Nonlinear Strain Measures, Shape Functions and Beam Elements for Dynamics of Flexible Beams
Sharf, I. [University of Victoria, Department of Mechanical Engineering (Canada)
1999-05-15
In this paper, we examine several aspects of the development of an explicit geometrically nonlinear beam element. These are: (i) linearization of the displacement field; (ii) the effect of a commonly adopted approximation for the nonlinear Lagrangian strain; and (iii) use of different-order shape functions for discretization. The issue of rigid-body check for a nonlinear beam element is also considered. An approximate check is introduced for an element based on an (approximate) intermediate strain measure. Several numerical examples are presented to support the analysis. The paper concludes with a discussion on the use of explicit nonlinear beam elements for multibody dynamics simulation.
Husain M. Husain
2013-05-01
Full Text Available In this work a program is developed to carry out the nonlinear analysis (material nonlinearity of prestressed concrete beams using tendons of carbon fiber reinforced polymer (CFRP instead of steel. The properties of this material include high strength, light weight, and insusceptibility to corrosion and magnetism. This material is still under investigation, therefore it needs continuous work to make it beneficial in concrete design. Four beams which are tested experimentally by Yan et al. are examined by the developed computer program to reach a certain analytical approach of the design and analysis of such beams because there is no available restrictions or recommendations covering this material in the codes. The program uses the finite element analysis by dividing the beams into isoparametric 20-noded brick elements. The results obtained are good in comparison with experimental results.
On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams
Alexahin, Y. [Fermilab; Gianfelice-Wendt, E. [Fermilab; Lebedev, V. [Fermilab; Valishev, A. [Fermilab
2016-09-30
Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.
Analysis of Retrofitting Non-Linear Finite Element Of RCC Beam And Column Using Ansys
T. Subramani
2014-12-01
Full Text Available Many of the existing reinforced concrete structures throughout the world are in urgent need of strengthening, repair or reconstruction because of deterioration due to various factors like corrosion, lack of detailing, failure of bonding between beam-column joints, increase in service loads, etc., leading to cracking, spalling, loss of strength, deflection, etc., Direct observation of these damaged structures has shown that damage occurs usually at the beam-column joints, with failure in bending or shear, depending on geometry and reinforcement distribution type.A nonlinear finite element analysis that is a simulation technique is used in this work to evaluate the effectiveness of retrofitting technique called “wrapping technique” for using carbon fibres (FRP for strengthening of RC beam-column connections damaged due to various reasons. After carrying out a nonlinear finite element analysis of a reinforced concrete frame (Controlled Specimen and reinforced concrete frame where carbon fibres are attached to the beam column joint portion in different patterns ,the measured response histories of the original and strengthened specimens are then subsequently compared. It is seen that the strengthened specimens exhibit significant increase in strength, stiffness, and stability as compared to controlled specimens. It appears that the proposed simulation technique will have a significant impact in engineering practice in the near future.
Finite Element Solution: Nonlinear Flapping Beams for Use with Micro Air Vehicle Design
2007-03-01
used to approximate the nonlinearity in a beam is the SDOF Duffing Oscillator ӱ + C ẏ + ω0 2 y + βy3 = P sin(ωt...Hilbert Transform.......................................................................................................19 Duffing Equation...Amplitude vs Nonlinear Frequency: Fixed-Fixed Steel................................. 36 Figure 26. Duffing Equation Plot: Fixed-Fixed Steel Beam
Muhammet Karaton
2014-01-01
Full Text Available A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.
2012-06-09
these formulations employ some form of either the Euler-Bernoulli or Timoshenko beam theories and are mostly restricted to small strain analysis. The...and Kadioglu [1], wherein a Timoshenko beam element is de- veloped using mixed variational principles. In their work, the finite element model...method in their analysis of cylindrical helical rods (based on the Timoshenko beam hypotheses). Additional numerical formulations for viscoelastic beams
S.C. Chin
2012-05-01
Full Text Available This study presents the experimental study and numerical analysis of Reinforced Concrete (RC beams with large square openings placed in the shear region, at a distance 0.5d and d away from the support, strengthened by Carbon Fiber Reinforced Polymer (CFRP laminates. This research aims to investigate the strength losses in RC beam due to the presence of large square openings placed at two different locations in shear region. Also, in order to re-gain the beam structural capacity loss due to the openings, strengthening by CFRP laminates around the openings were studied. A total of six RC beams were tested to failure under four point loading including control beams, un-strengthened and strengthened RC beams with large square openings in shear region at a distance 0.5d and d away from the support. The CFRP strengthening configuration considered in this study was a full wrapping system around the square openings. A nonlinear finite element program, ATENA was used to validate the results of the tested beams. Comparisons between the finite element predictions and experimental results in terms of crack patterns and load deflection relationships are presented. The crack pattern results of the finite element model show good agreement with the experimental data. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption between the concrete and steel reinforcement.
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Al-Rousan, R. Z.
2015-09-01
The main objective of this study was to assess the effect of the number and schemes of carbon-fiber-reinforced polymer (CFRP) sheets on the capacity of bending moment, the ultimate displacement, the ultimate tensile strain of CFRP, the yielding moment, concrete compression strain, and the energy absorption of RC beams and to provide useful relationships that can be effectively utilized to determine the required number of CFRP sheets for a necessary increase in the flexural strength of the beams without a major loss in their ductility. To accomplish this, various RC beams, identical in their geometric and reinforcement details and having different number and configurations of CFRP sheets, are modeled and analyzed using the ANSYS software and a nonlinear finite-element analysis.
Abd El Baky, Hussien
This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond
Jonker, J.B.; Meijaard, J.P.
2013-01-01
A beam finite element formulation for large deflection problems in the analysis of flexible multibody systems has been proposed. In this formulation, a set of independent discrete deformation modes are defined for each element which are related to conventional small deflection beam theory in a co-ro
Finite Elements for a Beam System With Nonlinear Contact Under Periodic Excitation
Hazim, Hamad
2009-01-01
Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each other; this may damage the structure. To prevent this, rubber snubbers are mounted at well chosen points of the structure; a prestress is applied to the snubber; but it is quite difficult to check the amount of prestress and the snubber may act only on one side; they will be modeled as one sided springs (see figure 2). In this article, some analysis for responses (displacements) in both time and frequency domains for a clamped-clamped Euler-Bernoulli beam model with a spring are presented. This spring can be unilateral or bilateral fixed at a point. The mounting (beam +spring) is fixed on a rigid support which has a sinusoidal motion of constant frequency. The system is also studied in the frequency domain by sweeping frequencies between two fixed values, in order to save the...
Vibration Analysis of Timoshenko Beams on a Nonlinear Elastic Foundation
MO Yihua; OU Li; ZHONG Hongzhi
2009-01-01
The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method (QEM) is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear de-formation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.
1965-01-01
Two of the beam transport elements for the slow ejection system. On the left, a quadrupole 1.2 m long with a 5 cm aperture, capable of producing a gradient of 5000 gauss. On the right, a 1 m bending magnet with a 4 cm gap; its field is 20 000 gauss.
RESEARCH AND DEVELOPMENT OF THREE NONLINEAR BEAM-COLUMN ELEMENTS%三种非线性梁柱单元的研究及单元开发
陈学伟; 韩小雷; 孙思为
2011-01-01
Since the elastoplastic damages occur in concrete structures and components in plastic stage under a severe earthquake, precise prediction of nonlinear behavior of structures in the earthquake is important to assess the seismic safety of the structures. A structural elastoplastic analysis program MEASP which bases on macro elements is compiled with object oriented language and three kinds of nonlinear beam-column elements are implemented in MESAP: stiffness-based fiber element, flexibility-based fiber element and flexibility-based plastic hinge element. Differences between the elements are compared by case study. Four kinds of integration methods for obtaining the flexibility matrix of the plastic hinge element are studied. The results show that a flexibility-based plastic binge element is an accurate macro element with low computation cost. Only two integration points are required by the Gauss-Radau integration method handling a nonlinear analysis. It is accuracy and its computational efficiency is applicable in the entire structure nonlinear analysis and practical in engineering.%罕遇地震作用下混凝土梁柱构件易进入塑性阶段而发生弹塑性损伤,正确地模拟结构进入非线性状态后的力学行为对评价结构的抗震安全性具有重要的意义.通过面向对象语言编制了基于宏观单元的结构弹塑性分析软件平台MESAP,增加了三种非线性梁柱单元:基于刚度法纤维单元、基于柔度法纤维单元及基于柔度法的塑性铰单元.通过算例分析三种非线性梁柱单元之间的差异.基于柔度法塑性铰单元的柔度矩阵积分方法可分为四种,通过算例讨论四种积分方法的差异.算例分析结果表明基于柔度法的塑性铰单元是一种精度高具计算成本低的宏观单元.Gauss-Radau积分法要求进行塑性计算的积分点只有两个,该积分法计算效率较高且精度良好,适用于整体结构的非线性分析之中,具有实际工程应用意义.
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Solution of Contact Problems for Nonlinear Gao Beam and Obstacle
J. Machalová
2015-01-01
Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.
Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam
Qing-xu Yan; Hui-chao Zou; De-xing Feng
2003-01-01
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
Boundary controllability for a nonlinear beam equation
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Nonlinear feedback control of Timoshenko beam
冯德兴; 张维弢
1995-01-01
This note is concerned with nonlinear boundary feedback control of a Timoshenko beam. Under some nonlinear boundary feedback control, first the nonlinear semigroup theory is used to show the existence and uniqueness of solution for the corresponding closed loop system. Then by using the Lyapunov method, it is proved that the vibration of the beam under the proposed control action decays in a negative power of time t as t→.
Methodology for nonlinear quantification of a flexible beam with a local, strong nonlinearity
Herrera, Christopher A.; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-02-01
This study presents a methodology for nonlinear quantification, i.e., the identification of the linear and nonlinear regimes and estimation of the degree of nonlinearity, for a cantilever beam with a local, strongly nonlinear stiffness element. The interesting feature of this system is that it behaves linearly in the limits of extreme values of the nonlinear stiffness. An Euler-Bernoulli cantilever beam with two nonlinear configurations is used to develop and demonstrate the methodology. One configuration considers a cubic spring attached at a distance from the beam root to achieve a smooth nonlinear effect. The other configuration considers a vibro-impact element that generates non-smooth effects. Both systems have the property that, in the limit of small and large values of a configuration parameter, the system is almost linear and can be modeled as such with negligible error. For the beam with a cubic spring attachment, the forcing amplitude is the varied parameter, while for the vibro-impact beam, this parameter is the clearance between the very stiff stops and the beam at static equilibrium. Proper orthogonal decomposition is employed to obtain an optimal orthogonal basis used to describe the nonlinear system dynamics for varying parameter values. The frequencies of the modes that compose the basis are then estimated using the Rayleigh quotient. The variations of these frequencies are studied to identify parameter values for which the system behaves approximately linearly and those for which the dynamical response is highly nonlinear. Moreover, a criterion based on the Betti-Maxwell reciprocity theorem is used to verify the existence of nonlinear behavior for the set of parameter values suggested by the described methodology. The developed methodology is general and applicable to discrete or continuous systems with smooth or nonsmooth nonlinearities.
CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM
张年梅; 杨桂通
2003-01-01
The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.
Application of gap element to nonlinear mechanics analysis of drillstring
刘巨保; 丁皓江; 张学鸿
2002-01-01
This paper presents a nonlinear finite element method to resolve the problem of the nonlinear contact between the drillstring and hole wall by using a Multi-directional Contact Gap Element (MCGE) contacting at appropriate positi o ns in each beam element. The method was successfully applied to the Daqing Oil F ield GP1 well. It was shown that the drillstring's contact resistance at any wel l depth could be obtained by calculations and that as the error in the calculati on of the hole top load is below 10%, the calculation result can provide theoret ical basis for the design and operation of drillstrings.
Nonlinear analysis of concrete beams strengthened by date palm fibers
Bouzouaid, Samia; Kriker, Abdelouahed
2017-02-01
The behaviour of concrete beams strengthened with date palm fibers was studied by Nonlinear Finite Element Analysis using ANSYS software. Five beams that were experimentally tested in a previous research were considered. The results obtained from the ANSYS finite element analysis are compared with the experimental data for the five beams with different amounts of fibres, ranging from 0.2% to 0.5% by a step equal to 0.1% and with a fibre length of 0.04 m. The results obtained by FEA showed good agreement with those obtained by the experimental program. This research demonstrates the ability of FEA in predicting the behaviour of beams strengthened with Date Palm fibers. It will help researchers in studying beams with different configurations without the need to go through the lengthy experimental testing programs.
