supported composite cylindrical shells under partial axial loading
Dey, Tanish; Ramachandra, L. S.
2015-09-01
The parametric vibration of a simply supported composite circular cylindrical shell under periodic partial edge loadings is discussed in this article. Donnell's nonlinear shallow shell theory considering first order shear deformation theory is used to model the shell. The applied partial edge loading is represented in terms of a Fourier series and stress distributions within the cylindrical shell are determined by prebuckling analysis. The governing equations of the dynamic instability of shells are derived in terms of displacements (u-v-w) and rotations (φx, φθ). Employing the Galerkin and Bolotin methods the dynamic instability regions are computed. Using the expression for the stress function derived in this paper, the pre-buckling stresses in the cylindrical shell due to partial loading can be calculated explicitly. Numerical results are presented to show the influence of radius-to-thickness ratio, different partial edge loading distributions and shear deformation on the dynamic instability regions. The linear and nonlinear responses in the stable and unstable regions are presented to bring out the characteristic features of the dynamic instability regions, such as the existence of beats, its dependence on forcing frequency and effect of nonlinearity on the response. The effect of dynamic load amplitude on the nonlinear response is also studied. It is found that for higher values of dynamic loading, the shell exhibits chaotic behavior.
PERFORATION OF PLASTIC SPHERICAL SHELLS UNDER IMPACT BY CYLINDRICAL PROJECTILES
NING Jian-guo; SONG Wei-dong
2006-01-01
The objective is to study the perforation of a plastic spherical shell impacted by a cylindrical projectile. First, the deformation modes of the shell were given by introducing an isometric transformation. Then, the perforation mechanism of the shell was analyzed and an analytical model was advanced. Based on Hamilton principle, the governing equation was obtained and solved using Runge-Kuta method. Finally, some important theoretical predictions were given to describe the perforation mechanism of the shell. The results will play an important role in understanding the perforation mechanism of spherical shells impacted by a projectile.
Reliability Analysis Of Thin-Walled Cylindrical Shells
Kala Zdeněk
2015-01-01
The subject of the article is the verification of the reliability of thin-walled rotationally symmetric cylindrical shells, using probabilistic approaches. Internal forces and stress of the shell are analysed assuming a membrane action. Material and geometric characteristics of the steel shell are considered as random variables. The reliability index is evaluated using the Latin Hypercube Sampling method. The results of the reliability analysis are derived in a general form, so that they may ...
Prediction of Vibrational Behavior of Grid-Stiffened Cylindrical Shells
Rahimi, G. H.; M. Hemmatnezhad; Ansari, R.
2014-01-01
A unified analytical approach is applied to investigate the vibrational behavior of grid-stiffened cylindrical shells with different boundary conditions. A smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole panel. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier ser...
Vibration analysis of bi-layered FGM cylindrical shells
Arshad, Shahid Hussain; Sultana, Nazra; Iqbal, Zafar [University of Sargodha, Department of Mathematics, Sargodha, Punjab (Pakistan); Naeem, Muhammad Nawaz [G C University Faisalabad, Department of Mathematics, Faisalabad, Punjab (Pakistan); Shah, Abdul Ghafar [The Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur, Punjab (Pakistan)
2011-03-15
In the present study, a vibration frequency analysis of a bi-layered cylindrical shell composed of two independent functionally graded layers is presented. The thickness of the shell layers is assumed to be equal and constant. Material properties of the constituents of bi-layered functionally graded cylindrical shell are assumed to vary smoothly and continuously through the thickness of the layers of the shell and are controlled by volume fraction power law distribution. The expressions for strain-displacement and curvature-displacement relationships are utilized from Love's first approximation linear thin shell theory. The versatile Rayleigh-Ritz approach is employed to formulate the frequency equations in the form of eigenvalue problem. Influence of material distribution in the two functionally graded layers of the cylindrical shells is investigated on shell natural frequencies for various shell parameters with simply supported end conditions. To check the validity, accuracy and efficiency of the present methodology, results obtained are compared with those available in the literature. (orig.)
The deformation of cylindrical shells subjected to radial loads
Madureira, M.L.R.; Fonseca, E.M.M.; Melo, F.J.M.Q. de
2010-01-01
Cylindrical shells have a simple geometry and application in pressure vessels and piping engineering. The development of calculation algorithms in structural project is impelled by a constant challenge in the search of more accurate and fast design tools in engineering. The objective of this work is to contribute with a simple and reliable numerical tool for the stress analysis of cylindrical vessels subjected to generalized forces. A hybrid formulation in the definition of forces...
Evolution of bulk strain solitons in cylindrical inhomogeneous shells
Shvartz, A., E-mail: andrew.shvartz@mail.ioffe.ru; Samsonov, A.; Dreiden, G.; Semenova, I. [Ioffe Institute, 26 Politekhnicheskaya, St Petersburg 194021 (Russian Federation)
2015-10-28
Bulk strain solitary waves in nonlinearly elastic thin-walled cylindrical shells with variable geometrical and physical parameters are studied, and equation for the longitudinal strain component with the variable coefficients is derived. A conservative finite difference scheme is proposed, and the results of numerical simulation of the strain soliton evolution in a shell with the abrupt variations of cross section and physical properties of the material are presented.
Strength Reliability Analysis of Stiffened Cylindrical Shells Considering Failure Correlation
Xu Bai; Liping Sun; Wei Qin; Yongkun Lv
2014-01-01
The stiffened cylindrical shell is commonly used for the pressure hull of submersibles and the legs of offshore platforms. There are various failure modes because of uncertainty with the structural size and material properties, uncertainty of the calculation model and machining errors. Correlations among failure modes must be considered with the structural reliability of stiffened cylindrical shells. However, the traditional method cannot consider the correlations effectively. The aim of this study is to present a method of reliability analysis for stiffened cylindrical shells which considers the correlations among failure modes. Firstly, the joint failure probability calculation formula of two related failure modes is derived through use of the 2D joint probability density function. Secondly, the full probability formula of the tandem structural system is given with consideration to the correlations among failure modes. At last, the accuracy of the system reliability calculation is verified through use of the Monte Carlo simulation. Result of the analysis shows the failure probability of stiffened cylindrical shells can be gained through adding the failure probability of each mode.
DYNAMICAL BEHAVIOR OF VISCOELASTIC CYLINDRICAL SHELLS UNDER AXIAL PRESSURES
程昌钧; 张能辉
2001-01-01
The hypotheses of the Kármán-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties,such as, hyperchaos , chaos, strange attractor, limit cycle etc., are discovered.
Vibration control of cylindrical shells using active constrained layer damping
Ray, Manas C.; Chen, Tung-Huei; Baz, Amr M.
1997-05-01
The fundamentals of controlling the structural vibration of cylindrical shells treated with active constrained layer damping (ACLD) treatments are presented. The effectiveness of the ACLD treatments in enhancing the damping characteristics of thin cylindrical shells is demonstrated theoretically and experimentally. A finite element model (FEM) is developed to describe the dynamic interaction between the shells and the ACLD treatments. The FEM is used to predict the natural frequencies and the modal loss factors of shells which are partially treated with patches of the ACLD treatments. The predictions of the FEM are validated experimentally using stainless steel cylinders which are 20.32 cm in diameter, 30.4 cm in length and 0.05 cm in thickness. The cylinders are treated with ACLD patches of different configurations in order to target single or multi-modes of lobar vibrations. The ACLD patches used are made of DYAD 606 visco-elastic layer which is sandwiched between two layers of PVDF piezo-electric films. Vibration attenuations of 85% are obtained with maximum control voltage of 40 volts. Such attenuations are attributed to the effectiveness of the ACLD treatment in increasing the modal damping ratios by about a factor of four over those of conventional passive constrained layer damping (PCLD) treatments. The obtained results suggest the potential of the ACLD treatments in controlling the vibration of 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.
Nonlinear dynamical behavior of shallow cylindrical reticulated shells
WANG Xin-zhi; LIANG Cong-xing; HAN Ming-jun; YEH Kai-yuan; WANG Gang
2007-01-01
By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylinmapping.
Tunable cylindrical shell as an element in acoustic metamaterial
Titovich, Alexey S
2014-01-01
Elastic cylindrical shells are fitted with an internal mechanism which is optimized so that, in the quasi-static regime, the combined system exhibits prescribed effective acoustic properties. The mechanism consists of a central mass supported by an axisymmetric distribution of elastic stiffeners. By appropriate selection of the mass and stiffness of the internal mechanism, the shell's effective acoustic properties (bulk modulus and density) can be tuned as desired. Subsonic flexural waves excited in the shell by the attachment of stiffeners are suppressed by including a sufficiently large number of such stiffeners. Effectiveness of the proposed metamaterial is demonstrated by matching the properties of a thin aluminum shell with a polymer insert to those of water. The scattering cross section in water is nearly zero over a broad range of frequencies at the lower end of the spectrum. By arranging the tuned shells in an array the resulting acoustic metamaterial is capable of steering waves. As an example, a cyl...
Nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow
del Prado, Z.; Gonçalves, P. B.; Païdoussis, M. P.
2009-10-01
The high imperfection sensitivity of cylindrical shells under static compressive axial loads is a well-known phenomenon in structural stability. On the other hand, less is known of the influence of imperfections on the nonlinear vibrations of these shells under harmonic axial loads. The aim of this work is to study the simultaneous influence of geometric imperfections and an axial fluid flow on the nonlinear vibrations and instabilities of simply supported circular cylindrical shells under axial load. The fluid is assumed to be non-viscous and incompressible and the flow to be isentropic and irrotational. The behavior of the thin-walled shell is modeled by Donnell's nonlinear shallow-shell equations. It is subjected to a static uniform compressive axial pre-load plus a harmonic axial load. A low-dimensional modal expansion, which satisfies the relevant boundary and continuity conditions, and takes into account all relevant nonlinear modal interactions observed in the past in the nonlinear vibrations of cylindrical shells with and without flow is used together with the Galerkin method to derive a set of eight coupled nonlinear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. The shell is considered to be initially at rest, in a position corresponding to a pre-buckling configuration. Then, a harmonic excitation is applied and conditions for parametric instability and dynamic snap-through are sought. The results clarify the marked influence of geometric imperfections and fluid flow on the dynamic stability boundaries, bifurcations and basins of attraction.
2DEG on a cylindrical shell with a screw dislocation
Filgueiras, Cleverson; Silva, Edilberto O.
2015-09-01
A two dimensional electron gas on a cylindrical surface with a screw dislocation is considered. More precisely, we investigate how both the geometry and the deformed potential due to a lattice distortion affect the Landau levels of such system. The case showing the deformed potential can be thought in the context of 3D common semiconductors where the electrons are confined on a cylindrical shell. We will show that important quantitative differences exist due to this lattice distortion. For instance, the effective cyclotron frequency is diminished by the deformed potential, which in turn enhances the Hall conductivity.
A mixed layerwise theory and differential quadrature (DQ) method (LW-DQ) for three-dimensional free vibration analysis of arbitrary laminated circular cylindrical shells is introduced. Using the layerwise theory in conjunction with the three-dimensional form of Hamilton's principle, the transversely discretized equations of motion and the related boundary conditions are obtained. Then, the DQ method is employed to discretize the resulting equations in the axial directions. The fast convergence behavior of the method is demonstrated and its accuracy is verified by comparing the results with those of other shell theories obtained using conventional methods and also with those of ANSYS software. In the case of arbitrary laminated shells with simply supported ends, the exact solution is developed for comparison purposes. It is shown that using few DQ grid points, converged accurate solutions are obtained. Less computational efforts of the proposed approach with respect to ANSYS software is shown
Plasticity around an Axial Surface Crack in a Cylindrical Shell
Krenk, Steen
1979-01-01
field in an axially cracked cylindrical shell arising from use of classical eighth order shallow shell theory is removed when use is made of a tenth order shell theory which accounts for transverse shear deformations. Although the membrane stresses are only moderately affected, the influence on the...... Ratwani,3–5 it generalises Dugdale's assumption of a concentrated yield zone in the plane of the crack but, contrary to that model, transverse shear effects are included and a continuous stress distribution is assumed in the yield zone. The inherent difficulties arising from the use of shell theory to...... model a three-dimensional problem can be overcome when the crack is sufficiently deep and the material is so ductile that full yield of the section around the crack develops before failure. In that case the calculations confirm the initial assumption of separation of the crack surfaces and the sides of...
Stresses at the intersection of two cylindrical shells
The stress analysis based on the theory of a thin shell is carried out for two normally intersecting cylindrical shells with a large diameter ratio. Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable to ρ0(R/T)1/2XXXX1, is used for the analysis of the shell with cut-out. The solution in terms of displacement function for the nozzle with a non-planar end is based on the Love equation. The boundary forces and displacements at the intersection are all transformed from Gaussian coordinates (α,β) on the shell, or Gaussian coordinates (ζ,θ) on the nozzle into three-dimensional cylindrical coordinates (ρ,θ,z). Their expressions on the intersecting curve are periodic functions of θ and expanded in Fourier series. Every harmonics of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature.The results obtained are in agreement with those from the finite element method and experiments for d/D≤0.8. ((orig.))
2DEG on a cylindrical shell with a screw dislocation
Filgueiras, Cleverson, E-mail: cleversonfilgueiras@yahoo.com.br [Unidade Acadêmica de Física, Universidade Federal de Campina Grande, POB 10071, 58109-970, Campina Grande, Paraíba (Brazil); Departamento de Física (DFI), Universidade Federal de Lavras (UFLA), Caixa Postal 3037, 37200-000, Lavras, Minas Gerais (Brazil); Silva, Edilberto O., E-mail: edilbertoos@pq.cnpq.br [Departamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, 65085-580, São Luís, Maranhão (Brazil)
2015-09-25
Highlights: • Electron gas on a cylindrical surface. • Quantum Hall effects. • Geometric potential induced by confinement. • Topological defect. - Abstract: A two dimensional electron gas on a cylindrical surface with a screw dislocation is considered. More precisely, we investigate how both the geometry and the deformed potential due to a lattice distortion affect the Landau levels of such system. The case showing the deformed potential can be thought in the context of 3D common semiconductors where the electrons are confined on a cylindrical shell. We will show that important quantitative differences exist due to this lattice distortion. For instance, the effective cyclotron frequency is diminished by the deformed potential, which in turn enhances the Hall conductivity.
Relativistic Gravitational Collapse of a Cylindrical Shell of Dust
Nakao, Ken-ichi; Kurita, Yasunari; Morisawa, Yoshiyuki; Harada, Tomohiro
2006-01-01
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust s...
Dynamic reponse of a cylindrical shell immersed in a potential fluid
A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, immersed in a potential fluid. The shell may be excited by an arbitrary radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. A numerical instability prevented direct solutions where the ratio of the hydrodynamic forces to shell inertial forces is greater than two. This instability is believed to be the result of the weak coupling between the equations describing the fluid to those describing the shell. To circumvent this instability, an effective mass was calculated and added to the shell. Comparison of numerical to experimental results are made using a 1/12 scale model of a nuclear reactor core support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies compare to experimental results to within 15%. The use of this numerical technique is illustrated by comparing it to an analytical solution for shell beam modes and an uncertainty in the analytical technique concerning the proper effective mass to use, is resolved
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
Dynamic reponse of a cylindrical shell immersed in a potential fluid
Cummings, G.E.
1978-04-18
A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, immersed in a potential fluid. The shell may be excited by an arbitrary radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. A numerical instability prevented direct solutions where the ratio of the hydrodynamic forces to shell inertial forces is greater than two. This instability is believed to be the result of the weak coupling between the equations describing the fluid to those describing the shell. To circumvent this instability, an effective mass was calculated and added to the shell. Comparison of numerical to experimental results are made using a /sup 1///sub 12/ scale model of a nuclear reactor core support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies compare to experimental results to within 15%. The use of this numerical technique is illustrated by comparing it to an analytical solution for shell beam modes and an uncertainty in the analytical technique concerning the proper effective mass to use, is resolved.