NONLINEAR FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE BEAMS IN FIRE%火灾下钢筋混凝土梁非线性有限元分析
廖艳芬; 漆雅庆; 马晓茜
2011-01-01
Through numerical simulation of the whole process of heat transfer and deformation on three different conditions groups of reinfored concrete beams,it is analysed the non-linear changing process of the temperature distribution and structural deformation of reinfored concrete beams in fire.Based on thermal characteristics and the temperature-strain-stress constitutive characteristics of reinforced concrete beams it is analysied the influences of the evolutionary processes of the reinfored concrete beams temperature distribution in fire,as well as reinforcement ratio,initial load and heating time on the fire resistance capacity of reinfored concrete beams.Results show that the overall instability of the beams is caused by the reduction of material strength,weight and the initial load,as well as the internal stress because of the uneven heating in fire.The influences of initial load on the residual bearing capacity is little,but increase the number of rebars can effectively improve the fire resistance capacity of reinforced concrete beams.%为分析钢筋混凝土梁在火灾过程中的温度分布、结构变形非线性变化过程,在三组不同条件下对火灾后钢筋混凝土梁构件内部传热及变形过程进行全过程仿真。基于钢筋混凝土热工特性、温度-应变-应力本构特性,分析钢筋混凝土梁在受火时的温度分布演化过程,以及配筋率、初始载荷和受火时间等参数对钢筋混凝土梁防火承载力的影响。结果表明：火灾中材料强度的降低,自重和初始载荷以及不均匀升温引起的内部应力共同作用引起了构件的整体失稳。初始载荷对梁剩余承载力的影响不大,提高混凝土中钢筋数量能有效地提高钢筋混凝土梁的防火承载力。
Non-linear finite element modeling
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Nonlinear optimization of beam lines
Tomás Garcia, Rogelio
2006-01-01
The current final focus systems of linear colliders have been designed based on the local compensation scheme proposed by P. Raimondi and A. Seryi [1]. However, there exist remaining aberrations that deteriorate the performance of the system. This paper develops a general algorithm for the optimization of beam lines based on the computation of the high orders of the transfer map using MAD-X [2] and PTC [3]. The algorithm is applied to the CLIC [4] Beam Delivery System (BDS).
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Modeling of the vibrating beam accelerometer nonlinearities
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Bending of a nonlinear beam reposing on an unilateral foundation
Machalová J.
2011-06-01
Full Text Available This article is going to deal with bending of a nonlinear beam whose mathematical model was proposed by D. Y. Gao in (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches,Mech. Research Communication, 23 (1 1996. The model is based on the Euler-Bernoulli hypothesis and under assumption of nonzero lateral stress component enables moderately large deflections but with small strains. This is here extended by the unilateralWinkler foundation. The attribution unilateral means that the foundation is not connected with the beam. For this problem we demonstrate a mathematical formulation resulting from its natural decomposition which leads to a saddle-point problem with a proper Lagrangian. Next we are concerned with methods of solution for our problem by means of the finite element method as the paper (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech. Research Communication, 23 (1 1996 has no mention of it. The main alternatives are here the solution of a system of nonlinear nondifferentiable equations or finding of a saddle point through the use of the augmented Lagrangian method. This is illustrated by an example in the final part of the article.
Nonlinear Finite Element Analysis of Ocean Cables
Nam-Il KIM; Sang-Soo JEON; Moon-Young KIM
2004-01-01
This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparametric curved cable element based on the Lagrangian formulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.
Nonlinear analysis of the forced response of structural elements
Nayfeh, A. H.; Mook, D. T.; Sridhar, S.
1974-01-01
A general procedure is presented for the nonlinear analysis of the forced response of structural elements to harmonic excitations. Internal resonances (i.e., modal interactions) are taken into account. All excitations are considered, with special consideration given to resonant excitations. The general procedure is applied to clamped-hinged beams. The results reveal that exciting a higher mode may lead to a larger response in a lower interacting mode, contrary to the results of linear analyses.
Periodic solutions of nonlinear vibrating beams
J. Berkovits
2003-01-01
Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.
几何非线性新梁柱单元及结构程序设计%A geometric nonlinear new beam-column element and structure program design
张俊峰; 王利娟; 郝际平; 李天
2011-01-01
基于更新拉格朗日构形的增量虚位移原理,在其势能项中引入了全部6个应力分量,采用可计人单元剪切变形影响的三次多项式插值函数,详细推导了考虑剪切变形及翘曲的空间梁一柱单元几何非线性切线刚度矩阵.根据面向对象的程序设计思想,将整个有限元域划分为8个基本类,在单元基类的基础上派生了新的单元类,采用C++语言编制了面向对象的空间钢结构分析程序.几何非线性算例分析结果表明,本文提出的理论分析方法和计算程序是正确的和高效的.%According to the increment virtual displacement principle based on the updated Lagrange configuration,the potential energy associated with all six stress components was taken into account. The cubic interpolation function which can be used to consider the shear deformation effects has been applied to derive the geometrical nonlinear stiffness matrix of the space beam-column element considering the shear deformation and warping effects. Based on the object-oriented design conception, the finite element analysis domain is divided into eight classes. A new class is derived from the base element class. Using C+ + language,the spatial steel frame advanced analysis program is complied. Numerical examples including both geometric and material nonlinearities are used to demonstrate the accuracy and efficiency of the proposed analytical method and computer program.
A review of flexibility-based finite element method for beam-column elements
LI Shuang; ZHAI Changhai; XIE Lili
2009-01-01
For material nonlinear problem, elements derived with the flexibility-based method are more accurate than classical elements derived with the stiffness-based method. A review of the current state of the art of the flexibility-based finite element method is provided to enhance the robustness of structure analysis. The research on beam-column elements is the mainstream in the research on flexibility-based finite element method at present. The original development of flexibility-based finite element method is reviewed, and the further development of this method is then presented in several specific aspects, such as geometrically nonlinear analysis and dynamic analysis. The further research needed to be carried out in the future is finally discussed.
Beam stability & nonlinear dynamics. Formal report
Parsa, Z. [ed.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Electromagnetic beam propagation in nonlinear media
V.V.Semak; M.N.Shneider
2015-01-01
We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.
Beam Combining by Phase Transition Nonlinear Media
1990-02-01
use the Redlich Kwong equation of state for the media we consider. This equation of state can be written RT a p - -b -FT(p.-’ + b)p ; 2-I M (2-1) where...as ac 3 dg-A7 C VA/\\CIIJT (6) The Redlich - Kwong equation of state; i.e., _ RT T-1/2 v-P v(v+P) (7) can be used to compute aP/lT, where the relevant...practical the application of nonlinear phase conjugate techniques to the beam combining of multiple lasers with a coherence characteristic of a
Şeref Doğuşcan Akbaş
2013-01-01
Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.
苏栋
2012-01-01
The p-y curve method is one of the most commonly used approaches in the analysis and design of piles under horizontal loadings. A p-y model is proposed within the framework of bounding surface elasto-plastic theory. In comparison with the traditional p-y curves, the model can simulate p-y relationships with different degrees of nonlinearity by choosing appropriate values for the model parameters, and can also simulate the soil-pile interaction under cyclic loadings. By adopting the incremental finite element method for beams on nonlinear foundation incorporating the proposed elasto-plastic p-y model, a finite element program is formulated. Soil-pile systems in the field or in the laboratory tests under monotonic or cyclic horizontal loadings are analyzed by use of the finite element program. By comparing the calculated and measured results, the capacity of the method and the proposed elasto-plastic p-y model in modeling the nonlinear response of the piles is demonstrated.%在水平受荷桩基的分析与计算中，P—Y曲线法是应用较为广泛的方法之一。在边界面弹塑性理论的框架内，建立了一个P—Y模型。与传统的P—Y曲线比较，该模型能通过不同的参数取值，模拟不同非线性特性的P—Y关系，并能模拟往复荷载作用下的桩土相互作用。同时采用非线性地基梁的增量有限元法，结合提出的弹塑性P—Y模型，编制了有限元分析程序，对单调和往复水平荷载作用下的桩土系统进行实例分析，结果表明该方法能有效的模拟水平荷载作用下的桩基非线性响应。
Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics
Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne
1988-12-01
The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).
Nonlinear Finite Element Analysis of Sloshing
Siva Srinivas Kolukula
2013-01-01
Full Text Available The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.
Chaitanya, N Apurv; Banerji, J; Samanta, G K
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-09-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
Effect of transverse shears on complex nonlinear vibrations of elastic beams
Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.
2011-09-01
Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ⩽ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.
Anisotropic damping of Timoshenko beam elements
Hansen, M.H.
2001-01-01
This report contains a description of a structural damping model for Timoshenko beam elements used in the aeroelastic code HawC developed at Risø for modeling wind turbines. The model has been developed to enable modeling of turbine blades which oftenhave different damping characteristics...
Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions
郭强; 刘曦; 钟宏志
2004-01-01
This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Nonlinearly Coupled Superconducting Lumped Element Resonators
Collodo, Michele C.; Potočnik, Anton; Rubio Abadal, Antonio; Mondal, Mintu; Oppliger, Markus; Wallraff, Andreas
We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust et al., Phys Rev. B 91 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light
Stojanović, Vladimir; Petković, Marko D.
2016-12-01
Geometrically nonlinear free and forced vibrations of damaged high order shear deformable beams resting on a nonlinear Pasternak foundation are investigated in this paper. Equations of motion are derived for the beam which is under subjected combined action of arbitrarily distributed or concentrated transverse loading as well as axial loading. To account for shear deformations, the concept of high order shear deformation is used in comparison with the concept of first order shear deformation theory. Analyses are performed to investigate the effects of the specific stiffness of the foundation on the damaged beam frequencies and displacements with the aim of equalising the response of a damaged and an intact beam. According to that, functions of the foundation stiffness are determined depending on the location and size of the damage as a result of the possibility for the damaged beam to behave like one that is intact. An advanced p-version of the finite element method is developed for geometrically nonlinear vibrations of damaged Reddy-Bickford beams. The present study gives a clear view of the nonlinear dynamical behaviour of four types of beams according to high order shear deformation theory - an intact beam, a damaged beam, a damaged beam on an elastic foundation and intact beam on elastic foundation. The paper also presents the derivation of a new set of two nonlinear partial differential equations where only the transverse and axial displacements figure. The forced nonlinear vibrations problem is solved in the time domain using the Newmark integration method. Free vibration analysis carried out by harmonic balance and the use of continuation methods and backbone curves are constructed.
Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam
W. Gafsi
2014-01-01
Full Text Available In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.
GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES
陈务军; 付功义; 何艳丽; 董石麟
2002-01-01
Geometrically nonlinear stiffness matrix due to large displacement-small strain was firstly formulated ex-plicitly for the basic components of pantographic foldable structures,namely, the uniplet, derived from a three-node beam element. The formulation of the uniplet stiffness matrix is based on the precise nonlinear finite elementtheory and the displacement-harmonized and internal force constraints are applied directly to the deformationmodes of the three-node beam element. The formulations were derived in general form, and can be simplified forparticular foldable structures, such as flat, cylindrical and spherical structures. Finally, two examples were pre-sented to illustrate the applications of the stiffness matrix evolved.
Solution and Positive Solution to Nonlinear Cantilever Beam Equations
无
2008-01-01
Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the "height" of nonlinear term is appropriate on a bounded set.
GAO Jie
2009-01-01
In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC Ⅱ. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.
Chortis, Dimitris I
2013-01-01
This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...
Optical Beams in Nonlocal Nonlinear Media
Królikowski, W.; Bang, Ole; Wyller, J.
2003-01-01
We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons.......We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons....
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Nonlinear images of scatterers in chirped pulsed laser beams
Hu Yong-Hua; Wang You-Wen; Wen Shuang-Chun; Fan Dian-Yuan
2010-01-01
The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer.It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image,while the negative one can enhance it,and that both effects are inversely proportional to the incident pulse duration.Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that,for negatively pre-chirped pulsed beam,the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions.Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.
A hybrid transfinite element approach for nonlinear transient thermal analysis
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
A new computational approach for transient nonlinear thermal analysis of structures is proposed. It is a hybrid approach which combines the modeling versatility of contemporary finite elements in conjunction with transform methods and classical Bubnov-Galerkin schemes. The present study is limited to nonlinearities due to temperature-dependent thermophysical properties. Numerical test cases attest to the basic capabilities and therein validate the transfinite element approach by means of comparisons with conventional finite element schemes and/or available solutions.
Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers
Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.
of nonlinear beam reshaping occurring on a short time scale before the establishment of a steady state regime. In experiment, a 532nm laser beam can be injected into a single hole of an infiltrated PCF cladding structure, and the temporal dynamics of the nonlinear response is measured by monitoring......Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio......-sensing as well as active devices for all-optical switching at low (mW) laser powers. Commercially available PCFs infiltrated with liquids also provide a versatile and compact tool for exploration of the fundamentals of nonlinear beam propagation in periodic photonic structures. To explore the full scientific...
Xueqiong; Chen; Xiaoyan; Li; Ziyang; Chen; Jixiong; Pu; Guowen; Zhang; Jianqiang; Zhu
2013-01-01
The intensity distributions of a high-power broadband laser beam passing through a nonlinear optical medium with defects and then propagating in free space are investigated based on the general nonlinear Schr¨odinger equation and the split-step Fourier numerical method. The influences of the bandwidth of the laser beam, the thickness of the medium,and the defects on the light intensity distribution are revealed. We find that the nonlinear optical effect can be suppressed and that the uniformity of the beam can be improved for a high-power broadband laser beam with appropriate wide bandwidth. It is also found that, under the same incident light intensity, a thicker medium will lead to a stronger self-focusing intensity, and that the influence of defects in the optical elements on the intensity is stronger for a narrowband beam than for a broadband beam.
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
Non-Linear Vibration of Euler-Bernoulli Beams
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Suppressing Transverse Beam Halo with Nonlinear Magnetic Fields
Webb, Stephen D; Abell, Dan T; Danilov, Viatcheslav; Nagaitsev, Sergei; Valishev, Alexander; Danilov, Kirill; Cary, John R
2012-01-01
High intensity proton storage rings are central for the development of advanced neutron sources, drivers for the production of pions in neutrino factories or muon colliders, and transmutation of radioactive waste. Fractional proton loss from the beam must be very small to prevent radioac- tivation of nearby structures, but many sources of beam loss are driven by collective effects that increase with intensity. Recent theoretical work on the use of nonlinear magnetic fields to design storage rings with integrable transverse dynamics is extended here to include collective effects, with numerical results showing validity in the presence of very high beam current. Among these effects is the formation of beam halo, where particles are driven to large amplitude oscillations by coherent space charge forces. The strong variation of particle oscillation frequency with amplitude results in nonlinear decoherence that is observed to suppress transverse halo development in the case studied. We also present a necessary gen...
Reflection of a Gaussian beam from a nonlinear interface.
Marcuse, D
1980-09-15
A numerical analysis of the reflection of a two dimensional Gaussian beam from the interface between a linear and a nonlinear medium is presented. The refractive index of the nonlinear medium is a function of the intensity of the radiation field, having a smaller value than the linear refractive index for zero field intensity. The Gaussian beam is incident from the linear medium and suffers total reflection at low intensity. At sufficiently high intensity nonlinear effects are observed. Above a threshold value the incident beam breaks up into a reflected wave and a surface wave. Once the beam is sufficiently strong for a surface wave to form, its interaction with the boundary becomes surprisingly independent of field intensity; but for very strong fields the reflectivity is increased at the expense of the surface wave. A very different behavior is observed when the refractive index is constrained to remain below a certain maximum value. Now the field detaches itself from the surface and penetrates into the nonlinear medium forming one or more distinct beams. The plane wave theory predicts the existence of hysteresis so that two different solutions should exist for the same physical parameters. A second solution was indeed found in one case with constrained refractive index, but its validity is somewhat uncertain at this time.
Intense DC beam nonlinear transport-analysis & simulation
L(U) Jian-Qin; ZHAO Xiao-Song
2009-01-01
The intense dc beam nonlinear transport was analyzed with the Lie algebraic method,and the particle trajectories of the second order approximation were obtained.Based on the theoretical analysis a computer code was designed.To get self-consistent solutions,iteration procedures were used in the code.As an example,we calculated a beam line(drift-electrostatic quadrupole doublet-drift).The results agree to the results calculated by using the PIC method.
Finite element analysis and structural design of pretensioned inverted T-beams with web openings
Hock Tian CHENG; Bashar S. MOHAMMED; Kamal Nasharuddin MUSTAPHA
2009-01-01
This paper presents the results of a research project aimed at providing standard circular web openings to the popular precast pretensioned inverted T-beam.Opening size and placement and required materials strengths were investigated. In this paper the nonlinear analysis and design of simply supported pretensioned inverted T-beam with circular web openings are presented.Two design parameters are varied: opening location and number of openings. The results from nonlinear finite element analysis were substantiated by test results from five pretensioned inverted T-beams with web opening and one solid beam. Good agreement is shown between the theoretical and the experimental results. The test results obtained from this investigation show that the performance of the specimens with web openings is almost identical to that of the specimen without web openings. A simple design method for pretensioned inverted T-beam with
Finite rotation and nonlinear beam kinematics
Hodges, Dewey H.
1987-01-01
Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.
Nonlinear analysis of lipid tubules by nonlocal beam model.
Shen, Hui-Shen
2011-05-07
Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
Nonlinearities and effects of transverse beam size in beam position monitors
Kurennoy, Sergey S.
2001-09-01
The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.
Nonlinearities and effects of transverse beam size in beam position monitors
Sergey S. Kurennoy
2001-09-01
Full Text Available The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM are calculated and compared to those produced by a pencil beam. The nonlinearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.
C. E. M. Oliveira
Full Text Available This work investigates the response of two reinforced concrete (RC plane frames after the loss of a column and their potential resistance for progressive collapse. Nonlinear dynamic analysis is performed using a multilayered Euler/Bernoulli beam element, including elasto-viscoplastic effects. The material nonlinearity is represented using one-dimensional constitutive laws in the material layers, while geometrical nonlinearities are incorporated within a corotational beam formulation. The frames were designed in accordance with the minimum requirements proposed by the reinforced concrete design/building codes of Europe (fib [1-2], Eurocode 2 [3] and Brazil (NBR 6118 [4]. The load combinations considered for PC analysis follow the prescriptions of DoD [5]. The work verifies if the minimum requirements of the considered codes are sufficient for enforcing structural safety and robustness, and also points out the major differences in terms of progressive collapse potential of the corresponding designed structures.
Experimental damage detection of cracked beams by using nonlinear characteristics of forced response
Andreaus, U.; Baragatti, P.
2012-08-01
Experimental evaluation of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed, where an actual fatigue crack was introduced instead - as usual - of a narrow slot. The nonlinear aspects of the dynamic response of the beam under harmonic excitation were considered and the relevant quantitative parameters were evaluated, in order to relate the nonlinear resonances to the presence and size of the crack. To this end, the existence of sub- and super-harmonic components in the Fourier spectra of the acceleration signals was evidenced, and their amplitudes were quantified. In particular, the acceleration signals were measured in different positions along the beam axis and under different forcing levels at the beam tip. The remarkable relevance of the above mentioned nonlinear characteristics, and their substantial independence on force magnitude and measurement point were worthily noted in comparison with the behavior of the intact beam. Thus, a reliable method of damage detection was proposed which was based on simple tests requiring only harmonically forcing and acceleration measuring in any point non-necessarily near the crack. Then, the time-history of the acceleration recorded at the beam tip was numerically processed in order to obtain the time-histories of velocity and displacement. The nonlinear features of the forced response were described and given a physical interpretation in order to define parameters suitable for damage detection. The efficiency of such parameters was discussed with respect to the their capability of detecting damage and a procedure for damage detection was proposed which was able to detect even small cracks by using simple instruments. A finite element model of the cantilever beam was finally assembled and tuned in order to numerically simulate the results of the experimental tests.
Laser beam propagation in non-linearly absorbing media
Forbes, A
2006-08-01
Full Text Available Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well...
Non-Linear Vibration of Euler-Bernoulli Beams
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams
Koissin, Vitaly; Shipsha, Andrey; Skvortsov, Vitaly
2010-01-01
This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accou
Nonlinear Evolution of the Ion-Ion Beam Instability
Pécseli, Hans; Trulsen, J.
1982-01-01
The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates...
Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams
Koysin, V.; Shipsha, Andrey; Skvortsov, Vitaly
2010-01-01
This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accou
Mei, Chuh
1987-01-01
A finite element method is presented for the large amplitude vibrations of complex structures that can be modelled with beam and rectangular plate elements subjected to harmonic excitation. Both inplane deformation and inertia are considered in the formulation. Derivation of the harmonic force and nonlinear stiffness matrices for a beam and a rectangular plate element are presented. Solution procedures and convergence characteristics of the finite element method are described. Nonlinear response to uniform and concentrated harmonic loadings and improved nonlinear free vibration results are presented for beams and rectangular plates of various boundary conditions.
A distortional semi-discretized thin-walled beam element
Andreassen, Michael Joachim; Jönsson, Jeppe
2013-01-01
Due to the increased consumption of thin-walled structural elements there has been increasing focus and need for more detailed calculations as well as development of new approaches. In this paper a thin-walled beam element including distortion of the cross section is formulated. The formulation...... is based on a generalized beam theory (GBT), in which the classic Vlasov beam theory for analysis of open and closed thin-walled cross sections is generalized by including distortional displacements. The beam element formulation utilizes a semi-discretization approach in which the cross section...... is discretized into wall elements and the analytical solutions of the related GBT beam equations are used as displacement functions in the axial direction. Thus the beam element contains the semi-analytical solutions. In three related papers the authors have recently presented the semi-discretization approach...
Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section
DUAN Hai-juan; SONG Zhen-sen
2008-01-01
A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of flexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.
Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads
A. Bellino
2012-01-01
Full Text Available It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.
A Simple Model for Nonlinear Confocal Ultrasonic Beams
ZHANG Dong; ZHOU Lin; SI Li-Sheng; GONG Xiu-Fen
2007-01-01
@@ A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented.Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.
Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems
严承华; 王赤忠; 程尔升
2001-01-01
A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domainsecond order theory of water waves. Liquid sloshing in a rectangular container subjected to a horizontal excitation is sim-ulated by the finite element method. Comparisons between the two theories are made based on their numerical results. Itis found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur forlarge amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features ofnonlinear wave and can be used instead of the fully nonlinear theory.
Nonlinear structural finite element model updating and uncertainty quantification
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Nonlinear free vibrations of beams in space due to internal resonance
Stoykov, S.; Ribeiro, P.
2011-08-01
The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.
Stancari, Giulio
2014-09-11
Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compensation in LHC luminosity upgrade scenarios with small crossing angles. At Fermilab, we are planning to install an electron lens in the Integrable Optics Test Accelerator (IOTA, a 40-m ring for 150-MeV electrons) as one of the proof-of-principle implementations of nonlinear integrable optics to achieve large tune spreads and more stable beams without loss of dynamic aperture.
Dynamic nonlinear focal shift in amplitude modulated moderately focused acoustic beams.
Jiménez, Noé; Camarena, Francisco; González-Salido, Nuria
2017-03-01
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behavior, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by using a focused mono-element transducer excited by an amplitude modulated signal.
Nonlinear Analysis of External Prestressed Reinforced Concrete Beams with BFRP and CFRP
Haleem K. Hussain
2017-05-01
Full Text Available The traditional strengthening methods for concrete structure (girders, beams, columns…. consuming time and could be an economical, a new modern repair methods using the Carbon Fiber Reinforced Polymers (CFRP and Basalt Fiber Reinforced Polymer (BFRP as a laminate strips or bars,and considered a competitive solution that will increase the life-cycle of repaired structures. This study investigated the strengthen reinforced concrete girder. Nonlinear analysis have been adopted to the models using FEM analysis (ANSYS to simulate the theoretical results compared with experimental results.Using finite element packages, more efficient and better analyses can be made to fully understand the response of individual structural components and their contribution to a structure as a whole.Three type of material are used in this study as an external prestressed wire (steel, CFRP and BFRP. The prestressed beam is modeled as simply supported beam with two concentrated point load. The results showed that all tested strengthening beam increased the load carryingcapacity of the beams depend on prestressing force. Obtained Result was compared for different type of beam.This study also was enlarged to include using CFRP and BFRPbarwhich are light weight and moredurable, lead to ease of handling and maintenance. The research conducted analytical work to evaluate the effectiveness of concrete beams reinforced normally by the use of CFRP and BFRP bars. The results showed a significant gain in the beam’s ultimate capacities using CFRP bars comparing with beam reinforced with BFRP bar and reference beam
An improved two-node Timoshenko beam finite element
Friedman, Z.; Kosmatka, J. B.
1993-05-01
The stiffness, mass, and consistent force matrices for a simple two-node Timoshenko beam element are developed based upon Hamilton's principle. Cubic and quadratic Lagrangian polynomials are used for the transverse and rotational displacements, respectively, where the polynomials are made interdependent by requiring them to satisfy the two homogeneous differential equations associated with Timoshenko's beam theory. The resulting stiffness matrix, which can be exactly integrated and is free of 'shear-locking', is in agreement with the exact Timoshenko beam stiffness matrix. Numerical results are presented to show that the current element exactly predicts the displacement of a short beam subjected to complex distributed loadings using only one element, and the current element predicts shear and moment resultants and natural frequencies better than existing Timoshenko beam elements.
Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances
Ali H. Nayfeh
1998-01-01
Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam
Yue Wu; Jingshi Dong; Xinbo Li; Zhigang Yang; Qingping Liu
2015-01-01
Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used t...
Tracking control of a flexible beam by nonlinear boundary feedback
Bao-Zhu Guo
1995-01-01
Full Text Available This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.
Timoshenko beam element with anisotropic cross-sectional properties
Stäblein, Alexander; Hansen, Morten Hartvig
2016-01-01
Beam models are used for the aeroelastic time and frequency domain analysis of wind turbines due to their computational efficiency. Many current aeroelastic tools for the analysis of wind turbines rely on Timoshenko beam elements with classical crosssectional properties (EA, EI, etc.). Those cross......-sectional properties do not reflect the various couplings arising from the anisotropic behaviour of the blade material. A twonoded, three-dimensional Timoshenko beam element was therefore extended to allow for anisotropic cross-sectional properties. For an uncoupled beam, the resulting shape functions are identical...