Plastic limit loads for cylindrical shell intersections under combined loading
In this research, applied methods of nonlinear analysis and results of determining the plastic limit loads for shell intersection configurations under combined internal pressure, in-plane moment and out-plane moment loadings are presented. The numerical analysis of shell intersections is performed using the finite element method, geometrically nonlinear shell theory in quadratic approximation and plasticity theory. For determining the load parameter of proportional combined loading, the developed maximum criterion of rate of change of relative plastic work is employed. The graphical results for model of cylindrical shell intersection under different two-parameter combined loadings (as generalized plastic limit load curves) and three-parameter combined loading (as generalized plastic limit load surface) are presented on the assumption that the internal pressure, in-plane moment and out-plane moment loads were applied in a proportional manner. - Highlights: • This paper presents nonlinear two-dimensional FE analysis for shell intersections. • Determining the plastic limit loads under combined loading is considered. • Developed maximum criterion of rate of change of relative plastic work is employed. • Plastic deformation mechanism in shell intersections is discussed. • Results for generalized plastic limit load curves of branch intersection are presented
Plastic limit load of cylindrical shells with cutouts subject to pure bending moment
In this paper, the results of limit analyses of thin-walled cylindrical shells with a circular hole under the action of a pure bending moment are presented in dimensionless form for a wide range of geometric parameters. Analytical estimation of lower bound limit load is carried out using the feasible sequential quadratic programming (FSQP) technique. The finite element calculations of limit load consist of elastic-plastic and lower and upper bound predictions by elastic compensation methods. A testing device was made to perform experiments to obtain limit bending moment of cylinders with circular openings. The analytical and finite element calculations are compared with experimental results and their correlation is discussed. The finite element calculation results were found to be in good agreement with lower bound estimations by the nonlinear mathematical programming (FSQP) method and the formula proposed by Shu
An Experimental Investigation of the Implosion of Cylindrical Shell Structures
Ikeda, C. M.; Wilkerling, J.; Duncan, J. H.
2009-11-01
An experimental study of the physics of the implosion of cylindrical shell structures in a high-pressure water environment was performed. The shell structures are filled with air at atmospheric pressure and the implosions occur when the water pressure is raised above the shell buckling stability limit. High-speed photography (27,000 fps) was used to observe and measure the motion of the structure during its implosion. High-frequency underwater blast sensors recorded dynamic pressure waves at 13 positions in the tank. The cylindrical models are made from various aluminum alloys (diameter D = 39.1 mm, wall thickness t = 0.89 mm) and brass (D = 16.7 to 25.4 mm, t = 0.33 to 0.36 mm). The ends of the tubes were sealed with Aluminum caps. The pressure records are interpreted in light of the high-speed movies. Cylinder length-to-diameter (L/D) ratios between 6 and 10 were examined; in this range the cylinders implode in a mode 2 cross-sectional shape at pressures between 6.9 and 28.7 bar. It is found that the pressure versus time records from sensors placed at the same dimensionless radial position (r/D) from the cylinder surface scale well with time and pressure scales from cavitation bubble collapse theory.
Explosion-Induced Implosions of Cylindrical Shell Structures
Ikeda, C. M.; Duncan, J. H.
2010-11-01
An experimental study of the explosion-induced implosion of cylindrical shell structures in a high-pressure water environment was performed. The shell structures are filled with air at atmospheric pressure and are placed in a large water-filled pressure vessel. The vessel is then pressurized to various levels P∞=αPc, where Pc is the natural implosion pressure of the model and α is a factor that ranges from 0.1 to 0.9. An explosive is then set off at various standoff distances, d, from the model center line, where d varies from R to 10R and R is the maximum radius of the explosion bubble. High-speed photography (27,000 fps) was used to observe the explosion and resulting shell structure implosion. High-frequency underwater blast sensors recorded dynamic pressure waves at 6 positions. The cylindrical models were made from aluminum (diameter D = 39.1 mm, wall thickness t = 0.89 mm, length L = 240 mm) and brass (D = 16.7 mm, t = 0.36 mm, L=152 mm) tubes. The pressure records are interpreted in light of the high-speed movies. It is found that the implosion is induced by two mechanisms: the shockwave generated by the explosion and the jet formed during the explosion-bubble collapse. Whether an implosion is caused by the shockwave or the jet depends on the maximum bubble diameter and the standoff distance.
Prediction of Vibrational Behavior of Grid-Stiffened Cylindrical Shells
G. H. Rahimi
2014-01-01
Full Text Available A unified analytical approach is applied to investigate the vibrational behavior of grid-stiffened cylindrical shells with different boundary conditions. A smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole panel. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke's transformation. A 3D finite element model is also built using ABAQUS software which takes into consideration the exact geometric configuration of the stiffeners and the shell. The achievements from the two types of analyses are compared with each other and good agreement has been obtained. The Influences of variations in shell geometrical parameters, boundary condition, and changes in the cross stiffeners angle on the natural frequencies are studied. The results obtained are novel and can be used as a benchmark for further studies. The simplicity and the capability of the present method are also discussed.
Study of laminated anisotropic cylindrical shells sensitive to transverse stresses
A variational method for the determination of stresses and displacements in a multilayered cylindrical shell is presented. All included materials are linearly anisotropic (monoclinic) - i.e. directional fibres reinforced materials. This study uses a functional which is derived from the potential energy of the structure. The incoming stresses are σRR, σRθ, σRZ, and the displacements are uθ and uZ. This mixed group is the main variables of the formulation. It is shown that the stationarity conditions of the functional are the equilibrium equations and the associated boundary conditions. An approximate solution can be found using a finite element method which realizes a tridimensional discretization of the structure. The program issued is a specific mean for studying the transverse shear stresses in laminated cylindrical structures. From the results obtained it can be concluded that it meets all requirements for the purposes of this range of problems. (author)
Sound radiation of a functionally graded material cylindrical shell in water by mobility method
无
2011-01-01
Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and th...
Nonlinear free vibrations of shallow cylindrical shells at elevated temperature
Modern structures are often subjected to severe vibrations and high temperatures. In such cases vibrations and thermal stresses play an important and even a primary role. The aim of the present paper is to investigate the behaviour of shallow cylindrical shells vibrating at large amplitudes including thermal effect. Though the present project of the author includes the nonlinear analysis under a general thermal boundary condition, the present paper concerns with a specific temperature distribution. The analysis is based on Karman-Tsien field equations extended to thermal loading. (orig./GL)
Linear stability analysis of capillary instabilities for concentric cylindrical shells
Liang, X; Nave, J -C; Johnson, S G
2010-01-01
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of N fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier--Stokes problem. Generalising previous work by Tomotika (N=2), Stone & Brenner (N=3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalised eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateau-style geometrical arguments that only axisymmetric instabilities need be considered. We show that the N=3 case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to N=2 problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full 3-dimensional simulations. Many $N > 3$ c...
Transverse shear effect in a circumferentially cracked cylindrical shell
Delale, F.; Erdogan, F.
1979-01-01
The objectives of the paper are to solve the problem of a circumferentially-cracked cylindrical shell by taking into account the effect of transverse shear, and to obtain the stress intensity factors for the bending moment as well as the membrane force as the external load. The formulation of the problem is given for a specially orthotropic material within the framework of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions as to moment and stress resultants on the crack surface. The effect of Poisson's ratio on the stress intensity factors and the nature of the out-of-plane displacement along the edges of the crack, i.e., bulging, are also studied.
Flow-induced vibration of circular cylindrical structures
Chen, S.S.
1985-06-01
This report summarizes the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders. 219 figs., 30 tabs. (JDB)
Flow-induced vibration of circular cylindrical structures
This report summarizes the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossflow, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders. 219 figs., 30 tabs
Effects of Shell-Buckling Knockdown Factors in Large Cylindrical Shells
Hrinda, Glenn A.
2012-01-01
Shell-buckling knockdown factors (SBKF) have been used in large cylindrical shell structures to account for uncertainty in buckling loads. As the diameter of the cylinder increases, achieving the manufacturing tolerances becomes increasingly more difficult. Knockdown factors account for manufacturing imperfections in the shell geometry by decreasing the allowable buckling load of the cylinder. In this paper, large-diameter (33 ft) cylinders are investigated by using various SBKF's. An investigation that is based on finite-element analysis (FEA) is used to develop design sensitivity relationships. Different manufacturing imperfections are modeled into a perfect cylinder to investigate the effects of these imperfections on buckling. The analysis results may be applicable to large- diameter rockets, cylindrical tower structures, bulk storage tanks, and silos.
Chaotic vibration of a liquid-filled thin cylindrical shell
Recently, a large number of thin walled cylindrical tanks have been widely used, such as oil-storage tanks, and LMFBR primary components. To assess the safety of these systems against earthquakes, it is of great technical importance to clarify the fluid-coupled vibration characteristics of the systems subjected to certain kinds of dynamic loads. This paper describes an experimental study on the chaos of a partially liquid-filled cylindrical tank under horizontal excitation. The test cylinder with a mean radius of 170 mm was made of polyester film with a nominal thickness of 0.188 mm which was lap-joined along a longitudinal seam and bonded with an aluminum end plate along one edge. Shaking table tests were conducted in order to investigate the dynamic characteristics of the shell response. Several types of limit cycles were observed at lower accelerations, and the instability phenomenon, which jumped at some excitation frequencies, occurred for acceleration amplitudes above a critical value. Finally, at higher excitation accelerations, the shell responses became chaotic. The occurrence of the chaos was recognized by the time history, Poincare map, phase trajectory, power spectrum and a positive Lyapunov exponent calculated from the orbits in the three dimensional phase space. In order to visualize the strange attractor, phase portraits were constructed by embedding the trajectories in the phase space
Nemeth, Michael P.
2014-01-01
Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
Elastic Buckling of Bionic Cylindrical Shells Based on Bamboo
Jian-feng Ma; Wu-yi Chen; Ling Zhao; Da-hai Zhao
2008-01-01
High load-bearing efficiency is one of the advantages of biological structures after the evolution of billions of years.Biomimicking from nature may offer the potential for lightweight design. In the viewpoint of mechanics properties, the culm of bamboo comprises of two types of cells and the number of the vascular bundles takes a gradient of distribution. A three-point bending test was carried out to measure the elastic modulus. Results show that the elastic modulus of bamboo decreases gradually from the periphery towards the centre. Based on the structural characteristics of bamboo, a bionic cylindrical structure was designed to mimic the gradient distribution of vascular bundles and parenchyma cells. The buckling resistance of the bionic structure was compared with that of a traditional shell of equal mass under axial pressure by finite element simulations. Results show that the load-bearing capacity of bionic shell is increased by 124.8%. The buckling mode of bionic structure is global buckling while that of the conventional shell is local buckling.
Resonant Excitation of a Truncated Metamaterial Cylindrical Shell by a Thin Wire Monopole
Kim, Oleksiy S.; Erentok, Aycan; Breinbjerg, Olav
2009-01-01
A truncated metamaterial cylindrical shell excited by a thin wire monopole is investigated using the integral equation technique as well as the finite element method. Simulations reveal a strong field singularity at the edge of the truncated cylindrical shell, which critically affects the matching...
Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout
Oterkus, E.; Madenci, E.; Nemeth, M. P.
2007-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Coupling cavity model for circular cylindrical waveguide with uniform cross section
Ayzatsky, M I
2016-01-01
We developed the general approach that gives possibility to calculate the coupling coefficients for arbitrary chain of resonators without using the great number of eigen functions. For understanding this method and having possibility to control the accuracy of obtained results, we applied this procedure for simplest structure that has the analytical solutions - a circular cylindrical waveguide with uniform cross section.
Non-linear Vibrations of Deep Cylindrical Shells by the p-Version Finite Element Method
Pedro Ribeiro; Bruno Cochelin; Sergio Bellizzi
2010-01-01
A p-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. Exter...
Efficient method for analyzing multiple circular cylindrical nanoparticles on a substrate
Lu, Xun; Lu, Ya Yan
2016-05-01
Due to the existing nanofabrication techniques, many metallic or dielectric nanoparticles are cylindrical objects with top and bottom surfaces parallel to a substrate and side boundaries perpendicular to the substrate. In this paper, we develop a relatively simple and efficient semi-analytic method for analyzing the scattering of light by a set of circular cylindrical objects (of finite height) on a layered background. The method relies on expanding the field in one-dimensional modes in layered regions where the material properties change with one spatial variable only, to establish a linear system on the boundaries separating the layered regions. Although the ‘expansion coefficients’ are two-dimensional (2D) functions, they satisfy scalar 2D Helmholtz equations which have analytic solutions due to the special geometry. The method is used to analyze dielectric and metallic circular cylindrical nanoparticles on a substrate or in free space.
A Semi-Analytical Model for Buckling of Stiffened Cylindrical Shells
2013-01-01
Cylindrical shells are common configurations within the technology. The transition from the side to the bottom on a ship has the shape of a fourth of a cylindrical shell. Both ring and stringer stiffeners can be added to the shell for support. Buckling of this type of structure is an important area of interest. The main purpose of this thesis has been to make a semi-analytical model that can describe how a ring stiffened shell and stringer stiffened shell respond during buckling. A va...
Analysis of circumferential waves on a water-filled cylindrical shell
FAN Wei; ZHENG Guoyin; FAN Jun
2012-01-01
The formation of scattering field from a water-filled cylindrical shell was studied. The analytic solutions of scattering field are derived using elastic thin shell theory and Sommerfeld-Watson Transformation （SWT） method. Complex wave-number poles of circumferential waves are found numerically, the phase speed and attenuation of circumferential waves between the situation of a hollow cylindrical shell and a water-filled cylindrical shell are compared. The synthesis of backscattering form functions which are sum of specular reflection component and circumferential waves is consistent with normal mode result. The calculated echo sequences of additional fluid circumferential waves are compared with experimental results. The results show that richer resonance peaks appeared in the backscattering form functions of a water-filled cylindrical shell and the formation of echo＇s structure are due to re-radiation effects of additional fluid circumferential waves.
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Liu Chang-Jiang; Zheng Zhou-Lian; Huang Cong-Bing; He Xiao-Ting; Sun Jun-Yi; Chen Shan-Lin
2011-01-01
This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular l...
Seung-Bok Choi
2013-02-01
Full Text Available In this work, active vibration control of an underwater cylindrical shell structure was investigated, to suppress structural vibration and structure-borne noise in water. Finite element modeling of the submerged cylindrical shell structure was developed, and experimentally evaluated. Modal reduction was conducted to obtain the reduced system equation for the active feedback control algorithm. Three Macro Fiber Composites (MFCs were used as actuators and sensors. One MFC was used as an exciter. The optimum control algorithm was designed based on the reduced system equations. The active control performance was then evaluated using the lab scale underwater cylindrical shell structure. Structural vibration and structure-borne noise of the underwater cylindrical shell structure were reduced significantly by activating the optimal controller associated with the MFC actuators. The results provide that active vibration control of the underwater structure is a useful means to reduce structure-borne noise in water.
Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading
Allahbakhsh, Hamidreza; Shariati, Mahmoud
2013-10-01
A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.
Qiu, Q.; Fang, Z. P.; Wan, H. C.; Zheng, L.
2013-07-01
Based on the Donnell assumptions and linear visco-elastic theory, the constitutive equations of the cylindrical shell with multilayer Passive Constrained Layer Damping (PCLD) treatments are described. The motion equations and boundary conditions are derived by Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equations in state space are established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor and the frequency response of clamped-clamped multi-layer PCLD cylindrical shell is obtained. The results show that multi-layer PCLD cylindrical shell is more effective than the traditional three-layer PCLD cylindrical shell in suppressing vibration and noise if the same amount of material is applied. It demonstrates a potential application of multi-layer PCLD treatments in many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles.
Based on the Donnell assumptions and linear visco-elastic theory, the constitutive equations of the cylindrical shell with multilayer Passive Constrained Layer Damping (PCLD) treatments are described. The motion equations and boundary conditions are derived by Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equations in state space are established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor and the frequency response of clamped-clamped multi-layer PCLD cylindrical shell is obtained. The results show that multi-layer PCLD cylindrical shell is more effective than the traditional three-layer PCLD cylindrical shell in suppressing vibration and noise if the same amount of material is applied. It demonstrates a potential application of multi-layer PCLD treatments in many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles
Li Li; Wen Ji-Hong; Cai Li; Zhao Hong-Gang; Wen Xi-Sen
2013-01-01
Using the multilayered cylinder model,we study acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials,which exhibit locally negative effective mass densities.A spring model is introduced to replace the traditional transfer matrix,which may be singular in the negative mass region.The backscattering form function and the scattering cross section are calculated to discuss the acoustic properties of the coated submerged cylindrical shell.
Seung-Bok Choi; Juncheol Jeon; Jung Woo Sohn; Heung Soo Kim
2013-01-01
In this work, active vibration control of an underwater cylindrical shell structure was investigated, to suppress structural vibration and structure-borne noise in water. Finite element modeling of the submerged cylindrical shell structure was developed, and experimentally evaluated. Modal reduction was conducted to obtain the reduced system equation for the active feedback control algorithm. Three Macro Fiber Composites (MFCs) were used as actuators and sensors. One MFC was used as an excite...
Using the multilayered cylinder model, we study acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials, which exhibit locally negative effective mass densities. A spring model is introduced to replace the traditional transfer matrix, which may be singular in the negative mass region. The backscattering form function and the scattering cross section are calculated to discuss the acoustic properties of the coated submerged cylindrical shell. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
吴林志; Kunio Funami
2002-01-01
The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. From the results obtained, it can be found that the electro-elastic field depends on the material constants of individual phases, the geometric parameters of the system and the applied antiplane shear stresses and electric fields at infinity. In addition, the specific cases when two circular cylindrical inclusions are tangent to each other and they are holes and/or rigid ones, are also studied in this paper.
Design guide for calculating hydrodynamic mass. Part I. Circular cylindrical structures
Many reactor and plant components contain, or are submerged in, a fluid. The fluid moving with a vibrating structure has an important effect on the dynamics of the structure, particularly on its natural frequencies. The effect of the fluid on natural frequencies can be accounted for using the hydrodynamic mass associated with the structure. The design guide provides formulas, graphs, and computer programs for calculating hydrodynamic masses of circular cylindrical structures
无
2009-01-01
We analyze thickness-shear vibration of an axially poled circular cylindrical tube with unattached electrodes and air gaps. Both free and electrically forced vibrations are studied. Exact solutions are obtained from the equations of linear piezoelectricity. Resonant frequencies and the impedance of the transducer are calculated from the solution. Results show that the resonant frequencies are sensitive to the dimensions of the air gaps when the gaps are thin. The impedance depends strongly on the air gaps.
The vector potential of a circular cylindrical antenna in terms of a toroidal harmonic expansion
Selvaggi, Jerry; Salon, Sheppard; Chari, M. V. K.
2008-08-01
A toroidal harmonic expansion is developed which is used to represent the vector potential due to a circular cylindrical antenna with a rectangular cross section at any arbitrary point in space. The singular part of the antenna kernel is represented by an associated toroidal harmonic expansion and the analytic part of the kernel is represented by a binomial expansion. A simple example is given to illustrate the application of the toroidal expansion.
Beirao Da Veiga, Lourenco
2001-01-01
We introduce, and numerically solve for decreasing thicknesses, particular toroidal and cylindrical shell problems which hold, due to load irregularity, an intermediate asymptotic behaviour. The numerical results are compared with those obtained applying a very recent asymptotic shell classification theory. Finally, we examine a local energy oscillation effect, with thickness-dependent frequency, that was found in all the problems treated.
A cylindrical shell with an axial crack under skew-symmetric loading.
Yuceoglu, U.; Erdogan, F.
1973-01-01
The skew-symmetric problem for a cylindrical shell containing an axial crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus may be evaluated from the measured Young's moduli and Poisson ratios and is not an independent material constant. The problem is solved within the confines of an eighth-order linearized shallow shell theory. As numerical examples, the torsion of an isotropic cylinder and that of a specially orthotropic cylinder (titanium) are considered. The membrane and bending components of the stress intensity factor are calculated and are given as functions of a dimensionless shell parameter. In the torsion problem for the axially cracked cylinder the bending effects appear to be much more significant than that found for the circumferentially cracked cylindrical shell. Also, as the shell parameter increases, unlike the results found in the pressurized shell, the bending stresses around crack ends do not change sign.
A note on the geometry of a cylindrical shell with screw dislocation
This Letter reports the equivalence of the geometries of a cylindrical shell with screw dislocation and another without defect but with a larger radius. The issue may have applications in condensed matter physics for models where quantum particles (such as electrons and holes) move on the walls of nanotubes. -- Highlights: ► Equivalence of effective geometries of cylindrical shells with defects. ► Physics of quantum particles moving on the shells will look the same. ► A nanotube could be replaced by a thinner nanotube with appropriate screw dislocation.
A note on the geometry of a cylindrical shell with screw dislocation
De Lorenci, Vitorio A., E-mail: delorenci@unifei.edu.br [Instituto de Ciências Exatas, Universidade Federal de Itajubá, Itajubá, MG 37500-903 (Brazil); Moreira, Edisom S., E-mail: moreira@unifei.edu.br [Instituto de Ciências Exatas, Universidade Federal de Itajubá, Itajubá, MG 37500-903 (Brazil)
2012-07-09
This Letter reports the equivalence of the geometries of a cylindrical shell with screw dislocation and another without defect but with a larger radius. The issue may have applications in condensed matter physics for models where quantum particles (such as electrons and holes) move on the walls of nanotubes. -- Highlights: ► Equivalence of effective geometries of cylindrical shells with defects. ► Physics of quantum particles moving on the shells will look the same. ► A nanotube could be replaced by a thinner nanotube with appropriate screw dislocation.
Crack Path Bifurcation at a Tear Strap in a Pressurized Stiffened Cylindrical Shell
Cowan, Amy Lorraine
1999-01-01
A finite element model of a fracture test specimen is developed using the STAGS computer code (STructural Analysis of General Shells). The test specimen was an internally pressurized, aluminum cylindrical shell reinforced with two externally bonded aluminum tear straps around its circumference. The shell contained an initial, axial through-crack centered between the straps. The crack propagated slowly in the axial direction as the pressure increased above a certain value until a maximum press...
Surya Narain
1981-04-01
Full Text Available This paper investigates magneto-elastic torsional waves in a composite non homogeneous cylindrical shell under initial stress. The non homogeneous character of the shell is due to the variable elastic constants C/sub ij/ and the variable density rho. The composite form of the shell is due to the combination of orthotropic elastic material and visco-elastic material of general linear type. Frequency equation for the said wave has been derived.
The bending vibration response and approximate calculation of elastic cylindrical shell
CHEN Xiao-li; SHENG Mei-ping; HE Chen
2006-01-01
Useful structure characteristics of elastic cylindrical shells have led them to being widely applied in virtual projects ,so it is important to conduct vibration research on the shells and find it's a simpler corresponding compact calculation method. Utilising the input and transfer point mobility of a thin plate structure, a theoretical expression of the cylindrical shell's bending vibration responsewas deduced and numerical simulations were done to simplify the theoretical expression within an acceptable error margin, greatly reducing the amount of computations. Furthermore, whole vibration response distributions of the cylindrical shell were analyzed. It was found thathe vibration energy propagates in helical form under mono-frequency excitation, while under bandwidth frequency excitation, it attenuates around in term of fluctuation. The axial attenuation rate of the vibration energy is larger than the circumferential attenuation rate.
Mechanical stability of cylindrical thin-shell wormholes
Sharif, M. [University of the Punjab, Department of Mathematics, Lahore (Pakistan); Azam, M. [University of Education, Division of Science and Technology, Lahore (Pakistan)
2013-04-15
In this paper, we apply the cut and paste procedure to the charged black string for the construction of a thin-shell wormhole. We consider the Darmois-Israel formalism to determine the surface stresses of the shell. We take the Chaplygin gas to deal with the matter distribution on shell. The radial perturbation approach (preserving the symmetry) is used to investigate the stability of static solutions. We conclude that stable static solutions exist both for uncharged and charged black string thin-shell wormholes for particular values of the parameters. (orig.)
A Circular-cylindrical Flux-rope Analytical Model for Magnetic Clouds
Nieves-Chinchilla, T.; Linton, M. G.; Hidalgo, M. A.; Vourlidas, A.; Savani, N. P.; Szabo, A.; Farrugia, C.; Yu, W.
2016-05-01
We present an analytical model to describe magnetic flux-rope topologies. When these structures are observed embedded in Interplanetary Coronal Mass Ejections (ICMEs) with a depressed proton temperature, they are called Magnetic Clouds (MCs). Our model extends the circular-cylindrical concept of Hidalgo et al. by introducing a general form for the radial dependence of the current density. This generalization provides information on the force distribution inside the flux rope in addition to the usual parameters of MC geometrical information and orientation. The generalized model provides flexibility for implementation in 3D MHD simulations. Here, we evaluate its performance in the reconstruction of MCs in in situ observations. Four Earth-directed ICME events, observed by the Wind spacecraft, are used to validate the technique. The events are selected from the ICME Wind list with the magnetic obstacle boundaries chosen consistently with the magnetic field and plasma in situ observations and with a new parameter (EPP, the Electron Pitch angle distribution Parameter) which quantifies the bidirectionally of the plasma electrons. The goodness of the fit is evaluated with a single correlation parameter to enable comparative analysis of the events. In general, at first glance, the model fits the selected events very well. However, a detailed analysis of events with signatures of significant compression indicates the need to explore geometries other than the circular-cylindrical. An extension of our current modeling framework to account for such non-circular CMEs will be presented in a forthcoming publication.
Relativistic dynamics of cylindrical shells of counter-rotating particles
Hamity, V H; Barraco, D E
2007-01-01
Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits of very small radius. We describe the analytical model using kinetic theory for the matter and the junction conditions through the shell to obtain its equation of motion. The nature of the static solutions are analyzed, both for a single shell as well as for two concentric shells. In this second case, for a time dependent external shell, we integrate numerically the equation of motion for several values of the constants of the system. Also, a brief description in terms of the Komar mass is given to account for the gravitational wave energy emitted by the system.
Ray-based modeling of reverberation in subsurface circular cylindrical void
Chen, Ping; Xia, Dan; Chen, Boyuan; Li, Lin; Li, Xiuzhong; Dong, Tian-lin
2011-03-01
Ray representation of electromagnetic resonance (reverberation) mode in subsurface circular cylindrical dielectric resonator (including void) is proposed. The modal ray path must be regular polygon or polystar. Travel time formulas for fundamental resonance multiples and the detecting conditions for non-exact-backscattering rays are derived. Simulation of time-distance curves of a modal hollow concrete block is generally concurred to the measured ground penetrating radar signal pattern. The proposed modeling method can be generalized to other resonant cavities with different profiles and provide a sound base for further applications of other more complicated geophysics science and engineering fields, particularly in ray-based tomography.
The purpose of this paper is the formulation of a Wave Concept Iterative Process (WCIP) for the analysis of the microwave planar circuits printed between two dielectric mediums in a cylindrical metallic box. This method is based on the transverse wave formulation. It also uses the Hankel Transform to express the integral relation in a spectral domain. An example of annular ring and circular patch loaded by annular ring has been studied and the obtained results validate the new approach. The good agreement between the simulation results and the experimental published data justifies the design procedure and validates the present analysis approach.
Paranin, Vyacheslav D.; Karpeev, Sergey V.; Kazanskiy, Nikolay L.; Krasnov, Andrey P.
2016-03-01
The optical system for converting laser beams with circular polarization to cylindrical vector beams on the basis of anisotropic crystals has been developed. The experimental research of beam formation quality has been carried out on the both polarization and structural characteristics. The research showed differences in the formation of the azimuthal and radial polarizations for Gaussian modes and Bessel beams. The boundaries of changes of the optical system parameters to form different types of polarizations with different amplitude and phase distributions have been identified.
Finite Element Modeling of a Fluid Filled Cylindrical Shell with Active Constrained Layer Damping
ZHANG Yi; ZHANG Zhi-yi; TONG Zong-peng; HUA Hong-xing
2005-01-01
On the basis of the piezoelectric theory, Mindlin plate theory, viscoelastic theory and ideal fluid equa tion, the finite element modeling of a fluid-filled cylindrical shell with active constrained layer damping (ACLD) was discussed. Energy methods and Lagrange's equation were used to obtain dynamic equations of the cylindrical shell with ACLD treatments, which was modeled as well with the finite element method. The GHM (Golla-Hughes-McTavish) method was applied to model the frequency dependent damping of viscoelastic material. Ideal and incompressible fluid was considered to establish the dynamic equations of the fluid-filled cylindrical shell with ACLD treatments, Numerical results obtained from the finite element analysis were compared with those from an experiment. The comparison shows that the proposed modeling method is accurate and reliable.
Effect of weld reinforcement on axial plastic buckling of welded steel cylindrical shells
Chu-lin YU; Zhi-ping CHEN; Ji WANG; Shun-juan YAN; Li-cai YANG
2012-01-01
The effect of weld reinforcement on axial plastic buckling of welded steel cylindrical shells is investigated through experimental and numerical buckling analysis using six welded steel cylindrical shell specimens.The relationship between the amplitude of weld reinforcement and the axial plastic buckling critical load is explored.The effect of the material yield strength and the number of circumferential welds on the axial plastic buckling is studied.Results show that circumferential weld reinforcement represents a severe imperfect form of axially compressed welded steel cylindrical shells and the axial plastic buckling critical load decreases with the increment of the mean amplitude of circumferential weld reinforcement.The material yield strength and the number of circumferential welds are found to have no significant effect on buckling waveforms; however,the axial plastic buckling critical load can be decreased to some extent with the increase of the number of circumferential welds.
Weak Formulation Study For Thermoelastic Buckling Analysis Of Thick Laminated Cylindrical Shells
Kewei Ding
2015-08-01
Full Text Available Weak formulations of mixed state equations of closed laminated cylindrical shells are presented in the Hamilton System. The Hamilton canonical equation of closed cylindrical shell is established. By means of applying the transfer matrix method and taking the advantage of Hamiltonian matrix in the calculation, a unified approach and three-dimensional thermoelastic solutions are obtained for the buckling analysis of closed thick laminated cylindrical shells. All equations of elasticity can be satisfied and all elastic constants can be taken into account. Numerical results are given to compare with those of FEM calculated using SAP5. The principle and method suggested here have clear physical concepts. The equations and boundary conditions proposed in this paper are weakened. The solutions and results given here may serve as a benchmark for other numerical procedures.
Electromagnetic Casimir densities for a cylindrical shell on de Sitter space
Saharian, A A; Saharyan, N A
2016-01-01
Complete set of cylindrical modes is constructed for the electromagnetic field inside and outside a cylindrical shell in the background of $(D+1)$% -dimensional dS spacetime. On the shell, the field obeys the generalized perfect conductor boundary condition. For the Bunch-Davies vacuum state, we evaluate the expectation values (VEVs) of the electric field squared and of the energy-momentum tensor. The shell-induced contributions are explicitly extracted. In this way, for points away from the shell, the renormalization is reduced to the one for the VEVs in the boundary-free dS bulk. As a special case, the VEVs are obtained for a cylindrical shell in the $(D+1)$% -dimensional Minkowski bulk. We show that the shell-induced contribution in the electric field squared is positive for both the interior and exterior regions. The corresponding Casimir-Polder forces are directed toward the shell. The vacuum energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component correspondin...
Frederico Martins Alves da Silva; Augusta Finotti Brazão; Paulo Batista Gonçalves
2015-01-01
This work investigates the influence of Young’s modulus, shells thickness, and geometrical imperfection uncertainties on the parametric instability loads of simply supported axially excited cylindrical shells. The Donnell nonlinear shallow shell theory is used for the displacement field of the cylindrical shell and the parameters under investigation are considered as uncertain parameters with a known probability density function in the equilibrium equation. The uncertainties are discretized a...
Kelker, D.; Langenberg, C.W.