Nonlinear/linear unified thermal stress formulations - Transfinite element approach
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
A new unified computational approach for applicability to nonlinear/linear thermal-structural problems is presented. Basic concepts of the approach including applicability to nonlinear and linear thermal structural mechanics are first described via general formulations. Therein, the approach is demonstrated for thermal stress and thermal-structural dynamic applications. The proposed transfinite element approach focuses on providing a viable hybrid computational methodology by combining the modeling versatility of contemporary finite element schemes in conjunction with transform techniques and the classical Bubnov-Galerkin schemes. Comparative samples of numerical test cases highlight the capabilities of the proposed concepts.
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Nonlinear Finite Element Analysis of Reinforced Concrete Shells
Mustafa K. Ahmed
2013-05-01
Full Text Available This investigation is to develop a numerical model suitable for nonlinear analysis of reinforced concrete shells. A nine-node Lagrangian element Figure (1 with enhanced shear interpolation will be used in this study. Table (1 describes shape functions and their derivatives of this element.An assumed transverse shear strain is used in the formulation of this element to overcome shear locking. Degenerated quadratic thick plate elements employing a layered discrelization through the thickness will be adopted. Different numbers of layers for different thickness can be used per element. A number of layers between (6 and 10 have proved to be appropriate to represent the nonlinear material behavior in structures. In this research 8 layers will be adequate. Material nonlinearities due to cracking of concrete, plastic flow or crushing of concrete in compression and yield condition of reinforcing steel are considered. The maximum tensile strength is used as a criterion for crack initiation. Attention is given to the tension stiffening phenomenon and the degrading effect of cracking on the compressive and shear strength of concrete. Perfect bond between concrete and steel is assumed. Attention is given also to geometric nonlinearities. An example have been chosen in order to demonstrate the suitability of the models by comparing the predicted behaviour with the experimental results for shell exhibiting various modes of failure.
Static Analysis of Steel Fiber Concrete Beam With Heterosis Finite Elements
James H. Haido
2014-08-01
Full Text Available Steel fiber is considered as the most commonly used constructional fibers in concrete structures. The formulation of new nonlinearities to predict the static performance of steel fiber concrete composite structures is considered essential. Present study is devoted to investigate the efficiency of utilizing heterosis finite elements analysis in static analysis of steel fibrous beams. New and simple material nonlinearities are proposed and used in the formulation of these elements. A computer program coded in FORTRAN was developed to perform current finite element static analysis with considering four cases of elements stiffness matrix determination. The results are compared with the experimental data available in literature in terms of central deflections, strains, and failure form, good agreement was found. Suitable outcomes have been observed in present static analysis with using of tangential stiffness matrix and stiffness matrix in second iteration of the load increment.
Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities
Qiuju Tuo
2015-01-01
Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.
LEADS-DC: A computer code for intense dc beam nonlinear transport simulation
无
2011-01-01
An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ~13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously,the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.
3D Nonlinear Numerical Simulation of Intact and Debonded Reinforced Concrete Beams
Chen Quan(陈权); Marcus L.
2004-01-01
To study the behaviour of reinforced concrete (RC) structures with sections of concrete removed and the reinforcement exposed, 3D nonlinear numerical analysis was performed upon both intact and debonded RC beams by using finite element techniques. The deformational characteristics and the ultimate loads were obtained through numerical models, as well as crack and stress distributions. The failure modes can also be deduced from computational results. Compared with intact beams, the normal assumptions of plane section behaviour is not hold true and the patterns of stress and strain are different in debonded RC beams. The numerical results show good consistency with experimental data. This kind of numerical simulation is a supplement to existing codes.
An Orthogonal Residual Procedure for Nonlinear Finite Element Equations
Krenk, S.
A general and robust solution procedure for nonlinear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state...
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
A Dual Orthogonality Procedure for Nonlinear Finite Element Equations
Krenk, S.; Hededal, O.
In the orthogonal residual procedure for solution of nonlinear finite element equations the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is here shown that the quasi-newton formulation of the orthogonal residual...
Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam
Yue Wu
2015-08-01
Full Text Available Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used to increase the output displacement at a lower voltage. The system is analytically modeled with Lagrangian functional and Euler–Lagrange equations, numerically simulated with MATLAB, and experimentally realized to demonstrate its enhanced capabilities. The model is validated using an experimental device with several pretensions of the loading spring, therein representing three interesting cases: a linear system, a low natural frequency system with a pre-buckled beam, and a system with a buckled beam. The motivating hypothesis for the current work is that nonlinear phenomena could be exploited to improve the effectiveness of the piezoelectric actuator’s displacement output. The most practical configuration seems to be the pre-buckled case, in which the proposed system has a low natural frequency, a high tip displacement, and a stable balanced position.
Generation of non-classical optical fields by a beam splitter with second-order nonlinearity
Prakash, Hari
2016-01-01
We propose quantum-mechanical model of a beam splitter with second-order nonlinearity and show that non-classical features such as squeezing and sub-Poissonian photon statistics of optical fields can be generated in output fundamental and second harmonic modes when we mix coherent light beams via such a nonlinear beam splitter.
Explicit free‐floating beam element
Nielsen, Martin Bjerre; Krenk, Steen
2014-01-01
via scalar products of the element related vectors. This leads to a homogeneous quadratic strain definition in terms of the generalized displacements, whereby the elastic energy becomes at most bi‐quadratic. Additionally, the use of independent equilibrium modes to set up the element stiffness avoids...
Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.
Shemer, Keren; Voloch-Bloch, Noa; Shapira, Asia; Libster, Ana; Juwiler, Irit; Arie, Ady
2013-12-15
We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process.
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
Quasi-periodic Solutions of the General Nonlinear Beam Equations
GAO YI-XIAN
2012-01-01
In this paper,one-dimensional (1D) nonlinear beam equations of the form utt - uxx + uxxxx + mu = f(u)with Dirichlet boundary conditions are considered,where the nonlinearity f is an analytic,odd function and f(u) = O(u3).It is proved that for all m ∈ (0,M*] (∈) R(M* is a fixed large number),but a set of small Lebesgue measure,the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system.The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.
Probabilistic finite elements for transient analysis in nonlinear continua
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
A nonlinear truss finite element with varying stiffness
Ďuriš R.
2007-11-01
Full Text Available This contribution deals with a new truss element with varying stiffness intended to geometric and physically nonlinear analysis of composite structures. We present a two-node straight composite truss finite element derived by new nonincremental full geometric nonlinear approach. Stiffness matrix of this composite truss contains transfer constants, which accurately describe the polynomial longitudinal variation of cross-section area and material properties. These variations could be caused by nonhomogenous temperature field or by varying components volume fractions of the composite or/and functionally graded materials (FGM´s. Numerical examples were solved to verify the established relations. The accuracy of the new proposed finite truss element are compared and discused.
An Electronically Controlled 8-Element Switched Beam Planar Array
Sharawi, Mohammad S.
2015-02-24
An 8-element planar antenna array with electronically controlled switchable-beam pattern is proposed. The planar antenna array consists of patch elements and operates in the 2.45 GHz ISM band. The array is integrated with a digitally controlled feed network that provides the required phases to generate 8 fixed beams covering most of the upper hemisphere of the array. Unlike typical switchable beam antenna arrays, which operate only in one plane, the proposed design is the first to provide full 3D switchable beams with simple control. Only a 3-bit digital word is required for the generation of the 8 different beams. The integrated array is designed on a 3-layer PCB on a Taconic substrate (RF60A). The total dimensions of the fabricated array are 187.1 × 261.3 × 1.3mm^{3}.
Finite element model calibration of a nonlinear perforated plate
Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.
2017-03-01
This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.
Beam and Truss Finite Element Verification for DYNA3D
Rathbun, H J
2007-07-16
The explicit finite element (FE) software program DYNA3D has been developed at Lawrence Livermore National Laboratory (LLNL) to simulate the dynamic behavior of structures, systems, and components. This report focuses on verification of beam and truss element formulations in DYNA3D. An efficient protocol has been developed to verify the accuracy of these structural elements by generating a set of representative problems for which closed-form quasi-static steady-state analytical reference solutions exist. To provide as complete coverage as practically achievable, problem sets are developed for each beam and truss element formulation (and their variants) in all modes of loading and physical orientation. Analyses with loading in the elastic and elastic-plastic regimes are performed. For elastic loading, the FE results are within 1% of the reference solutions for all cases. For beam element bending and torsion loading in the plastic regime, the response is heavily dependent on the numerical integration rule chosen, with higher refinement yielding greater accuracy (agreement to within 1%). Axial loading in the plastic regime produces accurate results (agreement to within 0.01%) for all integration rules and element formulations. Truss elements are also verified to provide accurate results (within 0.01%) for elastic and elastic-plastic loading. A sample problem to verify beam element response in ParaDyn, the parallel version DYNA3D, is also presented.
Finite Element Vibration Analysis of Beams, Plates and Shells
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element vibration analysis of beams, plates and shells that were published in 1994–1998. It contains 361 citations. Also included, as separated subsections, are vibration analysis of composite materials and vibration analysis of structural elements with cracks/contacts.
On two transverse nonlinear models of axially moving beams
无
2009-01-01
Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.
On two transverse nonlinear models of axially moving beams
DING Hu; CHEN LiQun
2009-01-01
Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit-ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av-eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif-ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte-gro-partial-differential equation gives better results for large amplitude vibration.
NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION
崔霞
2002-01-01
A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.
A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation
Crivelli, Luis A.; Felippa, Carlos A.
1992-01-01
A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.
Finite element analysis of rotating beams physics based interpolation
Ganguli, Ranjan
2017-01-01
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Nonlinear dynamics for charges particle beams with a curved axis in the matrix - recursive model
Dymnikov, A.D. [University of St Petersburg, (Russian Federation). Institute of Computational Mathematics and Control Process
1993-12-31
In this paper a new matrix and recursive approach has been outlined for treating nonlinear optics of charged particle beams. This approach is a new analytical and computational tool for designers of optimal beam control systems. 9 refs.
Nonlinear Finite Element Analysis of Nanoindentation of Viral Capsids
Gibbons, M M; Gibbons, Melissa M.; Klug, William S.
2006-01-01
Recent Atomic Force Microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick shell models are proposed for two capsids: the spherical Cowpea Chlorotic Mottle Virus (CCMV), and the ellipsocylindrical bacteriophage $\\phi 29$. As analyzed by the finite element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive details, and greatly influenced by geometry. Nonlinear stiffening and softening of the force response is dependent on ...
Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors
M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan
2011-09-01
The beam position monitors at CEBAF have four antenna style pickups that are used to measure the location of the beam. There is a strong nonlinear response when the beam is far from the electrical center of the device. In order to conduct beam experiments at large orbit excitation we need to correct for this nonlinearity. The correction algorithm is presented and compared to measurements from our stretched wire BPM test stand.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Arc-length technique for nonlinear finite element analysis
MEMON Bashir-Ahmed; SU Xiao-zu(苏小卒)
2004-01-01
Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, Received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.
2011-11-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Maker, B.N.
1995-04-14
This report provides a user`s manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.
Woo-Young Jung
2015-04-01
Full Text Available For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.
Dynamic Stiffness Matrix for a Beam Element with Shear Deformation
Walter D. Pilkey
1995-01-01
Full Text Available A method for calculating the dynamic transfer and stiffness matrices for a straight Timoshenko shear beam is presented. The method is applicable to beams with arbitrarily shaped cross sections and places no restrictions on the orientation of the element coordinate system axes in the plane of the cross section. These new matrices are needed because, for a Timoshenko beam with an arbitrarily shaped cross section, deflections due to shear in the two perpendicular planes are coupled even when the coordinate axes are chosen to be parallel to the principal axes of inertia.
Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.
2015-03-01
This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.
E. Mardani
2008-01-01
Full Text Available A prismatic beam made of a behaviorally nonlinear material was analyzed under a concentrated load moving with a known velocity on a nonlinear elastic foundation with a reaction the vibration equation of motion was derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculated by the presented solution. Considering the response of the beam, in the sense of its resonance, it was found that there is no critical velocity when the behavior of the beam and foundation material is assumed to be physically nonlinear and there are finite values for the deflection, stress and bending moment of the beam when
A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis
Jokhio, G. A.; Izzuddin, B. A.
2015-05-01
This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.
FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
文双春; 范滇元
2001-01-01
The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing
Karamehmedovic, Emir; Pedersen, Christian; Jensen, Ole Bjarlin;
2009-01-01
We investigate the possibility of improving the beam quality and obtaining high conversion efficiency in nonlinear sum-frequency generation. A 765 nm beam from an external cavity tapered diode laser is single-passed through a nonlinear crystal situated in the high intracavity field of a 1342 nm Nd...
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells
Humberto Breves Coda
2009-01-01
Full Text Available This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.