1988-08-01
A folded surface can be represented by the orientation of normals to the surface measured at several locations. When plotted on the unit sphere, the pattern of normals determines the type of fold. Poles from a cylindrical fold give a great circle on the unit sphere, whereas poles of a circular conical fold give a small circle, and poles from an elliptical conical fold give the projection of an ellipse onto the surface of the sphere. Several statistical tests that appear in the literature for classifying folds are discussed and compared. All but one of the tests use quantities obtained from an iterative least-squares procedure that fits the appropriate curve on the sphere. The classification procedure is illustrated with folds from the Canadian Rocky Mountains and uses for examples a cylindrical fold and a circular conical fold from the Smoky River coal field near Grande Cache, Alberta, and an elliptical conical fold near Jasper, Alberta. This methodology has resulted in new coal reserves in the Grande Cache area.
Circular-cylindrical flux-rope analytical model for Magnetic Clouds
Nieves-Chinchilla, Teresa; Linton, Mark; Hidalgo, Miguel A.; Vourlidas, Angelos; Savani, Neel P.; Szabo, Adam; Farrugia, Charlie; Yu, Wenyuan
2016-05-01
We present an analytical model to describe magnetic flux-rope topologies. When these structures are observed embedded in Interplanetary Coronal Mass Ejections (ICMEs) with a depressed proton temperature, they are called Magnetic Clouds ( MCs). The model extends the circular-cylindrical concept of Hidalgo et al. (2000) by introducing a general form for the radial dependence of the current density. This generalization provides information on the force distribution inside the flux rope in addition to the usual parameters of MC geometrical information and orientation.The generalized model provides flexibility for implementation in 3D MHD simulations. Here, we evaluate its performance in the reconstruction of MCs in in-situ observations. Four Earth directed ICME events, observed by the Wind spacecraft, are used to validate the technique. The events are selected from the ICME Wind list with the magnetic obstacle boundaries chosen consistently with the magnetic fi eld and plasma in situ observations and with a new parameter (EPP, Electron Pitch angle distribution Parameter) which quantifies the bidirectionally of theplasma electrons. The goodness of the fit is evaluated with a single correlation parameter to enable comparative analysis of the events. In general, at first glance, the model fits the selected events very well. However, a detailed analysis of events with signatures of significant compression indicates the need to explore geometries other than the circular-cylindrical.
Cylindrical acoustic levitator/concentrator having non-circular cross-section
Kaduchak, Gregory; Sinha, Dipen N.
2003-11-11
A low-power, inexpensive acoustic apparatus for levitation and/or concentration of aerosols and small liquid/solid samples having particulates up to several millimeters in diameter in air or other fluids is described. It is constructed from a commercially available, hollow piezoelectric crystal which has been formed with a cylindrical cross-section to tune the resonance frequency of the breathing mode resonance of the crystal to that of the interior cavity of the cylinder. When the resonance frequency of the interior cylindrical cavity is matched to the breathing mode resonance of the cylindrical piezoelectric transducer, the acoustic efficiency for establishing a standing wave pattern in the cavity is high. By deforming the circular cross-section of the transducer, the acoustic force is concentrated along axial regions parallel to the axis of the transducer. The cylinder does not require accurate alignment of a resonant cavity. The concentrated regions of acoustic force cause particles in the fluid to concentrate within the regions of acoustic force for separation from the fluid.
Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique
Free vibration analysis of rotating cylindrical shells is presented. Discrete singular convolution (DSC) method has been proposed for numerical solution of vibration problem. The formulations are based on Love's first approximation shell theory, and include the effects of initial hoop tension and centrifugal and Coriolis accelerations due to rotation. Frequencies are obtained for different types of boundary conditions and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.
Temme, Michael W.
2003-01-01
CIVINS The thesis compares the analytical solution, two marine classification society design rules, and numerical analysis against experimental results for predicting the failure modes (general instability, axisymmetric buckling, and asymmetric collapse of the shell) and failure pressures of ring-stiffened cylindrical shells. The analytical solution is first summarized based on several sources. Design rules for the classification societies are then presented with brief explanations for e...
Non-linear Vibrations of Deep Cylindrical Shells by the p-Version Finite Element Method
Pedro Ribeiro
2010-01-01
Full Text Available A p-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with the p-model are found to be close to the ones computed using a commercial FE package. In all numerical tests the p-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.
Rose, Cheryl A.; Young, Richard D.; Starnes, James H., Jr.
1999-01-01
Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or "bulging factors" that account for increased stresses due to curvature for longitudinal cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in graphs of the bulging factor as a function of the applied load and as a function of geometric parameters that include the shell radius, the shell thickness and the crack length. The computed bulging factors are compared with solutions based on linear shallow shell theory, and with semi-empirical solutions that approximately account for the nonlinear deformation in the vicinity of the crack. The effect of biaxial loads on the computed bulging factors is also discussed.
Vibrational power flow of a finite cylindrical shell with discrete axial stiffeners
LIU Yanmei; HUANG Xieqing
2002-01-01
The structural wave power flows in an elastic finite cylindrical shell with discrete axial stiffeners are studied when a simple harmonic force is applied on it. The equations of motion of the shell are derived by using Flugge equation and Hamilton variational principle,and the responses of the shell are obtained. By use of the basic definition of the power flow, the characteristics of axial propagation of the power flow supplied by input structure and carried by different shell internal forces of a forced shell are investigated. The effects of parameters, such as relative location of driving force and stringer, driving force type and structural damping on the vibrational power flows in the shell, are discussed. These provide some theoretical bases for vibration control and noise reduction of this kind of structure.
薛明德; 王和慧; 陈伟; 黄克智
1999-01-01
The stress analysis based on the theory of a thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to external moment loads on the ends of shells with a large diameter ratio （ρ0≤0.8）. Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable to ρ0 （R/T）1/2（?）1, is used for the analysis of the shell with cutout. The solution in terms of displacement function for the nozzle with a nonplanar end is based on the Goldenveizer equation. The boundary forces and displacements at the intersection are all transformed from Gaussian coordinates （α, β） on the shell, or Gaussian coordinates （ζ, θ） on the nozzle into three-dimensional cylindrical coordinates （ρ, θ, z）. Their expressions on the intersecting curve are periodic functions of θ and expanded in Fourier series. Every harmonic of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature. The results obtained are in agreement with
Demagnetization factors for cylindrical shells and related shapes
Beleggia, M.; Vokoun, David; De Graef, M.
2009-01-01
Roč. 321, č. 9 (2009), s. 1306-1315. ISSN 0304-8853 EU Projects: European Commission(XE) 46559 - CERINKA Institutional research plan: CEZ:AV0Z10100520 Keywords : demagnetization factor * magnetostaticenergy * nano-ring * core-shell * dipolar interaction * shape anisotropy Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.204, year: 2009
王吉; 王肖钧; 王峰; 赵凯
2004-01-01
With finite-element software ANSYS 7.0 and simple thermal-mechanical coupling constitutive relations,the buckling failure of preloaded cylindrical shell irradiated by high power laser beam was studied by numerical simulations. The buckling mode and buckling critical loading were analysed for different preloading conditions. The influence of laser intensity, beam irradiation time, preloading conditions and geometric parameters of cylindrical shell on the buckling mode were discussed. The numerical results show that: ① the buckling deformation of the cylindrical shell was concentrated in the area of laser spot and the radial buckling was the main buckling mode, ② a linear relationship between the buckling eigenvalue and the maximum temperature at the center of laser spot was approached, ③ the buckling failure of cylindrical shell was attributed to the coupling effect of the material softening and the radial deformation in the laser spot, and hence to raise the stiffness of the material would enhance the ability for anti-irradiation of structure substantially.
Thin Circular Disc Shells of Radio Sources Around Supernova Remnant G16.2-2.7
俞志尧
2002-01-01
We propose a new model of distinct thin circular disc shells to analyse the radio map of the supernova remnant (SNR) G16.2-2.7 from NRAO VLA Sky Survey at 1.4 GHz and the radio sources around it. It is obtained that the 20 radio sources around the SNR G16.2-2.7 distribute on the four thin circular disc shells. The results support the shell-like structure strongly and further indicate that the shell-like structure is several thin circular disc shells. Because the shell-like structure dominates the total sample, our result is important for research of the radio morphology of SNRs.
Buckling characteristic of multi-laminated composite elliptical cylindrical shells
Kassegne, Samuel Kinde; Chun, Kyoung-Sik
2015-03-01
Fiber-reinforced composite materials continue to experience increased adoption in aerospace, marine, automobile, and civil structures due to their high specific strength, high stiffness, and light weight. This increased use has been accompanied by applications involving non-traditional configurations such as compression members with elliptical cross-sections. To model such shapes, we develop and report an improved generalized shell element called 4EAS-FS through a combination of enhanced assumed strain and the substitute shear strain fields. A flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. We use the element developed to determine specifically buckling loads and mode shapes of composite laminates with elliptical cross-section including transverse shear deformations. The combined influence of shell geometry and elliptical cross-sectional parameters, fiber angle, and lay-up on the buckling loads of an elliptical cylinder is examined. It is hoped that the critical buckling loads and mode shapes presented here will serve as a benchmark for future investigations.
Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys
Asadi, H.; Akbarzadeh, A. H.; Chen, Z. T.; Aghdam, M. M.
2015-04-01
The present paper deals with the nonlinear thermal instability of geometrically imperfect sandwich cylindrical shells under uniform heating. The sandwich shells are made of a shape memory alloy (SMA)-fiber-reinforced composite and functionally graded (FG) face sheets (FG/SMA/FG). The Brinson phenomenological model is used to express the constitutive characteristics of SMA fibers. The governing equations are established within the framework of the third-order shear deformation shell theory by taking into account the von Karman geometrical nonlinearity and initial imperfection. The material properties of constituents are assumed to be temperature dependent. The Galerkin technique is utilized to derive expressions of the bifurcation points and bifurcation paths of the sandwich cylindrical shells. Using the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of the SMA fiber volume fraction, SMA pre-strain, core thickness, non-homogeneity index, geometrical imperfection, geometry parameters of sandwich shells and temperature dependency of materials on the stability of shells. The results reveal that proper application of SMA fibers postpones the thermal bifurcation point and dramatically decreases thermal post-buckling deflection. Moreover, the induced tensile recovery stress of SMA fibers could also stabilize the geometrically imperfect shells during the inverse martensite phase transformation.
Active structural acoustic control of a smart cylindrical shell using a virtual microphone
Loghmani, Ali; Danesh, Mohammad; Kwak, Moon K.; Keshmiri, Mehdi
2016-04-01
This paper investigates the active structural acoustic control of sound radiated from a smart cylindrical shell. The cylinder is equipped with piezoelectric sensors and actuators to estimate and control the sound pressure that radiates from the smart shell. This estimated pressure is referred to as a virtual microphone, and it can be used in control systems instead of actual microphones to attenuate noise due to structural vibrations. To this end, the dynamic model for the smart cylinder is derived using the extended Hamilton’s principle, the Sanders shell theory and the assumed mode method. The simplified Kirchhoff-Helmholtz integral estimates the far-field sound pressure radiating from the baffled cylindrical shell. A modified higher harmonic controller that can cope with a harmonic disturbance is designed and experimentally evaluated. The experimental tests were carried out on a baffled cylindrical aluminum shell in an anechoic chamber. The frequency response for the theoretical virtual microphone and the experimental actual microphone are in good agreement with each other, and the results show the effectiveness of the designed virtual microphone and controller in attenuating the radiated sound.
Free vibration of composite skewed cylindrical shell panel by finite element method
Haldar, Salil
2008-03-01
In this paper a composite triangular shallow shell element has been used for free vibration analysis of laminated composite skewed cylindrical shell panels. In the present element first-order shear deformation theory has been incorporated by taking transverse displacement and bending rotations as independent field variables. The interpolation function used to approximate transverse displacement is one order higher than for bending rotations. This has made the element free from locking in shear. Two types of mass lumping schemes have been recommended. In one of the mass lumping scheme the effect of rotary inertia has been incorporated in the element formulations. Free vibration of skewed composite cylindrical shell panels having different thickness to radius ratios ( h/R=0.01-0.2), length to radius ratios ( L/R), number of layers and fiber orientation angles have been analyzed following the shallow shell method. The results for few examples obtained in the present analysis have compared with the published results. Some new results of composite skewed cylindrical shell panels have been presented which are expected to be useful to future research in this direction.
Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.
2000-01-01
Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.
Initial imperfection survey on a cylindrical shell at the Ultra-Centrifuge Nederland n.v
The results of the initial imperfection survey of a circular shell, with an inner- and outer-skin made out of carbon fibres with an aluminium honey-comb in between, are presented. At UCN the shell is called the ''Demonstrator Model'' shortly the ''Demonstrator''. The modal components of the measured imperfection surface as a function of the circumferential and axial wave numbers are calculated. The characteristic imperfection distributions associated with the fabrication process used are presented. (orig.)
Kim, Young-Wann
2015-12-01
The free vibration characteristics of fluid-filled functionally graded cylindrical shells buried partially in elastic foundations are investigated by an analytical method. The elastic foundation of partial axial and angular dimensions is represented by the Pasternak model. The motion of the shells is represented by the first-order shear deformation theory to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shells are composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The governing equation is obtained using the Rayleigh-Ritz method and a variation approach. The fluid is described by the classical potential flow theory. Numerical examples are presented and compared with existing available results to validate the present method.
Dispersion of axially symmetric waves in fluid-filled cylindrical shells
Bao, X.L.; Überall, H.; Raju, P. K.;
2000-01-01
in striking contrast to the results for double (outside and inside) loading by two fluids of comparable density, where circumferential waves in both external and internal fluids were found, their interaction causing segmentation and repulsion phenomena of their dispersion curves. The condition of......Acoustic waves normally incident on an elastic cylindrical shell can cause the excitation of circumferential elastic waves on the shell. These shells may be empty and fluid immersed, or fluid filled in an ambient medium of air, or doubly fluid loaded inside and out. Circumferential waves on such......, 317 (1972)]. We have extended the work of Kumar to the case of fluid-filled aluminum shells and steel shells imbedded in air. These cases demonstrate the existence of circumferential waves traveling in the filler fluid, exhibiting a certain simplicity of the dispersion curves of these waves. This is...
CAPILLARY EFFECT ON VERTICALLY EXCITED SURFACE WAVE IN CIRCULAR CYLINDRICAL VESSEL
JIAN Yong-jun; E Xue-quan; ZHANG Jie
2006-01-01
In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension. A nonlinear slowly varying amplitude equation, which incorporates cubic nonlinear term,external excitation and the influence of surface tension, was derived from potential flow equation. The results show that, when forced frequency is lower, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is higher, the surface tension can not be neglected. This proved that the surface tension causes free surface returning to equilibrium location. In addition, due to considering the effect of surface tension, the theoretical result approaches to experimental results much more than that of no surface tension.
Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Mixing in Stratified Cylindrical Shells
Mikaelian, K O
2004-04-15
We study the linear stability of an arbitrary number N of cylindrical concentric shells undergoing a radial implosion or explosion.We derive the evolution equation for the perturbation {eta}{sub i} at interface i; it is coupled to the two adjacent interfaces via {eta}{sub i{+-}1}. For N=2, where there is only one interface, we verify Bell's conjecture as to the form of the evolution equation for arbitrary {rho}{sub 1} and {rho}{sub 2}, the fluid densities on either side of the interface. We obtain several analytic solutions for the N=2 and 3 cases. We discuss freeze-out, a phenomenon that can occur in all three geometries (planar, cylindrical, or spherical), and ''critical modes'' that are stable for any implosion or explosion history and occur only in cylindrical or spherical geometries. We present numerical simulations of possible gelatin-ring experiments illustrating perturbation feedthrough from one interface to another. We also develop a simple model for the evolution of turbulent mix in cylindrical geometry and define a geometrical factor G as the ratio h{sub cylindrical}/h{sub planar} between cylindrical and planar mixing layers. We find that G is a decreasing function of R/R{sub o}, implying that in our model h{sub cylindrical} evolves faster (slower) than h{sub planar} during an implosion (explosion).
Study of the vibration of bulkhead-stiffened cylindrical shells by laser-based methods
Zhu, Ninghui
The first part of this dissertation work deals with an experimental study of the vibration behavior of bulkhead stiffened cylindrical shells by using laser-based vibration measurement methods. Holographic interferometry and laser speckle photography are first demonstrated on revealing the dynamic behavior of a 22 ft long cylindrical shell. These methods are thereafter further explored to study the vibration characteristic of cylindrical shells with different stiffeners such as a full bulkhead or a partial bulkhead. Many experimentally obtained holograms and specklegrams reveal interesting features of the vibration of bulkhead stiffened cylindrical shells. The experimentally obtained results are compared with those obtained from a finite element model developed by General Dynamic Electric Boat Division, and the finite element model is generally validated. Mode localization theory is used to explain some interesting findings in experiments and the reason of some discrepancies between the finite element analysis and experiment results. The presence of irregularities in a weakly coupled structure such as a bulkhead-stiffened cylindrical shell is shown to be able to localize the modes of vibration and inhibit the propagation of vibration within the shell. A numerical simulation based on the finite element modal analysis indicates the validation of this explanation of the experimental findings. Thereafter, the eigensolutions of disordered, plate-stiffened cylindrical shell stiffened are derived by the use of receptance method. Numerical calculations are thereafter performed based upon this model and indeed reveal the exist of localized vibration in this kind of structure. This analytical study provides physical insights into the mode localization phenomenon in stiffened cylindrical shell type of structures from a more systematic manner. The conditions and the effect of mode localization on natural frequencies and mode shapes of cylindrical shell structure are also
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Liu Chang-Jiang
2011-01-01
Full Text Available This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM with spline function method (SFM to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.
Effectiveness of the magnetostatic shielding by the cylindrical shells
Grabchikov, S. S.; Trukhanov, A. V.; Trukhanov, S. V.; Kazakevich, I. S.; Solobay, A. A.; Erofeenko, V. T.; Vasilenkov, N. A.; Volkova, O. S.; Shakin, A.
2016-01-01
The experimental research of the magnetostatic shielding effectiveness and the analytical calculations of the average magnetic permeability of single-layer cylindrical sample of the shields based on electrolytically deposited Ni80Fe20 alloy are carried out. The locations of maxima on the Ef(H) and μ(H) curves do not match each other, which is difficult to interpret in terms of the shunting model. The results are explained by the non-linear distribution of the magnetic permeability through the thickness of the shield. It has been shown that in the magnetic fields range from 100 A/m up to 2700 A/m, the shields based on the Ni80Fe20 alloy are preferred over ones based on the 84KHSR amorphous ribbon. It is concluded that at the selection of shield materials it should take into account not only the main magnetic characteristics - μ; Hs; Hc but also Hmax parameter, which is important to evaluate the effectiveness of magnetic shielding.
Characterization of plasticity and fracture of shell casing of lithium-ion cylindrical battery
Zhang, Xiaowei; Wierzbicki, Tomasz
2015-04-01
Most of the literature on lithium-ion battery cells is concerned with modeling of jellyroll with little attention to properties of shell casing. However, shell casing provides substantial strength and fracture resistance under mechanical loading and therefore must be an important part of modeling of lithium-ion batteries. The paper reports on a comprehensive test program on commercially available empty shell casing of 18650 lithium-ion cylindrical cells. Part of the tests was used to determine plastic and fracture properties from sub-size specimens cut from lateral part of the cans. The other part served to validate plasticity and fracture models under various loading conditions. The associated flow rule was used to simulate plasticity behavior and Modified Mohr-Coulomb (MMC) fracture model was adopted to predict crack initiation and propagation of shell casing. Simulation results confirmed that present plasticity and fracture models could predict global plastic behavior of the cells under different loading conditions. The jellyroll model with volumetric hardening was introduced to compare the performance of empty shell casing, bare jellyroll and complete battery cell. It was shown that in many loading situations, for example, three point bending of the cylindrical cells, the metallic shell casing provides most of mechanical resistance.
Modal analysis of thin cylindrical shells with cardboard liners and estimation of loss factors
Koruk, Hasan; Dreyer, Jason T.; Singh, Rajendra
2014-04-01
Cardboard liners are often installed within automotive drive shafts to reduce radiated noise over a certain frequency range. However, the precise mechanisms that yield noise attenuation are not well understood. To overcome this void, a thin shell (under free boundaries) with different cardboard liner thicknesses is examined using analytical, computational and experimental methods. First, an experimental procedure is introduced to determine the modal behavior of a cylindrical shell with a cardboard liner. Then, acoustic and vibration frequency response functions are measured in acoustic free field, and natural frequencies and the loss factors of structures are determined. The adverse effects caused by closely spaced modes during the identification of modal loss factors are minimized, and variations in measured natural frequencies and loss factors are explored. Material properties of a cardboard liner are also determined using an elastic plate treated with a thin liner. Finally, the natural frequencies and modal loss factors of a cylindrical shell with cardboard liners are estimated using analytical and computational methods, and the sources of damping mechanisms are identified. The proposed procedure can be effectively used to model a damped cylindrical shell (with a cardboard liner) to predict its vibro-acoustic response.
Investigating the transitional state between circular plates and shallow spherical shells
Moayyad Al-Nasra; Mohamad Daoud
2015-01-01
The stiffness of circular plates can be increased by inducing a rise at the center of these plates; this rise converts the circular plates from two-dimensional stiffness elements into three-dimensional stiffness elements. This slight change in the geometry shifts the state of stresses from mainly bending stresses to tensilecompressive stresses. The rise at the center of a circular plate is increased gradually to the point where a shell element is formed. This paper focuses on this particul...
Villalobos Mendoza, Brenda; Cordero Davila, Alberto [Benemerita Universidad Autonoma de Puebla, 4 Sur 104 Centra Historico C.P. 72000, Puebla, Pue. (Mexico); Gonzalez Garcia, Jorge, E-mail: bvillalobosmendoza@gmail.com [Universidad Tecnologica de la Mixteca, Carretera Huajuapan-Acatlima, Km 2.5, CP. 6900, Huajuapan de Leon, Oaxaca (Mexico)
2011-01-01
This paper describes the construction of an elliptical-cylindrical model without spherical aberration using vertical rotating tools. The engine of the circular tool is placed on one arm so that the tool fits on the surface and this in turn is moved by an X-Y table. The test method and computer algorithms that predict the desired wear are described.
This paper describes the construction of an elliptical-cylindrical model without spherical aberration using vertical rotating tools. The engine of the circular tool is placed on one arm so that the tool fits on the surface and this in turn is moved by an X-Y table. The test method and computer algorithms that predict the desired wear are described.
In this paper, an analytical approach to the static behavior of functionally graded material (FGM) cylindrical shells with simply supported edges is developed. The Poisson's ratios of the FGM shell are assumed to be constant, but it is the modulus of elasticity which varies continuously through the radial direction according to the exponential function. The shell has finite length and embedded piezoelectric layers. The partial differential equilibrium equations as well as the stress–displacement relations are reduced to the ordinary one with constant coefficient by using the Fourier series expansion. Finally, the problem is solved by using the state space method. Numerical results are given to demonstrate the accuracy of the presented method. The influences of the gradient index, applied voltage and radius to thickness ratios on the static behavior of FGM shells are also studied
This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)
Free Vibration Characteristics of Cylindrical Shells Using a Wave Propagation Method
A. Ghoshal
2001-01-01
Full Text Available In the present paper, concept of a periodic structure is used to study the characteristics of the natural frequencies of a complete unstiffened cylindrical shell. A segment of the shell between two consecutive nodal points is chosen to be a periodic structural element. The present effort is to modify Mead and Bardell's approach to study the free vibration characteristics of unstiffened cylindrical shell. The Love-Timoshenko formulation for the strain energy is used in conjunction with Hamilton's principle to compute the natural propagation constants for two shell geometries and different circumferential nodal patterns employing Floquet's principle. The natural frequencies were obtained using Sengupta's method and were compared with those obtained from classical Arnold-Warburton's method. The results from the wave propagation method were found to compare identically with the classical methods, since both the methods lead to the exact solution of the same problem. Thus consideration of the shell segment between two consecutive nodal points as a periodic structure is validated. The variations of the phase constants at the lower bounding frequency for the first propagation band for different nodal patterns have been computed. The method is highly computationally efficient.
TAO Meng; FAN Jun; TANG Weilin
2009-01-01
The effect of multiple compliant layers on sound radiation from a finite cylindrical shell immersed in an infinite acoustic medium is studied. The transfer matrix is derived according to the continuous boundary conditions at each adjacent interface of the multi-layer system.With the shell theory and the acoustic wave equation, the theoretical model is developed to estimate the characteristics of sound radiation. The numerical calculation results show that the amount of the acoustic radiation power reduction increases as the wave speed or the density of the compliant layer decreases, and using multi-layer system could be more effective on noise reduction than the corresponding uniform single layer.
Analyses of a Dipole Antenna Loaded by a Cylindrical Shell of Double Negative (DNG Metamaterial
Khan M. Z. Shams
2007-10-01
Full Text Available The current distribution, input impedance, and radiation pattern of a cylindrical dipole antenna enclosed by a thin cylindrical shell of double negative (DNG metamaterial are computed using the piecewise sinusoidal Galerkin formulation. In the presence of the DNG shell, the dipole antenna exhibits three interesting characteristics. The input impedance shows potentials for wide bandwidth due to the relative insensitivity of the impedance with frequency. Within specific ranges of DNG material parameter values, the dipole shows resonance at much lower frequencies than its resonant frequency in free space. The dipole does not show change in the direction of the principal beam nor does it show signs of beam splitting and side lobes even when the antenna length approaches one and a half wavelength.
LOAD CARRYING CAPABILITY OF LIQUID FILLED CYLINDRICAL SHELL STRUCTURES UNDER AXIAL COMPRESSION
QASIM H. SHAH
2011-08-01
Full Text Available Empty and water filled cylindrical Tin (Sn coated steel cans were loaded under axial compression at varying loading rates to study their resistance to withstand accidental loads. Compared to empty cans the water filled cans exhibit greater resistance to axially applied compression loads before a complete collapse. The time and load or stroke and load plots showed three significant load peaks related to three stages during loading until the cylinder collapse. First peak corresponds to the initial structural buckling of can. Second peak occurs when cylindrical can walls gradually come into full contact with water. The third peak shows the maximum load carrying capability of the structure where pressurized water deforms the can walls into curved shape until can walls fail under peak pressure. The collapse process of water filled cylindrical shell was further studied using Smooth Particle Hydrodynamics (SPH technique in LSDYNA. Load peaks observed in the experimental work were successfully simulated which substantiated the experimental work.
Stress of anisotropic structure vaults consisting of cylindrical shells. Part I
A method is described for the numerical solution of problems based on analytical relations derived for bending deformation of a cylindrical shell stressed with radially flat, rotationally asymmetrical loads. The relations are expressed and processed by a matrix representation suitable for cascade-type calculation with free parameters and for computer processing. The method thus permits the designing of vaults of arbitrary eccentricities and variable thicknesses. A vault of this particular type is fairly common in nuclear reactor constructions. (M.S.)
The graduated cylindrical shell (GCS) model developed by Thernisien et al. has been used with the goal of studying the three-dimensional morphology, position, and kinematics of coronal mass ejections observed by coronagraphs. These studies focused more on the results rather than the details of the model itself. As more researchers begin to use the model, it becomes necessary to provide a deeper discussion on how it is derived, which is the purpose of this paper. The model is built using the following features and constraints: (1) the legs are conical, (2) the front is pseudo-circular, (3) the cross section is circular, and (4) it expands in a self-similar way. We derive the equation of the model from these constraints. We also show that the ice-cream cone model is a limit of the GCS when the two legs overlap completely. Finally, we provide formulae for the calculation of various geometrical dimensions, such as angular width and aspect ratio, as well as the pseudo-code that is used for its computer implementation.
Gonçalves, P. B.; Silva, F. M. A.; Del Prado, Z. J. G. N.
2008-08-01
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases where time-consuming numerical procedures are required. This paper discusses the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells. In order to understand the peculiarities inherent to this class of structural problems, the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads. Geometric nonlinearities due to finite-amplitude shell motions are considered by using Donnell's nonlinear shallow-shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the Galerkin method using modal expansions for the displacements that satisfy all the relevant boundary and symmetry conditions. Next, the model is analyzed via the Karhunen-Loève expansion to investigate the relative importance of each mode obtained by the perturbation solution on the nonlinear response and total energy of the system. The responses of several low-dimensional models are compared. It is shown that rather low-dimensional but properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.
Analysis of Experimental Research on Cyclones with Cylindrical and Spiral Shells
Aleksandras Chlebnikovas
2012-12-01
Full Text Available The conducted investigation is aimed at providing information on air flow parameters in the cylindrical and spiral shell (devices are designed for separating solid particles from air flow having tangent flow inlet. Experimental research has employed multi-cyclones created by the Department of Environmental Protection at Vilnius Gediminas Technical University. The study is focused on investigating and comparing the distribution of the dynamic pressure of the airflow in six-channel cyclones inside the structures of devices. The paper establishes and estimates the efficiency of air cleaning changing air phase parameters using different particulate matters. The efficiency of the cyclone has been defined applying the weighted method based on LAND 28-98/M-08 methodology. The article presents the results of experimental research on the air cleaning efficiency of cylindrical and spiral shells using 20 µm glass and clay particulate matter under the initial concentration that may vary from 500 mg/m3 to 15 g/m3 using semi-rings with windows at different positions. The obtained results has shown that the maximum efficiency of the cylindrical shell increases up to 87,3 % while the initial concentration of glass makes 15 g/m3.Article in Lithuanian
Parametric Analysis of A Submerged Cylindrical Shell Subjected to Shock Waves
LI Shang-ming; FAN Sau-Cheong
2007-01-01
In this study,an FEM-SBFEM (scaled boundary finite element method) coupling procedure proposed by Fan et al.(2005) is adopted to obtain the dynamic responses of a submerged cylindrical shell subjected to plane step or exponential acoustic shock waves.The coupling procedure can readily be applied to three-dimensional problem,however for clarity,the problems to be presented are limited to two-dimensional domain.In the analyses,the cylindrical shell is modeled by simple beam elements (using FEM),while the effects of the surrounding infinite fluid is modeled by the SBFEM.In it,no free surface and seabed are involved.Compared with Fan and his co-authors' works,the FEM-SBFEM coupling procedure is further verified to be feasible for shock waves by benchmark examples.Furthermore,parametric studies are performed and presented to gain insight into effects of the geometric and material properties of the cylindrical shell on its dynamic responses.
Cavitation problems in plant's piping system have been investigated on the basis of high-speed observation. Cavitation is one of the important factors with potential damage in piping system at nuclear power plant. In a power plant, there is cavitation occurrence to be expected in some local places such as an orifice, a valve and a pressure reducer. We have investigated about unsteady behavior and impact of cavitation in a long orifice with an abruptly expanding pipe. In this study, some detailed cavitation behaviors are observed by varying cavitating condition in the orifice throat and downstream of the orifice. High-speed behaviors of cavitation are observed by means of a high-speed video camera with a laser sheet in order to observe the inside of the circular orifice. Then images are analyzed using a frame difference method. As a result, we observe a series of cavitation developing process with decrease in cavitation number such as 1: cavitation inception occurs at the inlet of orifice, 2: cavitation develops in the throat of the orifice, 3: large-scale cavitation clouds appear downstream of the orifice, 4: liquid jet appears when the pressure downstream of the orifice decrease to about vapor pressure. Cavitation clouds in a circular cylindrical orifice with abruptly expanding part show some unsteadiness even in the steady operating condition. Cavitation clouds also show a large-scale shedding behavior in the transition stage to a liquid jet condition. In addition, we observe that the interface instability of a liquid jet downstream of the orifice depends on the cavitation instability in the orifice throat. (author)
LOW-FREQUENCY MAGNETIC FIELD SHIELDING BY A CIRCULAR PASSIVE LOOP AND CLOSED SHELLS
V.S. Grinchenko
2016-05-01
Full Text Available Purpose. To analyze the shielding factors for a circular passive loop and conductive closed shells placed in a homogeneous low-frequency magnetic field. Methodology. We have obtained simplified expressions for the shielding factors for a circular passive loop and a thin spherical shell. In addition, we have developed the numerical model of a thin cubical shell in a magnetic field, which allows exploring its shielding characteristics. Results. We have obtained dependences of the shielding factors for passive loops and shells on the frequency of the external field. Analytically determined frequency of the external magnetic field, below which field shielding of a passive loop is expedient to use, above which it is advisable to use a shielding shell.