林倩; 邓志恒; 刘其舟
2012-01-01
Based on a low-cyclic loading experimental study on 4 full-scale specimens of a new type of steel truss coupling beam, the failure patterns and the load-displacement hysteretic curves of the beams＇ loading point were studied, and the beams＇ ductility, rigidity degradation discipline and energy dissipation mechanism were analyzed as well. Nonlinear finite element analyses were conducted on these beams under monotonic loading and low cyclic loading using ABAQUS. The result of finite element calculation and test shows that the load-displacement curves and bearing capacities＇ characteristic points of both methods are in a good agreement, which all prove that the steel truss coupling beam has good ductility and good ability of dissipating earthquake energy. Parametric analyses were carried on to investigate the influences of the sections of web members and chord members, and the span-to-depth ratio on the beams＇ mechanical property, which can be available for reference of further research and aseismic design of the steel truss coupling beam system.%对4个足尺的新型钢桁架连梁试件进行了低周反复荷载试验，研究了试件的破坏形态，测量分析了连梁加载点的荷载位移滞回曲线，并分析了连梁的延性、刚度退化规律和耗能能力。采用通用软件ABAQUS对钢桁架连梁进行了单调加载及低周反复加载作用下的非线性有限元分析。有限元计算和试验结果对比分析表明：两者的荷载位移曲线及承载力特征点吻合较好，都证明钢桁架连梁具有较好的延性，能够耗散较大的地震能量。在此基础上对钢桁架连梁进行了参数分析，研究了腹杆截面、弦杆截面和跨高比对连梁受力性能的影响，以供进一步研究和工程设计参考。
Large areas elemental mapping by ion beam analysis techniques
Silva, T. F.; Rodrigues, C. L.; Curado, J. F.; Allegro, P.; Moro, M. V.; Campos, P. H. O. V.; Santos, S. B.; Kajiya, E. A. M.; Rizzutto, M. A.; Added, N.; Tabacniks, M. H.
2015-07-01
The external beam line of the Laboratory for Material Analysis with Ion Beams (LAMFI) is a versatile setup for multi-technique analysis. X-ray detectors for Particle Induced X-rays Emission (PIXE) measurements, a Gamma-ray detector for Particle Induced Gamma- ray Emission (PIGE), and a particle detector for scattering analysis, such as Rutherford Backscattering Spectrometry (RBS), were already installed. In this work, we present some results, using a large (60-cm range) XYZ computer controlled sample positioning system, completely developed and build in our laboratory. The XYZ stage was installed at the external beam line and its high spacial resolution (better than 5 μm over the full range) enables positioning the sample with high accuracy and high reproducibility. The combination of a sub-millimeter beam with the large range XYZ robotic stage is being used to produce elemental maps of large areas in samples like paintings, ceramics, stones, fossils, and all sort of samples. Due to its particular characteristics, this is a unique device in the sense of multi-technique analysis of large areas. With the continuous development of the external beam line at LAMFI, coupled to the robotic XYZ stage, it is becoming a robust and reliable option for regular analysis of trace elements (Z > 5) competing with the traditional in-vacuum ion-beam-analysis with the advantage of automatic rastering.
STIFFNESS EQUATION OF FINITE SEGMENT FOR FLEXIBLE BEAM-FORMED STRUCTURAL ELEMENTS
无
2000-01-01
The finite segment modelling for the flexible beam-formed structural elemens is presented,in which the discretization views of the finite segment method and the difference from the finite element method are introduced. In terms of the nodal model, the joint properties are described easily by the model of the finite segment method,and according to the element properties,the assumption of the small strain is only met in the finite segment method, i. e., the geometric nonlinear deformation of the flexible bodies is allowable.Consequently, the finite segment method is very suited to the flexible multibody structure. The finite segment model is used and the arc differentiation is adopted for the differential beam segments.The stiffness equation is derived by the use of the principle of virtual work. The new modelling method shows its normalization, clear physical and geometric meanings and simple computational process.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Limit Analysis of 3D Reinforced Concrete Beam Elements
Larsen, Kasper P.; Nielsen, Leif Otto; Poulsen, Peter Noe
2012-01-01
A new finite-element framework for lower-bound limit analysis of reinforced concrete beams, subjected to loading in three dimensions, is presented. The method circumvents the need for a direct formulation of a complex section-force-based yield criterion by creating a discrete representation of th...
Walasik, Wiktor T.; Silahli, Salih Z.; Litchinitser, Natalia M.
2016-09-01
Colloidal metamaterials are a robust and flexible platform for engineering of optical nonlinearities and studies of light filamentation. To date, nonlinear propagation and modulation instability of Gaussian beams and optical vortices carrying orbital angular momentum were studied in such media. Here, we investigate the propagation of necklace beams and the conservation of the orbital angular momentum in colloidal media with saturable nonlinearity. We study various scenarios leading to generation of helical necklace beams or twisted beams, depending on the radius, power, and charge of the input vortex beam. Helical beams are build of two separate solitary beams with circular cross-sections that spiral around their center of mass as a result of the equilibrium between the attraction force of in-phase solitons and the centrifugal force associated with the rotational movement. A twisted beam is a single beam with an elliptical cross-section that rotates around it's own axis. We show that the orbital angular momentum is converted into the rotational motion at different rates for helical and twisted beams. While earlier studies reported that solitary beams are expelled form the initial vortex ring along straight trajectories tangent to the vortex ring, we show that depending on the charge and the power of the initial beam, these trajectories can diverge from the tangential direction and may be curvilinear. These results provide a detailed description of necklace beam dynamics in saturable nonlinear media and may be useful in studies of light filamentation in liquids and light propagation in highly scattering colloids and biological samples.
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Modeling colliding beams with an element by element representation of the storage ring guide field
D. L. Rubin
2006-01-01
Full Text Available A detailed model of the Cornell Electron Storage Ring (CESR guide field, including beam-beam interaction computed in the weak-strong regime, is the basis for a multiturn simulation of luminosity. The simulation reproduces the dependence of luminosity on bunch current that is measured in the storage ring, at both high-energy (5.3 GeV/beam and in the wiggler-dominated low energy (CESR-c configuration (1.9 GeV/beam. Dynamics are determined entirely by the physics of propagation through the individual guide field elements with no free parameters. Energy dependence of the compensation of the transverse coupling introduced by the experimental solenoid is found to significantly degrade specific luminosity. The simulation also indicates a strong dependence of limiting beam-beam tune shift parameter on the geometric mean of synchrotron tune and bunch length.
Hashemi, Seyed M.; Roach, Andrew
2011-12-01
The application of a Dynamic Finite Element (DFE) technique to the extensional-torsional free vibration analysis of nonuniform composite beams, in the absence of flexural coupling, is presented. The proposed method is a fusion of the Galerkin weighted residual formulation and the Dynamic Stiffness Matrix (DSM) method, where the basis functions of approximation space are assumed to be the closed form solutions of the differential equations governing uncoupled extensional and torsional vibrations of the beam. The use of resulting dynamic trigonometric interpolation (shape) functions leads to a frequency dependent stiffness matrix, representing both mass and stiffness properties of the beam element. Assembly of the element matrices and the application of the boundary conditions then leads to a frequency dependent nonlinear eigenproblem, which is solved to evaluate the system natural frequencies and modes. Two illustrative examples of uniform and tapered cantilevered, Circumferentially Uniform Stiffness ( CUS), hollow, composite beams are presented. The influence of ply fibre-angle on the natural frequencies is also studied. The correctness of the theory and the superiority of the proposed DFE over the contrasting DSM and conventional FEM methods are confirmed by the published results and numerical checks. The discussion of results is followed by some concluding remarks.
Vibration Analysis of Beams by Spline Finite Element
YANG Hao; SUN Li
2011-01-01
In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.
Suppression of space charge induced beam halo in nonlinear focusing channel
Batygin, Yuri K.; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao
2016-04-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel
Batygin, Yuri K; Kurennoy, Sergey; Li, Chao
2016-01-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media
Qiu, Yunli; Chen, Zhaoxi; He, Yingji
2017-04-01
Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.
Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays.
Cao, Zheng; Tan, Qinggui; Li, Xiaojun; Qi, Xinyuan
2016-08-20
We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.
Finite Element Analysis of a Natural Fiber (Maize Composite Beam
D. Saravana Bavan
2013-01-01
Full Text Available Natural fiber composites are termed as biocomposites or green composites. These fibers are green, biodegradable, and recyclable and have good properties such as low density and low cost when compared to synthetic fibers. The present work is investigated on the finite element analysis of the natural fiber (maize composite beam, processed by means of hand lay-up method. Composite beam material is composed of stalk-based fiber of maize and unsaturated polyester resin polymer as matrix with methyl ethyl ketone peroxide (MEKP as a catalyst and Cobalt Octoate as a promoter. The material was modeled and resembled as a structural beam using suitable assumption and analyzed by means of finite element method using ANSYS software for determining the deflection and stress properties. Morphological analysis and X-ray diffraction (XRD analysis for the fiber were examined by means of scanning electron microscope (SEM and X-ray diffractometer. From the results, it has been found that the finite element values are acceptable with proper assumptions, and the prepared natural fiber composite beam material can be used for structural engineering applications.
Beam section stiffness properties usig 3D finite elements
Couturier, Philippe; Krenk, Steen; Høgsberg, Jan Becker
2013-01-01
The cross-section properties of a beam is characterized by a six by six stiffness matrix, relating the six generalized strains to the conjugate section forces. The problem is formulated as a single-layer finite element model of a slice of the beam, on which the six deformation modes are imposed via...... Lagrange multipliers. The Lagrange multipliers represent the constraining forces, and thus combine to form the cross-section stiffness matrix. The theory is illustrated by a simple isotropic cross-section....
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
Atilgan, Ali R.; Hodges, Dewey H.
1991-01-01
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.;
2011-01-01
The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when...... nonlinear model....
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Jianqin Lü; Xiaosong Zhao
2008-01-01
Nonlinear transport of intense continuous beam in the axial-symmetric electrostatic fields is analyzed with the Lie algebraic method.The K-V particle distribution is adopted in the analysis. The results obtained can be used in the calculations of the intense continuous beam dynamics in the beam optical systems consisting of drift spaces, electrostatic lenses, and DC electrostatic accelerating tubes. A com-puter code has been designed for practical simulations. To meet the needs of accurate calculation, all the elements are divided into many small segments, the electric fields in each segment are regarded as uniform fields, and the dividing points are treated as thin lenses. Iter-ation procedures are adopted in the code to obtain self-consistent solutions. The code can be used to design low energy dc beam transport systems, electrostatic accelerators, and ion implantation machines.
Intermittent Giant Goos-Hanchen shifts from Airy beams at nonlinear interfaces
Chamorro-Posada, Pedro; Aceves, Alejandro B; McDonald, Graham S
2013-01-01
We study the giant Goos-Hanchen shift obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the numerical solution of the nonlinear Helmholtz equation. We report the existence of non-standard intermittent and oscillatory regimes for the nonlinear Goos-Hanchen shifts which can be explained in terms of the competition between the critical coupling to a surface mode of the reflected component of the Airy beam and the soliton emission from the refracted beam component.
Reciprocity breaking during nonlinear propagation of adapted beams through random media.
Palastro, J P; Peñano, J; Nelson, W; DiComo, G; Helle, M; Johnson, L A; Hafizi, B
2016-08-22
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
Widely varying giant Goos-Hänchen shifts from Airy beams at nonlinear interfaces.
Chamorro-Posada, Pedro; Sánchez-Curto, Julio; Aceves, Alejandro B; McDonald, Graham S
2014-03-15
We present a numerical study of the giant Goos-Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence of multiple critical values. These intermittent and oscillatory regimes can be explained in terms of competition between critical coupling to a surface mode and soliton emission from the refracted beam component and how this interplay varies with localization of the initial Airy beam.
Analytical modeling of sandwich beam for piezoelectric bender elements
无
2007-01-01
Piezoelectric bender elements are widely used as electromechanical sensors and actuators. An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory (FSDT), which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.
Nonlinear Stability of Intense Mismatched Beams in a Uniform Focusing Field
Pakter, Renato; Simeoni, Wilson
2005-01-01
We investigate the nonlinear coupling between axisymmetric and elliptic oscillations in the dynamics of intense beams propagating in a uniform magnetic focusing field. It is shown that finite amplitude mismatched oscillations of an initially round beam may destabilize elliptic oscillations, heavily affecting stability and the shape of the beam. This is a potential mechanics for beam particle loss in such systems. Self consistent simulations are performed to verify the findings.
Identification of cracks in thick beams with a cracked beam element model
Hou, Chuanchuan; Lu, Yong
2016-12-01
The effect of a crack on the vibration of a beam is a classical problem, and various models have been proposed, ranging from the basic stiffness reduction method to the more sophisticated model involving formulation based on the additional flexibility due to a crack. However, in the damage identification or finite element model updating applications, it is still common practice to employ a simple stiffness reduction factor to represent a crack in the identification process, whereas the use of a more realistic crack model is rather limited. In this paper, the issues with the simple stiffness reduction method, particularly concerning thick beams, are highlighted along with a review of several other crack models. A robust finite element model updating procedure is then presented for the detection of cracks in beams. The description of the crack parameters is based on the cracked beam flexibility formulated by means of the fracture mechanics, and it takes into consideration of shear deformation and coupling between translational and longitudinal vibrations, and thus is particularly suitable for thick beams. The identification procedure employs a global searching technique using Genetic Algorithms, and there is no restriction on the location, severity and the number of cracks to be identified. The procedure is verified to yield satisfactory identification for practically any configurations of cracks in a beam.