Mahadev, Sthanu
Continued research and development efforts devoted in recent years have generated novel avenues towards the advancement of efficient and effective, slender laminated fiber-reinforced composite members. Numerous studies have focused on the modeling and response characterization of composite structures with particular relevance to thin-walled cylindrical composite shells. This class of shell configurations is being actively explored to fully determine their mechanical efficacy as primary aerospace structural members. The proposed research is targeted towards formulating a composite shell theory based prognosis methodology that entails an elaborate analysis and investigation of thin-walled cylindrical shell type laminated composite configurations that are highly desirable in increasing number of mechanical and aerospace applications. The prime motivation to adopt this theory arises from its superior ability to generate simple yet viable closed-form analytical solution procedure to numerous geometrically intense, inherent curvature possessing composite structures. This analytical evaluative routine offers to acquire a first-hand insight on the primary mechanical characteristics that essentially govern the behavior of slender composite shells under typical static loading conditions. Current work exposes the robustness of this mathematical framework via demonstrating its potential towards the prediction of structural properties such as axial stiffness and bending stiffness respectively. Longitudinal ply-stress computations are investigated upon deriving the global stiffness matrix model for composite cylindrical tubes with circular cross-sections. Additionally, this work employs a finite element based numerical technique to substantiate the analytical results reported for cylindrically shaped circular composite tubes. Furthermore, this concept development is extended to the study of thin-walled, open cross-sectioned, curved laminated shells that are geometrically
Vibration analysis of axisymmetric and beam like cylindrical shells containing flowing fluid
The free vibration characteristics of anisotropic laminated thin cylindrical shells partially or completely filled with liquid or subjected to a flowing fluid are studied in this work for two circumferential wave number n=0, axisymmetric, and n=1, beam-like. The shear deformation effects are taken into account in this theory therefore the equations of motion are determined with displacements and transverse shear as independent variables. The present method is a combination of finite element analysis and refined shell theory in which the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear coordinates. Mass and stiffness matrices are determined by precise analytical integration. A finite element is developed for the liquid in case of potential flow which yields three forces (inertial, centrifugal and Coriolis) of moving fluid. The mass, stiffness and damping matrices due to the fluid effect are obtained by an analytical integration of the fluid pressure over the liquid element. The available solution based on the Sanders' theory is also obtained from the present theory in the limiting case of the transverse shear rigidities. The natural frequencies of the isotropic and anisotropic cylindrical shells in cases of empty, partially or completely filled with liquid as well as subjected to a flowing fluid are given and compared with the corresponding results of existing available theories, very good agreement is obtained. (authors)
Thermal stresses in a spherical shell with a circular elastic inclusion
Thermal stress analysis of a spherical shell with a circular elastic inclusion is presented. Using Reissner's theory for thin shallow spherical shells, displacements and stresses are obtained in the shell and the inclusion in terms of Hankel and Bessel function. The thermal loading is assumed to be given by a temperature which is uniform on the inner and outer surfaces of the shell and the inclusion but may vary linearly across the thickness. The thermal stress problem is converted into an equivalent static loading problem. The satisfaction of the boundary conditions at the shell inclusion junction leads to the evaluation of the unknowns in the solutions. Results obtained show the inadequacy of flat plate solutions and the effect of curvature. The effect of various parameters of the problem such as elastic moduli, coefficients of linear expansion, curvature parameters is studied. Limiting cases of a rigid circular inclusion either free to move with the shell or clamped are also considered and the results are compared with the existing analytical solutions. Stress concentrations that are developed are presented in graphical form which is useful in the design of spherical shells containing a rigid or an elastic inclusion. It is found that a clamped rigid inclusion results in a more severe stress concentration than a rigid inclusion free to move with the shell. The maximum principal stress in a uniformly heated spherical shell with a circular elastic inclusion is found to be tensile in the shell and compressive in the inclusion. An increase in Esub(c)/Esub(s) or αsub(c)/αsub(s) (Esub(c), αsub(c), Esub(s), αsub(s) are the elastic modulus and coefficient of linear expansion of the inclusion and the shell material, respectively) causes an increase in the shell stresses and a reduction in the inclusion stresses
INTERNAL RESONANT INTERACTIONS OF THREE FREE SURFACE-WAVES IN A CIRCULAR CYLINDRICAL BASIN
马晨明
2003-01-01
The basic equations of free capillary-gravity surface-waves in a circular cylindrical basin were derived from Luke' s principle. Taking Galerkin ' s expansion of the velocity potential and the free surface elevation, the second-order perturbation equations were derived by use of expansion of multiple scale. The nonlinear interactions with the second order internal resonance of three free surface-waves were discussed based on the above. The results include:derivation of the couple equations of resonant interactions among three waves and the conservation laws; analysis of the positions of equilibrium points in phase plane; study of the resonant parameters and the non-resonant parameters respectively in all kinds of circumstances; derivation of the stationary solutions of the second-order interaction equations corresponding to different parameters and analysis of the stability property of the solutions; discussion of the effective solutions only in the limited time range. The analysis makes it clear that the energy transformation mode among three waves differs because of the different initial conditions under nontrivial circumstance. The energy may either exchange among three waves periodically or damp or increase in single waves.
Extension, inflation and torsion of a residually stressed circular cylindrical tube
Merodio, José; Ogden, Ray W.
2016-03-01
In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.
Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel
Jian Yong-Jun; E Xue-Quan
2004-01-01
Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.
Ali Nouri
2014-01-01
Full Text Available The maximizing of sound transmission loss (TL across a functionally graded material (FGM cylindrical shell has been conducted using a genetic algorithm (GA. To prevent the softening effect from occurring due to optimization, the objective function is modified based on the first resonant frequency. Optimization is performed over the frequency range 1000–4000 Hz, where the ear is the most sensitive. The weighting constants are chosen here to correspond to an A-weighting scale. Since the weight of the shell structure is an important concern in most applications, the weight of the optimized structure is constrained. Several traditional materials are used and the result shows that optimized shells with aluminum-nickel and aluminum-steel FGM are the most effective at maximizing TL at both stiffness and mass control region, while they have minimum weight.
Influence of transverse shear on plasticity around an axial crack in a cylindrical shell
The paper presents a plasticity model for deep axial surface cracks in pressurized pipes. The model is used in an investigation of the relative merits of fracture criteria based on COD and plastic instability. Recent investigations have shown that the inconsistency of the singular bending stress field in an axially cracked cylindrical shell arising from use of classical 8th order shallow shell theory is removed, when use is made of a 10th order shell theory, which accounts for transverse shear deformations. Although the membrane stresses are only moderately affected, the influence on the bending stresses is considerable. In the case of surface cracks moments are induced to the eccentricity of the crack, and transverse shear effects should therefore be included. (Auth.)
Sound scattering by free surface piercing and fluid-loaded cylindrical shells.
Avital, Eldad J; Miloh, Touvia
2011-07-28
A vertical flexible, thin, cylindrical shell is considered to be clamped to a rigid base in shallow water and piercing its surface. The shell is composed of an isotropic and homogeneous material and may be empty inside or filled with compressible fluid. Linear acoustics and structural dynamics are used to model sound scattering caused by an external incident sound wave. A solution is derived using a Fourier transform in the tangential and vertical directions. A collocation technique coupled with an orthogonalization procedure is used to account for the edge conditions of the shell. It is shown that zero sound scattering, indicating acoustic invisibility, is theoretically attainable and can be achieved when a continuous distribution of an oscillating pressure load is applied on the shell's wall. Similarly, zero sound transmission into the shell's inner fluid can also be considered. The possibility of using a pre-determined discrete distribution of the applied pressure load is also discussed. The derived equations are numerically solved to examine sound scattering by a thin aluminium shell in shallow water. PMID:21690137
Wave motion of a compressible viscous fluid contained in a cylindrical shell
Terhune, J.H.; Karim-Panahi, K. (General Electric Co., San Jose, CA (United States). GE Nuclear Energy)
1993-08-01
The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Fluegge's equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, the authors modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity mode shapes are computed for a typical case and displayed in nondimensional graphs.
Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells
Kunte, M. V.; Sarkar, Abhijit; Sonti, Venkata R.
2010-12-01
Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order ( n). The shallow shell theory (which is more accurate at higher frequencies) is used to model the cylinder. Initially, the in vacuo shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high- and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter μ, we find solutions for the limiting cases of small and large μ. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases, Poisson's ratio ν is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory ( in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders ( n).
Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel
Nagai, K.; Maruyama, S.; Murata, T.; Yamaguchi, T.
2007-08-01
Detailed experimental results and analytical results are presented on chaotic vibrations of a shallow cylindrical shell-panel subjected to gravity and periodic excitation. The shallow shell-panel with square boundary is simply supported for deflection. In-plane displacement at the boundary is elastically constrained by in-plain springs. In the experiment, the cylindrical shallow shell-panel with thickness 0.24 mm, square form of length 140 mm and mean radius 5150 mm is used for the test specimen. All edges around the shell boundary are simply supported by adhesive flexible films. First, to find fundamental properties of the shell-panel, linear natural frequencies and characteristics of restoring force of the shell-panel are measured. These results are compared with the relevant analytical results. Then, geometrical parameters of the shell-panel are identified. Exciting the shell-panel with lateral periodic acceleration, nonlinear frequency responses of the shell-panel are obtained by sweeping the frequency of periodic acceleration. In typical ranges of the exciting frequency, predominant chaotic responses are generated. Time histories of the responses are recorded for inspection of the chaos. In the analysis, the Donnell equation with lateral inertia force is introduced. Assuming mode functions, the governing equation is reduced to a set of nonlinear ordinary differential equations by the Galerkin procedure. Periodic responses are calculated by the harmonic balance method. Chaotic responses are integrated numerically by the Runge-Kutta-Gill method. The chaotic responses, which are obtained by the experiment and the analysis, are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. It is found that the dominant chaotic responses of the shell-panel are generated from the responses of the sub-harmonic resonance of {1}/{2} order and of the ultra-sub-harmonic resonance of {2}/{3} order. By the
Khudayarov B. A.
2010-09-01
Full Text Available In this work is investigated the flutter of visco-elastic cylindrical shells streamlined by gas current. The basic direction of work is consisted in taking into account of visco-elastic material’s properties at supersonic speeds. Critical speeds for shell flutter are defined.
Khudayarov B.A.
2010-01-01
In this work is investigated the flutter of visco-elastic cylindrical shells streamlined by gas current. The basic direction of work is consisted in taking into account of visco-elastic material’s properties at supersonic speeds. Critical speeds for shell flutter are defined.
Vibration characteristics of thin rotating cylindrical shells with various boundary conditions
Sun, Shupeng; Chu, Shiming; Cao, Dengqing
2012-08-01
An analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of Fourier series expansion method. Based on Sanders' shell equations, the governing equations of motion which take into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotating are derived. The displacement field is expressed as a product of Fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements. Stokes' transformation is employed to derive the derivatives of the Fourier series expressions. Then, through the process of formula derivation, an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type. Once the frequency equation has been determined, the frequencies are calculated numerically. To validate the present analysis, comparisons between the results of the present method and previous studies are performed and very good agreement is achieved. Finally, the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries, and the results are presented.
Torki, Mohammad Ebrahim; Kazemi, Mohammad Taghi; Reddy, Junuthula N.; Haddadpoud, Hassan; Mahmoudkhani, Saeid
2014-02-01
In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the critical circumferential mode number and the minimum flutter load is investigated. As expected, the flutter load increases as the follower force changes from the so-called Beck's load into the so-called Leipholz's and Hauger's loadings. The increased flutter load was calculated for homogeneous shell with different mechanical properties, and it was found that the difference in elasticity moduli bears the most significant effect on the flutter load increase in short, thick shells. Also, for an FGM shell, the increase in the flutter load was calculated directly, and it was found that it can be derived from the simple power law when the corresponding increase for the two base phases are known.
Gangolu Vijay Kumar
2012-01-01
Full Text Available A four-node composite facet-shell element is developed, accounting for electromechanical coupling of Macrofiber Composite (MFC and conventional PZT patches. Further a warping correction is included in order to capture correctly the induced strain of conformable MFC, surface bonded on a cylindrical shell. The element performance to model the relations between in-plane electric field to normal strains is examined with the help of experiment and ANSYS analysis. In ANSYS, a simple modeling scheme is proposed for MFC using a parallel capacitors concept. The independent modal space control technique has been revisited to address the control of combination resonances through a selective modal space control scheme, where two or more modes can be combined to form the vibrating system or plant in modal domain. The developed control schemes are implemented in a digital processor using DS1104 and the closed-loop vibration control experiments are conducted on a CFRP shell structure. The influence of directionally induced actuation of MFC actuators on elastic couplings of composite shell is studied theoretically and is subsequently demonstrated in experiments. MFC actuators provide the much needed optimization domain for achieving the vibration control of combination resonances of elastically coupled deep-shell structure.
Effect of vertical seismic load on shear-bending buckling strength of thin cylindrical shells
The main vessels of Fast Breeder Reactors (FBR) are cylindrical structures containing liquid, and have to be thin-walled in order to withstand severe thermal condition. One of the most critical factors in the design of earthquake-resistant FBRs is the buckling strength of the cylinder part of the reactor vessel. In order to investigate various non-linear response characteristics, including buckling, of thin cylindrical shells under vertical and horizontal seismic motion, pseudo-dynamic experiments and non-linear response simulation analysis is performed. It is confirmed that buckling is caused mainly by horizontal seismic loads, and that vertical seismic loads reduce the lateral load-carrying capacity of cylinders and amplify response displacement for a given horizontal seismic load. To evaluate the amplification of non-linear horizontal responses due to vertical input motions, the authors define a response amplification factor, which is calculated from floor response spectra of seismic waves
无
2009-01-01
Current patch test for Mindlin plate element only satisfies the zero shear deformation condition.The patch test of non-zero constant shear for Mindlin plate problem cannot be performed.For shell element, the patch test does not even exist.Based on the theory of enhanced patch test proposed by Chen W J (2006),the authors proposed the enhanced patch test function for Mindlin plate and thin cylindrical shell elements.This enhanced patch test function can be used to assess the convergence of the Mindlin plate and cylindrical thin shell elements.
Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
Rubín de Celis, Emilio
2015-01-01
The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${\\kappa^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential prod...
Arshad, Shahid Hussain; Sultana, Nazra; Iqbal, Zafar [University of Sargodha, Department of Mathematics, Sargodha (Pakistan); Naeem, Muhammad Nawaz [G. C. University Faisalabad, Department of Mathematics, Faisalabad (Pakistan); Shah, Abdul Ghafar [Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur (Pakistan)
2011-08-15
In the present work, vibration characteristics of thin functionally graded cylindrical shells are studied under the influence of various boundary conditions. Fabrication of FGM cylindrical shell is carried out by using exponential volume fraction law. Strain- and curvature-displacements relationships are taken from Love's thin shell theory. The frequency equation in the form of eigenvalue problem is obtained by adapting the Rayleigh-Ritz method. Characteristic beam functions are assumed to approximate the axial modal dependence. Effects of exponential volume fraction law on the natural frequencies of the FGM cylindrical shells for various boundary conditions are studied against circumferential wave number, length to radius ratio and thickness to radius ratio for different values of power law exponents. Results evaluated show good agreement with those available in the literature. (orig.)
A viscoplastic model of expanding cylindrical shells subjected to internal explosive detonations
Martineau, R.L.
1998-04-01
Magnetic flux compression generators rely on the expansion of thin ductile shells to generate magnetic fields. These thin shells are filled with high explosives, which when detonated, cause the shell to expand to over 200% strain at strain-rates on the order of 10{sup 4} s{sup {minus}1}. Experimental data indicate the development and growth of multiple plastic instabilities which appear in a quasi-periodic pattern on the surfaces of the shells. These quasi-periodic instabilities are connected by localized zones of intense shear that are oriented approximately 45{degree} from the outward radial direction. The quasi-periodic instabilities continue to develop and eventually become through-cracks, causing the shell to fragment. A viscoplastic constitutive model is formulated to model the high strain-rate expansion and provide insight into the development of plastic instabilities. The formulation of the viscoplastic constitutive model includes the effects of shock heating and damage in the form of microvoid nucleation, growth, and coalescence in the expanding shell. This model uses the Johnson-Cook strength model with the Mie-Grueneisen equation of state and a modified Gurson yield surface. The constitutive model includes the modifications proposed by Tvergaard and the plastic strain controlled nucleation introduced by Neeleman. The constitutive model is implemented as a user material subroutine into ABAQUS/Explicit, which is a commercially available nonlinear explicit dynamic finite element program. A cylindrical shell is modeled using both axisymmetric and plane strain elements. Two experiments were conducted involving plane wave detonated, explosively filled, copper cylinders. Instability, displacement, and velocity data were recorded using a fast framing camera and a Fabry-Perot interferometer. Good agreement is shown between the numerical results and experimental data. An additional explosively bulged cylinder experiment was also performed and a photomicrograph of
Steady-state temperature distribution in living tissue modeled as cylindrical shells.
Shitzer, A.; Chato, J. C.
1971-01-01
Closed form, analytical solutions to the problem of steady-state heat transfer in living tissue modeled as cylindrical shells are presented and discussed. These solutions are particularly useful for the study of temperature distributions in the extremities. Metabolic heat generation, conduction, and heat transported by the blood perfusing the tissue are considered in the model. The results demonstrate the important role that the blood stream plays in the transfer of heat inside living tissue. Solutions are also presented for the limiting cases of diminishing blood flow that would occur during vasoconstriction or occlusion of blood by external means.
无
2000-01-01
An FAE (Fuel-Air-Explosives) device is used to develop a numerical and theoretical analysis of a thin cylindrical shell with inner explosive loading. The dynamic fracture process is simulated numerically in the DYNA3D program using the finite element method. The material's dynamic properties are described by a strain hardening viscoplastic constitution. A damage variable is introduced in the determination of the dynamic fracture criterion. Final rupture of structure is decided by a rupture-strain criterion which is deduced in terms of a critical damage variable. The numerical results have been compared with theoretical solutions.
SHENG Hong-yu; LI He-ping; XU Hai-yan
2009-01-01
Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of varions approximate and numerical models.
Ray and wave scattering in smoothly curved thin shell cylindrical ridges
Sondergaard, Niels
2016-01-01
We propose wave and ray approaches for modelling mid- and high- frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model is analysed via an appropriate phase-plane analysis, from which the fixed points can be interpreted in terms of the reflection and transmission properties. The corresponding full wave scattering model is studied using the finite difference method to investigate the scattering properties of an incident plane wave. Through both models we uncover the scattering properties of smoothed joints in the interesting mid-frequency region close to the ring frequency, where there is a qualitative change in the dynamics from anisotropic to simple geodesic propagation.
Surya Narain
2004-10-01
Full Text Available This study investigates magnetoelastic torsional vibration of a non-homogeneous aeolotropic cylindrical shell of viscoelastic solids. The non-homogeneity of the shell obeyingpower law variation of elastic constants and density given by Aij= Crjf', p = por"(i, j = 1,2 ,... 6, where Cu (i, j = 1,2, ... 6 and po are constants and r is the radius vector. Frequency equation and phase velocity in several cases have been derived. Such problems of interaction of elastic and electromagnetic fields have numerous applications in various branches of science, particularly in the detection of mechanical explosions in the interior of the earth and in the electromagnetic energy into vacuum.
Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a bulk field and a shell field. The bulk part corresponds to a field sourced by the test charge placed in a space-time without the shell. The shell field accounts for the discontinuity of the extrinsic curvature κpq. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge Q, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge q in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if κpq = κ < 0 (ordinarymatter) and attracted toward the shell if κ > 0 (exotic matter). The total image charge is zero for exterior problems, while for interior problems Q/q = κre, with re the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found Q-+wh/q = -1/(κwhr±). (orig.)
Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
Rubín de Celis, Emilio
2016-02-01
The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a bulk field and a shell field. The bulk part corresponds to a field sourced by the test charge placed in a space-time without the shell. The shell field accounts for the discontinuity of the extrinsic curvature {κ ^p}_q. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge Q, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge q in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if {κ p}p=κ attracted toward the shell if κ >0 (exotic matter). The total image charge is zero for exterior problems, while for interior problems Q/q=-κ r_e, with r_e the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found Q_{∓}^{wh}/q=-1/ (κ_{wh} r_{± }).
Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge
Rubin de Celis, Emilio [Universidad de Buenos Aires y IFIBA, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2016-02-15
The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a bulk field and a shell field. The bulk part corresponds to a field sourced by the test charge placed in a space-time without the shell. The shell field accounts for the discontinuity of the extrinsic curvature κ{sup p}{sub q}. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge Q, to interpret the shell field in both the interior and exterior regions of the space-time. The self-force on a point charge q in a locally flat geometry with a cylindrical thin-shell of matter is calculated. The charge is repelled from the shell if κ{sup p}{sub q} = κ < 0 (ordinarymatter) and attracted toward the shell if κ > 0 (exotic matter). The total image charge is zero for exterior problems, while for interior problems Q/q = κr{sub e}, with re the external radius of the shell. The procedure is general and can be applied to interpret self-forces in other space-times with shells, e.g., for locally flat wormholes we found Q{sub -+}{sup wh}/q = -1/(κ{sub wh}r{sub ±}). (orig.)
Radial oscillations of highly stressed nonhomogenous, thick-walled cylindrical and spherical shells
The present work investigates the infinitesimal breathing motions of spherical and long cylindrical shells of arbitrary wall thickness subject to a finite, axisymmetric deformation field caused by uniform internal and/or external pressures. A neo-Hookean material with a material constant varying continuously along the radial direction is used. The shell is first subject to finite, axisymmetric, static deformations and is then exposed to a secondary, axisymmetric, static deformations and is then exposed to a secondary, axisymmetric, dynamic displacement field. Based on the theory of small deformations superposed on large deformations, closed form expressions are obtained for the frequency of small oscillations about the highly prestressed state. Frequency versus initial deformation parameter curves are given for several nonhomogeneity functions and for various wall thicknesses. The softening or the hardening behaviors of the shells for varying prestress values are observed from these curves. When the frequency of breathing motions cease to be real valued, the superposed secondary motions are no larger periodic. Thus, the critical value of the prestress causing instability is defined as the one which corresponds to zero frequency. It is seen that when the nonhomogeneity parameters are taken zero, the known results of the homogeneous case are obtained. Although the material is assumed to be incompressible, the theory is general enough to include compressible materials. However, in this case, the governing equations of the problem become more complicated for a closed form solution. An interesting and practical extension of the problem is the vibration analysis of layered shells
Steel, Robin; Fish, Peter J
2002-02-01
Flow phantoms used in medical ultrasound usually employ a plastic tube as a blood vessel mimic. These tubes often have acoustic properties differing significantly from the tissue and blood-mimicking media, which results in distortion of the acoustic pressure field within the tubes and, hence, of the Doppler flow spectra. Previous analyses of this problem have used some form of the infinite plate transmission coefficient, although at least one ray-based analysis has considered a cylindrical interface but with zero wall thickness. In this paper, we compare these approximate pressure fields with the exact solution for oblique incidence on a viscoelastic cylindrical shell at 5 MHz to find for which materials the plate approximation is valid. The shell has water both inside and outside, but it can be modified to use a different fluid inside and also to include absorption in either fluid. We find the plate approximation is reasonable for soft tubes such as the copolymer Cflex (Cole-Palmer, Niles, IL) but much less so for hard tubes such as polymethylmethacrylate (PMMA). PMID:11885684
Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding.
Rajabi, M; Hasheminejad, Seyyed M
2009-12-01
The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established. PMID:19586650
Self-force on a charge in a locally flat geometry with a cylindrical thin-shell
de Celis, Emilio Rubín
2015-01-01
The electrostatic self-interaction of a point charge is calculated for an arbitrary position in a locally flat space-time with a cylindrical thin-shell of matter centred at a straight cosmic string. The results show a radial self-force. Near the string or asymptotically far from the thin-shell the charge is repelled from the central axis, this interaction is produced by the global deficit angle of the geometry. In the neighbourhood of the shell the charge is repelled from it if the surface energy density is positive (ordinary matter) and attracted towards the shell if the surface energy density is negative (exotic matter).
Plattenburg, Joseph; Dreyer, Jason T.; Singh, Rajendra
2016-06-01
This paper proposes a new analytical model for a thin cylindrical shell that utilizes a homogeneous cardboard liner to increase modal damping. Such cardboard liners are frequently used as noise and vibration control devices for cylindrical shell-like structures in automotive drive shafts. However, most prior studies on such lined structures have only investigated the associated damping mechanisms in an empirical manner. Only finite element models and experimental methods have been previously used for characterization, whereas no analytical studies have addressed sliding friction interaction at the shell-liner interface. The proposed theory, as an extension of a prior experimental study, uses the Rayleigh-Ritz method and incorporates material structural damping along with frequency-dependent viscous and Coulomb interfacial damping formulations for the shell-liner interaction. Experimental validation of the proposed model, using a thin cylindrical shell with three different cardboard liner thicknesses, is provided to validate the new model, and to characterize the damping parameters. Finally, the model is used to investigate the effect of the liner and the damping parameters on the modal attenuation of the shell vibration, in particular for the higher-order coupled shell modes.
Kriegesmann, Benedikt; Hilburger, Mark W.; Rolfes, Raimund
2012-01-01
Results from a numerical study of the buckling response of a thin-walled compressionloaded isotropic circular cylindrical shell with initial geometric and loading imperfections are used to determine a lower bound buckling load estimate suitable for preliminary design. The lower bound prediction techniques presented herein include an imperfection caused by a lateral perturbation load, an imperfection in the shape of a single stress-free dimple (similar to the lateral pertubation imperfection), and a distributed load imperfection that induces a nonuniform load in the shell. The ABAQUS finite element code is used for the analyses. Responses of the cylinders for selected imperfection amplitudes and imperfection types are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. The results indicate that compression-loaded shells subjected to a lateral perturbation load or a single dimple imperfection, and a nonuniform load imperfection, exhibit similar buckling behavior and lower bound trends and the predicted lower bounds are much less conservative than the corresponding design recommendation NASA SP-8007 for the design of buckling-critical shells. In addition, the lateral perturbation technique and the distributed load imperfection produce response characteristics that are physically meaningful and can be validated via laboratory testing.
Model-based failure detection for cylindrical shells from noisy vibration measurements.
Candy, J V; Fisher, K A; Guidry, B L; Chambers, D H
2014-12-01
Model-based processing is a theoretically sound methodology to address difficult objectives in complex physical problems involving multi-channel sensor measurement systems. It involves the incorporation of analytical models of both physical phenomenology (complex vibrating structures, noisy operating environment, etc.) and the measurement processes (sensor networks and including noise) into the processor to extract the desired information. In this paper, a model-based methodology is developed to accomplish the task of online failure monitoring of a vibrating cylindrical shell externally excited by controlled excitations. A model-based processor is formulated to monitor system performance and detect potential failure conditions. The objective of this paper is to develop a real-time, model-based monitoring scheme for online diagnostics in a representative structural vibrational system based on controlled experimental data. PMID:25480059
Deng, D S; Johnson, S G; Fink, Y
2010-01-01
Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in concentric cylindrical shells of viscous fluids. In this paper, we focus on a single instability mechanism: classical capillary instabilities in the form of radial fluctuations, solving the full Navier--Stokes equations numerically. In equal-viscosity cases where an analytical linear theory is available, we compare to the full numerical solution and delineate the regime in which the linear theory is valid. We also consider unequal-viscosity situations (similar to experiments) in which there is no published linear theory, and explain the numerical results with a simple asymptotic analysis. These results are then applied to experimental thermal drawing systems. We show that the observed instabilities are consistent with radial-fluctuation analysis, but cannot be predicted by radi...
Fast Prediction of Acoustic Radiation from a Hemi-capped Cylindrical Shell in Waveguide
Hongyang Chen; Qi Li; Dejiang Shang
2014-01-01
In order to predict acoustic radiation from a structure in waveguide, a method based on wave superposition is proposed, in which the free-space Green’s function is used to match the strength of equivalent sources. In addition, in order to neglect the effect of sound reflection from boundaries, necessary treatment is conducted, which makes the method more efficient. Moreover, this method is combined with the sound propagation algorithms to predict the sound radiated from a cylindrical shell in waveguide. Numerical simulations show the effect of how reflections can be neglected if the distance between the structure and the boundary exceeds the maximum linear dimension of the structure. It also shows that the reflection from the bottom of the waveguide can be approximated by plane wave conditionally. The proposed method is more robust and efficient in computation, which can be used to predict the acoustic radiation in waveguide.
Design Optimization and Residual Strength Assessment of a Cylindrical Composite Shell Structure
Rais-Rohani, Masoud
2000-01-01
A summary of research conducted during the specified period is presented. The research objectives included the investigation of an efficient technique for the design optimization and residual strength assessment of a semi-monocoque cylindrical shell structure made of composite materials. The response surface methodology is used in modeling the buckling response of individual skin panels under the combined axial compression and shear loading. These models are inserted into the MSC/NASTRAN code for design optimization of the cylindrical structure under a combined bending-torsion loading condition. The comparison between the monolithic and sandwich skin design cases indicated a 35% weight saving in using sandwich skin panels. In addition, the residual strength of the optimum design was obtained by identifying the most critical region of the structure and introducing a damage in the form of skin-stringer and skin-stringer-frame detachment. The comparison between the two skin design concepts indicated that the sandwich skin design is capable of retaining a higher residual strength than its monolithic counterpart. The results of this investigation are presented and discussed in this report.
Mallon, N.; Fey, R.H.B.; Nijmeijer, H.
2010-01-01
Considering both an experimental and a numerical approach, the dynamic stability of a harmonically base-excited thin orthotropic cylindrical shell carrying a top mass is examined. To be able to compare the experimentally obtained results with numerical results, a semi-analytical coupled shaker-struc
K Athiannan; R Palaninathan
2004-02-01
This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision for in-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections $\\delta_{\\text{max}}$ are of the order of $\\pm 3t$ (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through ﬁnite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen inﬂuences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.
Honeycutt, T. E.; Roberts, T. G.
1986-05-01
Brass retainer rings are currently fastened to artillery shells by spinning each shell at a high rate and then jamming the ring on it so that it is fastened or welded by friction between the two objects. This is an energy-inefficient process which heats and weakens more material than is desirable. The shell spinning at a high rate is also potentially dangerous. A laser welder is provided that generates output energy focused on a circular or cylindrical shape for simultaneously welding around a 360 degs circumference without unnecessarily heating large amounts of material. The welder may be used to fasten cylindrical shaped objects, gears and shafts together, which is difficult to do by conventional means. The welder may also be used to fasten one cylinder to another. To accomplish the welding, a laser has an unstable optical cavity arranged with its feedback mirror centered to generate a circular output beam having an obscuration in the center. A circularly-symmetric, off-axis concave mirror focuses the output beam onto the objects being fastened and away from the center line or axis of the circular beam.