Efficient Coupler for a Bessel Beam Dispersive Element
Savchenkov, Anatoliy; Iltchenko, Vladimir; Matsko, Andrey; Le, Thanh; Yu, nan; Maleki, Lute
2008-01-01
A document discusses overcoming efficient optical coupling to high orbital momentum modes by slightly bending the taper dispersive element. This little shape distortion is not enough to scramble the modes, but it allows the use of regular, free-beam prism coupling, fiber coupling, or planar fiber on-chip coupling with, ultimately, 100 percent efficiency. The Bessel-beam waveguide is bent near the contact with the coupler, or a curved coupler is used. In this case, every Bessel-beam mode can be successfully coupled to a collimated Gaussian beam. Recently developed Bessel-beam waveguides allow long optical delay and very high dispersion. Delay values may vary from nanoseconds to microseconds, and dispersion promises to be at 100 s/nm. Optical setup consisted of a red laser, an anamorphic prism pair, two prism couplers, and a bent, single-mode fiber attached to prisms. The coupling rate increased substantially and corresponded to the value determined by the anamorphic prism pair.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J. [Argonne National Lab., IL (United States); Ramirez, M.R.; Gupta, S. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J. (Argonne National Lab., IL (United States)); Ramirez, M.R.; Gupta, S. (Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Riedlbauer, Daniel; Steinmann, Paul; Mergheim, Julia
2014-07-01
The present contribution is concerned with the macroscopic modelling of the selective electron beam melting process by using the finite element method. The modelling and simulation of the selective electron beam melting process involves various challenges: complex material behaviour, phase changes, thermomechanical coupling, high temperature gradients, different time and length scales etc. The present contribution focuses on performance considerations of solution approaches for thermomechanically coupled problems, i.e. the monolithic and the adiabatic split approach. The material model is restricted to nonlinear thermoelasticity with temperature-dependent material parameters. As a numerical example a straight scanning path is simulated, the predicted temperatures and stresses are analysed and the performance of the two algorithms is compared. The adiabatic split approach turned out to be much more efficient for linear thermomechanical problems, i.e. the solution time is three times less than with the monolithic approach. For nonlinear problems, stability issues necessitated the use of the Euler backward integration scheme, and therefore, the adiabatic split approach required small time steps for reasonable accuracy. Thus, for nonlinear problems and in combination with the Euler backward integration scheme, the monolithic solver turned out to be more efficient.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Chortis, Dimitris I.; Chrysochoidis, Nikos A.; Varelis, Dimitris S.; Saravanos, Dimitris A.
2011-11-01
A theoretical framework is presented for predicting the nonlinear damping and damped vibration of laminated composite strips due to large in-plane forces. Nonlinear Green-Lagrange axial strains are introduced in the governing equations of a viscoelastic composite and new nonlinear damping and stiffness matrices are formulated including initial stress effects. Building upon the nonlinear laminate mechanics, a damped beam finite element is developed. Finite element stiffness and damping matrices are synthesized and the static equilibrium is predicted using a Newton-Raphson solver. The corresponding linearized damped free-vibration response is predicted and modal frequencies and damping of the in-plane deflected strip are calculated. Numerical results quantify the nonlinear effect of in-plane loads on structural modal damping of various laminated composite strips. The modal loss-factors and natural frequencies of cross-ply Glass/Epoxy beams subject to in-plane loading are measured and correlated with numerical results.
Tunable nonlinear beam defocusing in infiltrated photonic crystal fibers
Rosberg, Christian Romer; Bennet, Francis H; Neshev, Dragomir N.;
2007-01-01
We demonstrate a novel experimental platform for discrete nonlinear optics based on infiltrated photonic crystal fibers. We observe tunable discrete diffraction and nonlinear self-defocusing, and apply the effects to realize a compact all-optical power limiter....
Suppression of beam halo-chaos using nonlinear feedback discrete control method
Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang
2002-01-01
Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally
Two-dimensional simulations of nonlinear beam-plasma interaction in isotropic and magnetized plasmas
Timofeev, I V
2012-01-01
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroying the BGK--type nonlinear wave are identified. In the weak magnetic field, the energy of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction goes predominantly to the short-wavelength upper-hybrid waves propagating parallel to the magnetic field, whereas in the strong magnetic field the spectral energy is transferred to the electrostatic whistlers with oblique propagation.
Notes on the nonlinear beam dynamics with strong damping in the CLIC Damping Ring
Levichev, Eugene; Shatilov, Dmitry
2010-01-01
The beam is injected into the CLIC damping ring with the relatively large emittance and energy spread and then is damped to the extremely low phase volume. During the damping process the betatron frequency of each particle changes due to the space charge tune shift and nonlinear dependence of the betatron tune on the amplitude. This nonlinearity is produced by the strong chromatic sextupoles, wiggler nonlinear field components and, again, by the space charge force. During the damping, the particle cross resonances, which can trap some fraction of the beam, cause the loss of intensity, the beam blow up and degrade the beam quality. In this paper we study the evolution of the beam distribution in time during the damping for the original lattice of the CLIC DR (May 2005). Geneva, Switzerland June 2010 CLIC – Note – 850
Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic Beams
Jiménez, Noé; González-Salido, Nuria
2016-01-01
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25 kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behaviour, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both, for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by ...
Fast character projection electron beam lithography for diffractive optical elements
Harzendorf, Torsten; Fuchs, Frank; Banasch, Michael; Zeitner, Uwe D.
2014-05-01
Electron beam lithography becomes attractive also for the fabrication of large scale diffractive optical elements by the use of the character projection (CP) technique. Even in the comparable fast variable shaped beam (VSB) exposure approach for conventional electron beam writers optical nanostructures may require very long writing times exceeding 24 hours per wafer because of the high density of features, as required by e.g. sub-wavelength nanostructures. Using character projection, the writing time can be reduced by more than one order of magnitude, due to the simultaneous exposure of multiple features. The benefit of character projection increases with increasing complexity of the features and decreasing period. In this contribution we demonstrate the CP technique for a grating of hexagonal symmetry at 350nm period. The pattern is designed to provide antireflective (AR) properties, which can be adapted in their spectral and angular domain for applications from VIS to NIR by changing the feature size and the etching depth of the nanostructure. This AR nanostructure can be used on the backside of optical elements e.g. gratings, when an AR coating stack could not be applied for the reason of climatic conditions or wave front accuracy.
Nonlinear dynamic characteristic analysis of jointed beam with clearance
Zhang, Jing; Guo, Hong-Wei; Liu, Rong-Qiang; Wu, Juan; Kou, Zi-Ming; Deng, Zong-Quan
2016-12-01
The impact and elasticity of discontinuous beams with clearance frequently affect the dynamic response of structures used in space missions. This study investigates the dynamic response of jointed beams which are the periodic units of deployable structures. The vibration process of jointed beams includes free-play and impact stages. A method for the dynamic analysis of jointed beams with clearance is proposed based on mode superposition and instantaneous static deformation. Transfer matrix, which expresses the relationship of the responses before and after the impact of jointed beams, is derived to calculate the response of the jointed beams after a critical position. The dynamic responses of jointed beams are then simulated. The effects of various parameters on the displacement and velocity of beams are investigated.
Element free Galerkin formulation of composite beam with longitudinal slip
Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad [Department of Civil Engineering, Universiti Selangor, Bestari Jaya, Selangor (Malaysia); Badli, Mohd Iqbal; Yassin, Airil Y. Mohd [Faculty of Civil Engineering, Universiti Teknologi Malaysia, Skudai, Johor (Malaysia)
2015-05-15
Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after been verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.
Beam Elements on Linear Variable Two-Parameter Elastic Foundation
Iancu-Bogdan Teodoru
2008-01-01
Full Text Available The traditional way to overcome the shortcomings of the Winkler foundation model is to incorporate spring coupling by assemblages of mechanical elements such as springs, flexural elements (beams in one-dimension, 1-D, plates in 2-D, shear-only layers and deformed, pretensioned membranes. This is the class of two-parameter foundations ? named like this because they have the second parameter which introduces interactions between adjacent springs, in addition to the first parameter from the ordinary Winkler?s model. This class of models includes Wieghardt, Filonenko-Borodich, Hetényi and Pasternak foundations. Mathematically, the equations to describe the reaction of the two-parameter foundations are equilibrium, and the only difference is the definition of the parameters. In order to analyse the bending behavior of a Euler-Bernoulli beam resting on linear variable two-parameter elastic foundation a (displacement Finite Element (FE formulation, based on the cubic displacement function of the governing differential equation, is introduced.
Finite Element Analysis of the Pseudo-elastic Behavior of Shape Memory Alloy Truss and Beam
Kamal M. Bajoria
2010-07-01
Full Text Available The pseudo-elastic behavior of Shape memory alloy (SMA truss and cantilever beam are investigated. Brinson’s one-dimensional material model, which uses the twinned and detwinned martensite fractions separately as internal variables, is applied in the algorithm to establish the SMA stress-strain characteristics. This material model also incorporates different young’s modulus for austenitic and martensite phase to represent the true SMA characteristics. In this model, a cosine function was used to express the evolution of the stress induced martensite fractions during the forward and reverse martensite phase transformation. A finite element formulation for the SMA truss member considering the geometric nonlinearity is proposed and the results are compared with the corresponding linear analysis. As a step forward, a finite element formulation for an SMA cantilever beam with an applied end moment is proposed. The load displacement characteristic for both the loading and unloading phases are considered to check the full pseudo-elastic hysteretic loop. In the numerical investigation, the stress-strain variation along the beam depth is also examined during the loading and unloading process to investigate the forward and reverse martensite phase transformation phenomena. Newton-Raphson’s iterative method is applied to get convergence to the equilibrium for each loading steps. During a complete loading-unloading process, the temperature is kept constant as the model is essentially an isothermal model. Numerical simulation is performed considering two different temperatures to demonstrate the effect of temperature on the hysteretic loop.
Johnson, J. M.; Reale, D. V.; Krile, J. T.; Garcia, R. S.; Cravey, W. H.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2016-05-01
In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.
Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX
Belova, E. V.; Gorelenkov, N. N.; Crocker, N. A.; Lestz, J. B.; Fredrickson, E. D.; Tang, S.; Tritz, K.
2017-04-01
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n =4 -9 , and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.
Bentley, Sean J; Heebner, John E; Boyd, Robert W
2006-04-01
We describe observations of various transverse instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe include two types of conical emission and the generation of a linear array of spots. These results can be understood in terms of the physical processes of self-diffraction, two-beam-excited conical emission, and seeded modulational instability.
Management of the orbital angular momentum of vortex beams in a quadratic nonlinear interaction
Bovino, Fabio A; Bertolotti, Mario; Sibilia, Concita
2011-01-01
Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.
Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation
Voss, Thomas; Scherpen, Jacquelien M. A.
2014-01-01
In this paper we develop a mathematical model for the dynamics of a nonlinear Timoshenko beam with piezoelectric actuation. This model can then be used to design controllers with the goal of achieving a desired shape of the beam. The control scheme can be used for several applications, e. g., vibrat
Singh, Navpreet; Gupta, Naveen; Singh, Arvinder
2016-12-01
This paper investigates second harmonic generation (SHG) of an intense Cosh-Gaussian (ChG) laser beam propagating through a preformed underdense collisional plasma with nonlinear absorption. Nonuniform heating of plasma electrons takes place due to the nonuniform irradiance of intensity along the wavefront of laser beam. This nonuniform heating of plasma leads to the self-focusing of the laser beam and thus produces strong density gradients in the transverse direction. The density gradients so generated excite an electron plasma wave (EPW) at pump frequency that interacts with the pump beam to produce its second harmonics. To envision the propagation dynamics of the ChG laser beam, moment theory in Wentzel-Kramers-Brillouin (W.K.B) approximation has been invoked. The effects of nonlinear absorption on self-focusing of the laser beam as well as on the conversion efficiency of its second harmonics have been theoretically investigated.
Rahman, T.
2009-01-01
In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is oft
SOME PROBLEMS CONCERNING FREE NON-LINEAR VIBRATIONS OF BEAM STRUCTURES
S. V. Bosakov
2008-01-01
Full Text Available The paper analyzes an influence of physical non-linearity material account on vibrations of single beams with various support fixing. The authors also analyze power criteria for existing stable periodic vibrations and dependence of vibration period on initial power is determined in the paper. Accurate values of an amplitude and non-linear bending vibration period of beams have been also determined as a conservative system with due account of initial conditions. A number of examples are given that clearly illustrate the obtained solutions and show an influence rate of the mentioned effects on amplitude-frequency characteristics of non-linear systems.
Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect
LIU Jin-yang; SHEN Ling-jie; HONG Jia-zhen
2005-01-01
Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with EulerBernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.
A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches
Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.
2013-10-01
This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.
Reciprocity breaking during nonlinear propagation of adapted beams through random media
Palastro, J P; Nelson, W; DiComo, G; Johnson, L A; Helle, M H; Hafizi, B
2016-01-01
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate profile aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
J. Awrejcewicz; A.V. Krysko; J. Mrozowski; O.A. Saltykova; M.V. Zhigalov
2011-01-01
Chaotic vibrations of flexible non-linear EulerBernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ωp, q0} is reported, and scenarios of the system transition into chaos are illustrated.
ZHANG Zhuo; L(U) Jian-Qin
2008-01-01
In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.