Vertical position control for non-circular plasma column by shell effect
The next tokamak fusion reactor, for example, INTOR, obtains a high beta under a non-circular plasma whose MHD equilibrium requires an external field configuration with negative decay index. It is well known that such a plasma in its external field has a positional instability in the vertical direction. How to control the instability is in general composed of two kinds of method. One is to use a passive position control, that is, the shell effect which will be effective up to the growth time of instability (= a few ten msec.) above that time constant. In this report some concrete shell-structures under which the shell effect will play its part in the next tokamak are proposed on taking account of practical forms of the first wall and the vacuum chamber in the device. Analyses of the shell effect contain a dipole current model, in which coupling of shell currents with a plasma column is replaced with that of the current with dipole currents, and an eddy current evaluation. (author)
Jian Yong-Jun; E Xue-Quan; Zhang Jie; Meng Jun-Min
2004-01-01
Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term,an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important.However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.
An analytical method was proposed for calculating radiative fluxes incident on a planar circular detector from a volume multiple point chemi- or bio-luminescent source inside a coaxial cylindrical reactor. The method was designed for a cylindrical reactor when the surface reflections were neglected and when chemi- or bio-luminescence reaches a detector embedded in the same homogeneous optical medium as the point emitters of the volume multiple point source model. The radiative fluxes from arbitrarily distributed point emitters were expressed by one generalized quadruple-integral formula. Then some double- and single-integral formulas were obtained for calculating radiative fluxes from identically radiating point emitters uniformly distributed within the reactor. Selected results were computed and illustrated graphically. The obtained formulas are suitable for optimizing and/or calibrating the considered source-detectors systems (optical radiometers or luminometers) and determining radiative fluxes generated by chemical, biological, and physical processes leading to chemi-, bio-, radio-, and sono-luminescence for example.
Mindle, W. L.; Torvik, P. J.
1986-01-01
The natural frequencies and associated mode shapes for three thick open cantilevered cylindrical shells were determined both numerically and experimentally. The shells ranged in size from moderately to very thick with length to thickness ratios of 16, 8 and 5.6, the independent dimension being the shell thickness. The shell geometry is characterized by a circumferential angle of the 142 degrees and a ratio of length to inner radii arc length near 1.0. The finite element analysis was performed using NASTRAN's (COSMIC) triangular plate bending element CTRIA2, which includes membrane effects. The experimental results were obtained through holographic interferometry which enables one to determine the resonant frequencies as well as mode shapes from photographs of time-averaged holograms.
Bakulin, V. N.; Volkov, E. N.; Nedbai, A. Ya.
2016-05-01
The dynamic stability of a cylindrical orthotropic shell reinforced by longitudinal ribs and a hollow cylinder under the action of axial forces changing harmonically with time was investigated with regard for the axial contact interaction of the shell with the ribs. A solution of the differential equations defining this process has been obtained in the form of trigonometric series in the angular and time coordinates. A two-term approximation of the Mathieu-Hill equations of motion was used for construction of the main region of instability of the shell. As a result, the problem was reduced to a system of algebraic equations for components of displacements of the shell at the locations of the ribs. The problem for uniformly spaced ribs was solved in the explicit form. A numerical example of this solution is presented.
Chaotic Energy Exchange Through Auto-Parametric Resonance in Cylindrical Shells
POPOV, A. A.; THOMPSON, J. M. T.; MCROBIE, F. A.
2001-11-01
Internal auto-parametric instabilities in the free non-linear vibrations of a cylindrical shell are studied numerically, focusing on two modes (a concertina mode and a chequerboard mode) whose non-linear interaction breaks the in-out symmetry of the linear vibration theory. The two-mode interaction leads to preferred vibration patterns with larger deflection inwards than outwards, and at internal resonance, significant energy transfer occurs between the modes. This has regular and chaotic features. Here, direct numerical integration is employed to examine chaotic motions. Using a set of 2-D Poincaré sections, each valid for a fixed level of the Hamiltonian, H, the instability under increasing H appears, as a supercritical period-doubling pitchfork bifurcation. Chaotic motions near a homoclinic separatrix appear immediately after the bifurcation, giving an irregular exchange of energy. This chaos occurs at arbitrarily low amplitude as perfect tuning is approached. The instability manifests itself as repeating excursions around the separatrix, and a number of practical predictions can be made. These include the magnitude of the excursion, the time taken to reach this magnitude and the degree of chaos and unpredictability in the outcome. The effect of small damping is to pull the motion away from what was the chaotic separatrix, giving a response that resembles, for a while, the lower-energy quasi-periodic orbits of the underlying Hamiltonian system.
The load carrying behaviour of cylindrical thin-walled shell structures under pressure load is strongly dependent on the nature and magnitude of the imperfections invariably caused by various manufacturing processes. The present paper examines instabilities of long homogeneous and isotropic thin elastic tubes, characterized by geometric imperfections like eccentricity or oval shape, on the buckling behaviour in conditions for which, at present, a complete theoretical analysis was not found in literature. Moreover, the additional aspect of the influence of the welded joint geometry and position is investigated over a wide range of diameter to thickness ratio, extending the findings of previous works. The experiments were conducted on test specimens with different materials, e.g. A-316 ASTM (with and without seam weld) and Inconel, as well as different loading conditions (lateral and hydrostatic external pressure). A validation of numerical evaluations by comparison with test results is also performed. A good agreement has been observed between the experimental data and the elasto-plastic finite element analyses results, highlighting also the different influence of the mentioned imperfections on the buckling loads. For all 3 tube families tested, the oval form was found to reduce the collapse pressure quite significantly. The local thickness variation along the longitudinal welding and the interaction between neighbouring imperfections have been shown to be important factors governing buckling
The effective conductivity of three-phase composite materials with circular cylindrical inclusions
We extend the Rayleigh method for the calculation of the effective conductivity to three-phase composite materials. The materials under study consist of two types of circular cylinders in a periodic arrangement embedded in a matrix. Highly accurate values for lattice sums were obtained using algorithms which have been recently developed. A series of explicit formulations, which are used to facilitate the calculation of the effective conductivity of the composites under study, are reported. We also perform a series of numerical calculations to study the behaviour of these composites
Alashti, R. Akbari, E-mail: raalashti@nit.ac.ir [Mechanical Engineering Department, Babol University of Technology, P.O. Box 484, Shariati Avenue, Babol (Iran, Islamic Republic of); Khorsand, M. [Mechanical Engineering Department, Babol University of Technology, P.O. Box 484, Shariati Avenue, Babol (Iran, Islamic Republic of)
2011-05-15
Three-dimensional thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. Numerical results of displacement, stress and thermal fields are obtained using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson's ratio is assumed to be constant. Shells are considered to be under the effect of the pressure loading in the form of cosine and ring pressure loads, electric potentials and temperature fields. Numerical results for various boundary conditions are obtained and the effects of the thickness of piezoelectric layers, grading index of material properties and the ratio of the thickness to the radius of the shell on these results is presented. - Highlights: > A numerical study of an FGM cylindrical shell with piezoelectric layers is made. > Governing equations are solved by two versions of differential quadrature methods. > The effect of layers thickness, grading index and geometrical ratios is presented.
Frederico Martins Alves da Silva
2015-01-01
Full Text Available This work investigates the influence of Young’s modulus, shells thickness, and geometrical imperfection uncertainties on the parametric instability loads of simply supported axially excited cylindrical shells. The Donnell nonlinear shallow shell theory is used for the displacement field of the cylindrical shell and the parameters under investigation are considered as uncertain parameters with a known probability density function in the equilibrium equation. The uncertainties are discretized as Hermite-Chaos polynomials together with the Galerkin stochastic procedure that discretizes the stochastic equation in a set of deterministic equations of motion. Then, a general expression for the transversal displacement is obtained by a perturbation procedure which identifies all nonlinear modes that couple with the linear modes. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Applying the standard Galerkin method, a discrete system in time domain that considers the uncertainties is obtained and solved by fourth-order Runge-Kutta method. Several numerical strategies are used to study the nonlinear behavior of the shell considering the uncertainties in the parameters. Special attention is given to the influence of the uncertainties on the parametric instability and time response, showing that the Hermite-Chaos polynomial is a good numerical tool.
Bezerra, V B; Klimchitskaya, G L; Mostepanenko, V M; Saharian, A A
2011-01-01
We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.
Bezerra, V.B.; Bezerra de Mello, E.R. [Federal University of Paraiba, Department of Physics, C.P. 5008, Joao Pessoa, Pb (Brazil); Klimchitskaya, G.L. [Federal University of Paraiba, Department of Physics, C.P. 5008, Joao Pessoa, Pb (Brazil); North-West Technical University, St. Petersburg (Russian Federation); Mostepanenko, V.M. [Federal University of Paraiba, Department of Physics, C.P. 5008, Joao Pessoa, Pb (Brazil); Noncommercial Partnership ' ' Scientific Instruments' ' , Moscow (Russian Federation); Saharian, A.A. [Yerevan State University, Department of Physics, Yerevan (Armenia)
2011-04-15
We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1R, where R is the radius of the cylinder. The developed methods are applicable in the theory of topological defects. (orig.)
Mohammad Zamani Nejad
2014-01-01
Full Text Available Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT. These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM is also presented and good agreement was found.
Yang Xiaomeng; Hu Yuantai; Yang Jiashi
2005-01-01
We study electromechanical fields in the anti-plane deformation of an infinite medium of piezoelectric materials of 6 mm symmetry with a circular cylindrical hole. The theory of electroelastic dielectrics with electric field gradient in the constitutive relations is used. Special attention is paid to the fields near the surface of the hole.
Matrix solution of coupling impedance in multi-layer circular cylindrical structures
Continuing interest in computing the coupling impedance of cylindrical multi-layer beam tubes led to several recent publications. A novel matrix method is here presented in which radial wave propagation is treated in analogy to longitudinal transmission lines. Starting from the Maxwell equations the solutions for monopole electromagnetic fields are in each layer described by a 2 x 2 matrix. Assuming isotropic material properties within one layer, the radially transverse field components at the inner boundary of a layer are uniquely determined by matrix transfer of the field components at its outer boundary. By imposing power flow constraints on the matrix, field matching between layers is enforced and replaced by matrix multiplication. The coupling impedance of a stainless steel beam tube defined by a matrix is given as a representative demonstration
LIU Hongmin; CHEN Suwen; PENG Yan; SUN Jianliang
2015-01-01
As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a typical rotary forming technology, and the upper and lower rolls have different radii and speeds. To quickly predict the three-dimensional stresses and eliminate fishtall defect, an improved strip layer method is developed, in which the asymmetry of the upper and lower rolls, non-uniform deformation and stress, as well as the asymmetrical spread on the end surface are considered. The deformation zone is divided into a certaln number of layers and strips along the thickness and width, respectively. The transverse displacement model is constructed by polynomial function, in order to increase the computation speed greatly. From the metal plastic mechanics principle, the three-dimensional stress models are established. The genetic algorithm is used for optimization calculation in an industrial experiment example. The results show that the rolling pressure, the normal stresses, the upper and lower friction stress distributions are not similar with those of a general plate rolling. There are two relative maximum values in rolling pressure distribution. The upper and lower longitudinal friction stresses change direction nearby the upper and lower neutral points, respectively. The fishtall profile of spread on the end surface is predicted satisfactorily. The reduction could be helpful to eliminate fishtall defect. The large cylindrical shell rolling example illustrates the calculation results acquired rapidly are good agreements with the finite element simulation and experimental values of previous study. A highly effective and reliable three-dimensional simulation method is proposed for large cylindrical shell rolling and other asymmetrical rolling.
Effect of radial electric boundary potential on a circular cylindrical magneto plasma, 3
In krypton gas plasma, the frequency shift was measured by applying an alternating potential to a cylindrical side wall. The experimental apparatus was similar to that for the former study. In the effect induced in plasma, there was no difference when an insulator was attached to the side wall or not, as for as the frequency shift phenomenon was concerned. The procedure of measurement was also the same as the former study. One of the strongest waves excited in this type of electron beam plasma systems can be observed near the upper hybrid frequency which is due to the interaction of the slow plasma waves in an electron beam with the cyclotron waves in the generated plasma. A negative going square wave potential was applied. The amount of frequency shift in relation to the amplitude of the applied potential is shown. When the side wall was at a static negative potential, the frequency of the spectral line did not change. When an oscillating potential was applied, the frequency decreased. The amount of frequency shift depended on the amplitude and frequency of a wall potential. When the amplitude was about 10 V, a remarkable difference arose. In the case of krypton plasma, the short circuit effect of beam current must be related. (Kako, I.)
Sun, Dongming; Wang, Sheng; Sakurai, Junpei; Choi, Kee-Bong; Shimokohbe, Akira; Hata, Seiichi
2010-04-01
A piezoelectric linear ultrasonic motor is proposed, with a cylindrical stator and slider structure. The length and diameter of the motor are about 10 and 1.5 mm, respectively. The stator consists of two piezoelectric ceramic (PZT) tubes connected by a thin film metallic glass (TFMG) pipe. The stator is designed based on theoretical analyses and finite element method (FEM) simulation. The traveling wave propagation is obtained in the FEM simulation under the proper geometrical sizes, suitable boundary conditions and driving voltage signals. The trajectories of particles on the TFMG pipe are elliptical motion. In the experiment, a 25 µm thick TFMG pipe is fabricated using the rotating magnetron sputtering technique and the vibration characteristics of the stator are measured by a laser Doppler vibrometer (LDV) system. Bidirectional motion of the slider is observed around 600 kHz, the maximum velocity is near to 40 mm s - 1 at 50 Vp-p for the loose slider and the maximum output force is 6 mN at 70 Vp-p for the tight slider.
On the Flutter of Cylindrical Shells and Panels Moving in a Flow of Gas
Stepanov, R. D.
1958-01-01
The equations of shells are taken in the form of the general technical theory of shallow shells and shells of medium length. The aerodynamic forces acting on a shell are taken into account only as forces of excess pressure according to the formula proposed by A.A. Iliushin in reference 3.
The load carrying behaviour of cylindrical thin-walled shell structures under pressure load is strongly dependent on the nature and magnitude of the imperfections invariably caused by various manufacturing processes. The present paper examines instabilities of long homogeneous and isotropic thin elastic tubes, characterized by geometric imperfections like eccentricity or ovality, on the buckling behaviour in conditions for which, at present, a complete theoretical analysis was not found in literature. Moreover, the additional aspect of the influence of the welded joint geometry and position is investigated over a wide range of diameter to thickness ratio, extending the findings of previous works. The problem of buckling for variable load conditions is relevant in the context of NPP applications as, for instance the optimisation of an integrated and innovative LWR Steam Generator (SG) tubes, according to the updated ASME rules. To the purpose, at Pisa University a rather intense research activity is being carried out on the buckling of thin walled metal specimens in the dimensional range suitable for the above mentioned application. Therefore a test equipment (with the necessary data acquisition facility), suitable for carrying out test series on this issue, as well as numerical models implemented on the MARC FEM code, were set up. The experiments were conducted on test specimens with different materials, e.g. A-316 ASTM (with and without seam weld) and Inconel 690 TT, as well as different loading conditions (lateral and hydrostatic external pressure). A validation of numerical evaluations by comparison with test results is also performed. A good agreement has been observed between the experimental data and the elasto-plastic finite element analyses results, highlighting also the different influence of the mentioned imperfections on the buckling loads
A hybrid finite element method is developed to predict the influence of large amplitude vibration of orthotropic, circumferentially non-uniform open and closed cylindrical shells submerged and subjected to an internal and/or external fluid flow. The open shells are assumed to be freely simply supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a combination of thin shell theory, fluid theory and the finite element method. The solution is divided into three parts. In part one, the displacement functions are obtained from Sanders' linear shell theory and the mass and linear stiffness matrices for an open shell element are obtained by the finite element procedure. In part two, the modal coefficients, derived from the Sanders-Koiter non-linear theory of thin shells, are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the open shell element are then determined through the finite element method. With the dynamic pressure of the moving fluid and the boundary condition of impermeability, we develop in the third part the mass and the stiffness matrices of a fluid finite element for the interaction shell-fluid system. The non-linear equation of motion is then solved by the fourth-order Runge-Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases. Here the uncoupled non-linear system is solved. The complete solution of the coupled non-linear system will be treated in a future work. (orig.)