Plasmon beams interaction at interface between metal and dielectric with saturable Kerr nonlinearity
Ignatyeva, Daria O.; Sukhorukov, Anatoly P. [Lomonosov Moscow State University, Moscow (Russian Federation)
2012-12-15
We present a novel theory of surface plasmon polariton interaction on the surface of dielectric with saturable Kerr nonlinearity. The effect of the total internal reflection of a weak signal plasmon beam from a high-power reference beam is discussed. Both ray and wave theories are used to describe signal propagation. The effect of the signal tunneling through the narrow inhomogeneity induced by the reference beam is considered. (orig.)
Yesayan, G L
2001-01-01
The equations for the width and curvature radius of the wave front for a Gaussian beam of light propagating along the axis of the longitudinally inhomogeneous graded index waveguide with gain and losses in the presence of third-order nonlinearity are obtained. By means of numerical calculations it is shown that in such waveguides the mode of stabilization of the beam width is possible, when the absorption of radiation on the edges of the beam compensates its spreading caused by the longitudinal inhomogeneity and nonlinearity of the waveguide
Dual Ion Beam Deposition Of Diamond Films On Optical Elements
Deutchman, Arnold H.; Partyka, Robert J.; Lewis, J. C.
1990-01-01
Diamond film deposition processes are of great interest because of their potential use for the formation of both protective as well as anti-reflective coatings on the surfaces of optical elements. Conventional plasma-assisted chemical vapor deposition diamond coating processes are not ideal for use on optical components because of the high processing temperatures required, and difficulties faced in nucleating films on most optical substrate materials. A unique dual ion beam deposition technique has been developed which now makes possible deposition of diamond films on a wide variety of optical elements. The new DIOND process operates at temperatures below 150 aegrees Farenheit, and has been used to nucleate and grow both diamondlike carbon and diamond films on a wide variety of optical :taterials including borosilicate glass, quartz glass, plastic, ZnS, ZnSe, Si, and Ge.
Determining critical load in the multispan beams with the nonlinear model
DemÑ-r, D. Dönmez; Sinir, B. G.; Usta, L.
2017-01-01
The beams which are one of the most commonly used structural members are quite important for many researchers. Mathematical models determining the response of beams under external loads are concluded from elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. In this study, the derivation of the nonlinear model is introduced to determine the critical load in the multispan beams. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. For this purpose, the nonlinear mathematical model of the multispan Euler-Bernoulli beam is firstly obtained. To be able to obtain the independent of the material and the geometry, the present model are became dimensionless. Then, the critical axial load can be determined via the nonlinear solution of the governing equation.
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and tran
Controlling Beam Halo-chaos Using a Special Nonlinear Method
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
盛冬发; 张燕; 程昌钧
2004-01-01
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.
L. F. Kong
2013-01-01
Full Text Available This paper presents a method to enhance computational efficiency of the nonlinear dynamic analysis of the large-scale deep-hole drilling machine. Based on finite element model, the drilling shaft system is constructed into Timoshenko beam element on the basis of flexible rotary shaft so as to increase the accuracy of numerical calculation. In order to save the calculation time and resources, modal synthesis technique is adopted to reduce the feature modal of linear freedom degrees of drilling shaft system. As a result, the accuracy required by the non-linear analysis will not be loss. On the basis of these, the whirling characteristics of drilling shaft system are studied under the conditions of different shaft lengths, and simultaneously, the stability patterns of drilling shaft motion and its stability region are obtained in the selected drilling depth and cutting speed parameters while drilling intersection holes.
Nonlinear dynamic response of beam and its application in nanomechanical resonator
Yin Zhang; Yun Liu; Kevin D. Murphy
2012-01-01
Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application.Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed.The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach.The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity,its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects.However,for the nanomechanical resonator of the curvature-dominant nonlinearity,its dynamic nonlinearity is only dependent on axial loading.Compared with the tension-dominant nonlinearity,the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects.The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.
Soliton pair generation in the interactions of Airy and nonlinear accelerating beams
Zhang, Yiqi; Wu, Zhenkun; Zheng, Huaibin; Lu, Keqing; Li, Yuanyuan; Zhang, Yanpeng
2013-01-01
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.
Nonlinear Dynamic Analysis of Functionally Graded Timoshenko Beam fixed to a Rotating Hub
Panigrahi, B.; Pohit, G.
2016-08-01
The present work accounts centrifugal stiffening effect on the nonlinear vibration response of an FGM Timoshenko beam. Analysis is carried out for a cantilever beam fixed with a rotating hub. Material is assumed to have a gradation relation along the depth of the beam. Centrifugal force and axial displacement raised due to the rotating hub is incorporated in the strain energy equations. Subsequent to this, an iterative technique is employed to obtain amplitude dependent vibration response of a rotating Timoshenko beam while material follows a gradation relation along the beam depth. Main objective of the work is to obtain the effects of rotational speeds, hub radius, and different gradation relations on the linear as well as nonlinear frequencies and mode shapes.
Hong Qin
2000-08-01
Full Text Available Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1% in axial momentum of the beam particles.
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System
FANG JinQing; CHEN GuanRong; ZHOU LiuLai; WENG JiaQiang
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky-Vladimirsky, full Gauss,3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.
Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam
Abbas Moallemi-Oreh
2013-01-01
Full Text Available A two-node element is suggested for analyzing the stability and free vibration of Timoshenko beam. Cubic displacement polynomial and quadratic rotational fields are selected for this element. Moreover, it is assumed that shear strain of the element has the constant value. Interpolation functions for displacement field and beam rotation are exactly calculated by employing total beam energy and its stationing to shear strain. By exploiting these interpolation functions, beam elements' stiffness matrix is also examined. Furthermore, geometric stiffness matrix and mass matrix of the proposed element are calculated by writing governing equation on stability and beam free vibration. At last, accuracy and efficiency of proposed element are evaluated through numerical tests. These tests show high accuracy of the element in analyzing beam stability and finding its critical load and free vibration analysis.
Joglekar, D. M.; Mitra, M.
2016-08-01
An analytical-numerical method, based on the use of wavelet spectral finite elements (WSFE), is presented for studying the nonlinear interaction of flexural waves with a breathing crack present in a slender beam. The cracked beam is discretized using wavelet spectral finite elements which use compactly supported Daubechies scaling functions for approximating the temporal dependence of the transverse displacement. Rotational spring is used to model the open crack condition, and behavior of the beam in closed-crack condition is assumed to be similar to that of an intact beam. An intermittent switching between the open- and closed-crack conditions simulates crack-breathing, leading to a set of nonlinear equations which is solved using an iterative method. Results of the proposed method are compared with those obtained using the Fourier spectral finite element (FSFE) and 1D finite element (FE) methods, which show a close agreement. Existence of the higher-order harmonic components, indicative of the crack-induced bilinearity, is confirmed in the frequency domain response. Moreover, the time domain analysis reveals separation of harmonics resulting from the dispersive nature of the waveguide, which is further used for localizing the damage. A parametric study is presented to bring out the influence of crack-severity and -location on the extent of harmonic separation and on the relative strength of higher order harmonic. In addition to elaborating the use of WSFE in addressing the nonlinear wave-damage interaction, results of the present investigation can be potentially useful in devising strategies for an inverse analysis.
Damkilde, Lars; Pedersen, Ronnie
2012-01-01
This paper describes a new triangular plane element which can be considered as a linear strain triangular element (LST) extended with incompatible displacement modes. The extended element will have a full cubic interpolation of strains and stresses. The extended LST-element is connected with other...... elements similar to the LST-element i.e. through three corner nodes and three mid-side nodes. The incompatible modes are associated with two displacement gradients at each mid-side node and displacements in the central node. The element passes the patch test and converges to the exact solution. The element...... has been tested on a standard linear test such as Cook’s panel, and is shown as expected to be somewhat more flexible than the LST-element and the compatible quadratic strain element (QST). The extended element has also been applied to material non-linear geotechnical problems. Geotechnical problems...
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
无
2000-01-01
Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of nonlinear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest that the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an efficient tool to investigate the nonlinear problems.
Polarization of a probe laser beam due to nonlinear QED effects
Shakeri, Soroush; Kalantari, Seyed Zafarollah; Xue, She-Sheng
2017-01-01
Nonlinear QED interactions induce different polarization properties on a given probe beam. We consider the polarization effects caused by the photon-photon interaction in laser experiments, when a laser beam propagates through a constant magnetic field or collides with another laser beam. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian for both time-dependent and constant background field to explore the time evolution of the Stokes parameters Q, U, and V describing polarization. Assuming an initially linearly polarized probe laser beam, we also calculate the induced ellipticity and rotation of the polarization plane.
Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qi
2003-01-01
A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, ...
Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems
Knabner, Peter; Summ, Gerhard
2016-01-01
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite element method with augmented Crouzeix-Raviart ansatz space. We discuss the reduction of unknowns by static condensation and propose Newton's method for the solution of local and global systems. Finally, we show, how such a nonlinear problem arises from the mixe...
Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators.
Nourmohammadi, Zahra; Joshi, Surabhi; Vengallatore, Srikar
2016-01-01
The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.
3D Finite Element Numerical Simulation of Residual Stresses on Electron Beam Welded BT20 Plates
Lixing HUO; Furong CHEN; Yufeng ZHANG; Li ZHANG; Fangjun LIU; Gang CHEN
2004-01-01
A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in aswelded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated.The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%～ 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3)The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results.Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.
Nonlinear generation of whistler waves by an ion beam
Akimoto, K.; Winske, D.
1989-01-01
An electromagnetic hybrid code is used to simulate a new mechanism for whistler wave generation by an ion beam. First, a field-aligned ion beam becomes unstable to the electromagnetic ion/ion right-hand resonant instability which generates large amplitude MHD-like waves. These waves then trap the ion beam and increase its effective temperature anisotropy. As a result, the growth rates of the electron/whistler instability are significantly enhanced, and whistlers start to grow above the noise level. At the same time, because of the reduced parallel drift speed of the ion beam, the frequencies of the whistlers are also downshifted. Full simulations were performed to isolate and separately investigate the electron/ion whistler instability. The results are in agreement with the assumption of fluid electrons in the hybrid simulations and with the linear theory of the instability.
Free-Space Nonlinear Beam Combining Towards Filamentation
Rostami, Shermineh; Kepler, Daniel; Baudelet, Matthieu; Litchinitser, Natalia M; Richardson, Martin
2016-01-01
Multi-filamentation opens new degrees of freedom for manipulating electromagnetic waves in air. However, without control, multiple filament interactions, including attraction, repulsion or fusion often result in formation of complex disordered filament distributions. Moreover, high power beams conventionally used in multi-filament formation experiments often cause significant surface damage. The growing number of applications for laser filaments requires fine control of their formation and propagation. We demonstrate, experimentally and theoretically, that the attraction and fusion of ultrashort beams with initial powers below the critical value enable the eventual formation of a filament downstream. Filament formation is delayed to a predetermined distance in space, avoiding optical damage to external beam optics while still enabling robust filaments with controllable properties as if formed from a single high power beam. This paradigm introduces new opportunities for filament engineering eliminating the nee...
Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma
Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.
2016-07-01
Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.
A theoretical and experimental study on geometric nonlinearity of initially curved cantilever beams
Sushanta Ghuku
2016-03-01
Full Text Available This paper presents a theoretical and experimental study on large deflection behavior of initially curved cantilever beams subjected to various types of loadings. The physical system as a straight cantilever beam subjected to a tip concentrated load is considered in this study. Nonlinear differential equations are obtained for large deflection analysis of such a straight cantilever beam, and this problem is known to involve geometrical nonlinearity. The equations are solved numerically with the help of MATLAB® computational platform to get deflection profiles of the concerned problem. These results are imposed subsequently on the center line of an initially curved beam to get theoretical load-deflection behavior of curved beam problems. To verify the theoretical model, experiment is carried out with the master leaf of a leaf spring bundle by modeling it as an initially curved cantilever beam. The effects of initial clamping and geometry variations in the eye-region are observed from experimental investigation which is commonly neglected in the mathematical formulation. Comparisons of the theoretical results with the experimental results are quite good, but the avenues for further improvement are also reported. The proposed approach is further extended to study large deflection behavior of an initially curved cantilever beam subjected to distributed and combined load. These results are successfully validated with existing results for straight beams and some new results are furnished for initially curved cantilever beams.
Efficiency enhancement of a two-beam free-electron laser using a nonlinearly tapered wiggler
Maryam Zahedian; B.Maraghechi; M.H.Rouhani
2012-01-01
A nonlinear and non-averaged model of a two-beam free-electron laser (FEL) wiggler that is tapered nonlinearly in the absence of slippage is presented.The two beams are assumed to have different energies,and the fundamental resonance of the higher energy beam is at the third harmonic of the lower energy beam.By using Maxwell's equations and the full Lorentz force equation of motion for the electron beams,coupled differential equations are derived and solved numerically by the fourth-order Runge-Kutta method.The amplitude of the wiggler field is assumed to decrease nonlinearly when the saturation of the third harmonic occurs.By simulation,the optimum starting point of the tapering and the slopes for reducing the wiggler amplitude are found.This technique can be applied to substantially improve the efficiency of the two-beam FEL in the XUV and X-ray regions.The effect of tapering on the dynamical stability of the fast electron beam is also studied.
An efficient and accurate method for calculating nonlinear diffraction beam fields
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
Rahmouni, A.; Beidouri, Z.; Benamar, R.
2013-09-01
The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the
Nonlinear features identified by Volterra series for damage detection in a buckled beam
Shiki S. B.
2014-01-01
Full Text Available The present paper proposes a new index for damage detection based on nonlinear features extracted from prediction errors computed by multiple convolutions using the discrete-time Volterra series. A reference Volterra model is identified with data in the healthy condition and used for monitoring the system operating with linear or nonlinear behavior. When the system has some structural change, possibly associated with damage, the index metrics computed could give an alert to separate the linear and nonlinear contributions, besides provide a diagnostic about the structural state. To show the applicability of the method, an experimental test is performed using nonlinear vibration signals measured in a clamped buckled beam subject to different levels of force applied and with simulated damages through discontinuities inserted in the beam surface.
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter β. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of β on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved β values can be obtained by considering the diffraction effects.
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Efficient generation of Hermite-Gauss and Ince-Gauss beams through kinoform phase elements.
Aguirre-Olivas, Dilia; Mellado-Villaseñor, Gabriel; Sánchez-de-la-Llave, David; Arrizón, Victor
2015-10-01
We discuss the generation of Hermite-Gauss and Ince-Gauss beams employing phase elements whose transmittances coincide with the phase modulations of such beams. A scaled version of the desired field appears, distorted by marginal optical noise, at the element's Fourier domain. The motivation to perform this study is that, in the context of the proposed approach, the desired beams are generated with the maximum possible efficiency. A disadvantage of the method is the distortion of the desired beams by the influence of several nondesired beam modes generated by the phase elements. We evaluate such distortion employing the root mean square deviation as a figure of merit.
Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel
Sonu Sen; Meenu Asthana Varshney; Dinesh Varshney
2014-01-01
In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have num...
A new solution procedure for a nonlinear infinite beam equation of motion
Jang, T. S.
2016-10-01
Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.
The Nonlinear Interaction of Two-Crossed Focussed Ultrasonic Beams in the Presence of Turbulence
1988-06-10
in water or any fluid medium can be obtained by the vibration of a solid body in the fluid, such as the vibration of a vocal chord or guitar string . In... physical phenomenon due to the nonlinearity of sound arises from the interaction of two sound beams. Nonlinear acoustic theory predictions by Westervelt in...known experimental data for the turbulent velocity field. Goals of this research include mapping out the turbulence and studying the physical
GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
Yin-nian He; Yan-ren Hou; Li-quan Mei
2001-01-01
A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh,defined respectively on one coarse grid with grid size H and one fine grid with grid size h ＜＜ H. Comparison is also made with the finite element Galerkin method. If we choose H = O(ε-1/4h1/2), ε＞ 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid increment finite element space Wh. Finally, we provide numerical test which shows above results stated.
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
The present paper describes the development of a new hybrid computational approach for applicability for nonlinear/linear thermal structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements in conjunction with transform methods and the classical Bubnov-Galerkin schemes. Applicability of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capablities of the proposed hybrid transfinite element methodology.
Measurement of nonlinear observables in the Large Hadron Collider using kicked beams
Maclean, E. H.; Tomás, R.; Schmidt, F.; Persson, T. H. B.
2014-08-01
The nonlinear dynamics of a circular accelerator such as the Large Hadron Collider (LHC) may significantly impact its performance. As the LHC progresses to more challenging regimes of operation it is to be expected that the nonlinear single particle dynamics in the transverse planes will play an increasing role in limiting the reach of the accelerator. As such it is vital that the nonlinear sources are well understood. The nonlinear fields of a circular accelerator may be probed through measurement of the amplitude detuning: the variation of tune with single particle emittance. This quantity may be assessed experimentally by exciting the beam to large amplitudes with kicks, and obtaining the tunes and actions from turn-by-turn data at Beam Position Monitors. The large amplitude excitations inherent to such a measurement also facilitate measurement of the dynamic aperture from an analysis of beam losses following the kicks. In 2012 these measurements were performed on the LHC Beam 2 at injection energy (450 GeV) with the nominal magnetic configuration. Nonlinear coupling was also observed. A second set of measurements were performed following the application of corrections for b4 and b5 errors. Analysis of the experimental results, and a comparison to simulation are presented herein.
Numerical simulation of nonlinear processes in a beam-plasma system
Efimova, A. A., E-mail: anna.an.efimova@gmail.com; Berendeev, E. A.; Vshivkov, V. A. [Institute of Computational Mathematics and Mathematical Geophysics SB RAS 6 Acad. Lavrentyev Ave., Novosibirsk 630090 (Russian Federation); Dudnikova, G. I. [University of Maryland, College Park, MD 20742 (United States); Institute of Computational Technologies SB RAS, 6 Acad. Lavrentyev Ave., Novosibirsk 630090 (Russian Federation)
2015-10-28
In the present paper we consider the efficiency of the electromagnetic radiation generation due to various nonlinear processes in the beam-plasma system. The beam and plasma parameters were chosen close to the parameters in the experiment on the GOL-3 facility (BINP SB RAS). The model of the collisionless plasma is described by system of the Vlasov-Maxwell equations with periodic boundary conditions. The parallel numerical algorithm is based on the particles-in-cell method (PIC) with mixed Euler-Lagrangian domain decomposition. Various scenarios of nonlinear evolution in the beam-plasma system under the influence of an external magnetic field in case of a low density beam were studied. The energy transfer from one unstable mode to the others modes was observed.
Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media
Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong
2017-10-01
We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.
Two-dimensional nonlinear dynamics of bidirectional beam-plasma instability
Pavan, J.; Ziebell, L. F.; Gaelzer, R.; Yoon, P. H.
2009-01-01
Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.
Active Vibration Control of a Nonlinear Beam with Self- and External Excitations
J. Warminski
2013-01-01
Full Text Available An application of the nonlinear saturation control (NSC algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.
ON THE NONLINEAR TIMOSHENKO-KIRCHHOFF BEAM EQUATION
A.AROSIO
1999-01-01
When an elastic string with fixed ends is subjected to transverse vibrations, its length vaxiewith the time: this introduces chvages of the tension in the string. Thls induced Kirchoffto propose a nonlinear correction of the classical D'Alembert equation. Later on, Wolnowsky-
Hammerand, Daniel C.
Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to
Mamaev, A.V.; Saffman, M.; Zozulya, A.A.
1996-01-01
We analyze the evolution of (1+1) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate....... Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices....
Fardad, Shima; Mills, Matthew S; Zhang, Peng; Man, Weining; Chen, Zhigang; Christodoulides, D N
2013-09-15
We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.
Ella, Lior, E-mail: lior.ella@weizmann.ac.il; Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal [Faculty of Electrical Engineering, Technion, Haifa 32000 (Israel)
2015-01-07
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Optimizing nonlinear beam coupling in low-symmetry crystals.
Shumelyuk, A; Volkov, A; Odoulov, S; Grabar, A; Stoyka, I; Evans, D R
2014-10-01
The purpose of this paper is to find the polarizations and spatial orientations of the two interacting counterpropagating coherent light waves which ensure the largest beam coupling in monoclinic photorefractive crystal. The results of calculations are presented that are verified experimentally with Sn₂P₂S₆.
Nonlinear Vibration of an Elastically Restrained Tapered Beam
Karimpour, S; Ganji, S.S; Barari, Amin;
2012-01-01
This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method (EBM) and the iteration perturbation method (IPM). To assess the accuracy of solutions, we compare the results with the harmonic balance method (HBM). The obtained re...
Non-Linear Beam Transport System for the LENS 7 MeV Proton Beam
Jones, William P; Derenchuk, Vladimir Peter; Rinckel, Thomas; Solberg, Keith
2005-01-01
A beam transport system has been designed to carry a high-intensity low-emittance proton beam from the exit of the RFQ-DTL acceleration system of the Indiana University Low Energy Neutron System (LENS)* to the neutron production target. The goal of the design was to provide a beam of uniform density over a 3cm by 3cm area at the target. Two octupole magnets** are employed in the beam line to provide the necessary beam phase space manipulations to achieve this goal. First order calculations were done using TRANSPORT and second order calculations have been performed using TURTLE. Second order simulations have been done using both a Gaussian beam distribution and a particle set generated by calculations of beam transport through the RFQ-DTL using PARMILA. Comparison of the design characteristics with initial measurements from the LENS commissioning process will be made.
Nonlinear dynamics and chaos in an optomechanical beam
Navarro-Urrios, D; Colombano, M F; Garcia, P D; Sledzinska, M; Alzina, F; Griol, A; Martinez, A; Sotomayor-Torres, C M
2016-01-01
Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning between an optical resonance and the excitation laser. However, the interplay between such mechanisms could also enable unexpected physical phenomena to be used in new applications. In the present work, we exploit those non-linearities and their intercoupling with the mechanical degrees of freedom of a silicon OM nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser, namely its power and wavelength, we demonstrate accurate control for activating bi-dimensional and tetra-dimensional limit-cycles, a period doubling route and chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between bi-dimensional and tetra-dimensional limit-cycles, be...
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS
Dan-ping Yang
2002-01-01
Two least-squares mixed finite element schemes are formulated to solve the initialboundary value problem of a nonlinear parabolic partial differential equation and the convergence of these schemes are analyzed.
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Barut, A.; Madenci, Erdogan; Tessler, A.
1997-01-01
This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.
Nachbagauer, Karin, E-mail: karin.nachbagauer@jku.at; Pechstein, Astrid S., E-mail: astrid.pechstein@jku.at; Irschik, Hans, E-mail: hans.irschik@jku.at [Johannes Kepler University Linz, Institute of Technical Mechanics (Austria); Gerstmayr, Johannes, E-mail: johannes.gerstmayr@lcm.at [Linz Center of Mechatronics GmbH (Austria)
2011-10-15
Many widely used beam finite element formulations are based either on Reissner's classical nonlinear rod theory or the absolute nodal coordinate formulation (ANCF). Advantages of the second method have been pointed out by several authors; among the benefits are the constant mass matrix of ANCF elements, the isoparametric approach and the existence of a consistent displacement field along the whole cross section. Consistency of the displacement field allows simpler, alternative formulations for contact problems or inelastic materials. Despite conceptional differences of the two formulations, the two models are unified in the present paper.In many applications, a nonlinear large deformation beam element with bending, axial and shear deformation properties is needed. In the present paper, linear and quadratic ANCF shear deformable beam finite elements are presented. A new locking-free continuum mechanics based formulation is compared to the classical Simo and Vu-Quoc formulation based on Reissner's virtual work of internal forces. Additionally, the introduced linear and quadratic ANCF elements are compared to a fully parameterized ANCF element from the literature. The performance of the respective elements is evaluated through analysis of conventional static and dynamic example problems. The investigation shows that the obtained linear and quadratic ANCF elements are advantageous compared to the original fully parameterized ANCF element.
GUO Qintao; ZHANG Lingmi; TAO Zheng
2008-01-01
Thin wall component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments (DOE) and principal component decomposition (PCD) approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.
Stancari, Giulio
2014-01-01
Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compens...
Concatenated beam splitters, optical feed-forward and the nonlinear sign gate
Jacobs, K; Jacobs, Kurt; Dowling, Jonathan P.
2006-01-01
We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel et al. [Scheel et al., Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.
Nonlinear fracture mechanics investigation on the ductility of reinforced concrete beams
A. Carpinteri
Full Text Available In the present paper, a numerical algorithm based on the finite element method is proposed for the prediction of the mechanical response of reinforced concrete (RC beams under bending loading. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing. According to this model, the concrete dam- age in compression is represented by means of a fictitious interpenetration. The larger is the interpenetration, the lower are the transferred forces across the damaged zone. The well-known Cohesive Crack Model in tension and an elastic-perfectly plastic stress versus crack opening displacement relationship describing the steel reinforcement behavior are also integrated into the numerical algorithm. The application of the proposed Cohesive-Overlapping Crack Model to the assessment of the minimum reinforcement amount neces- sary to prevent unstable tensile crack propagation and to the evaluation of the rotational capacity of plastic hinges, permits to predict the size-scale effects evidenced by several experimental programs available in the literature. According to the obtained numerical results, new practical design formulae and diagrams are proposed for the improvement of the current code provisions which usually disregard the size effects.
A Spectral Element Method for Nonlinear and Dispersive Water Waves
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Spata, Michael [Old Dominion Univ., Norfolk, VA (United States)
2012-08-01
An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.
Tanjia, Fatema; Fedele, Renato; Shukla, P K; Jovanovic, Dusan
2011-01-01
A numerical analysis of the self-interaction induced by a relativistic electron/positron beam in the presence of an intense external longitudinal magnetic field in plasmas is carried out. Within the context of the Plasma Wake Field theory in the overdense regime, the transverse beam-plasma dynamics is described by a quantumlike Zakharov system of equations in the long beam limit provided by the Thermal Wave Model. In the limiting case of beam spot size much larger than the plasma wavelength, the Zakharov system is reduced to a 2D Gross-Pitaevskii-type equation, where the trap potential well is due to the external magnetic field. Vortices, "beam halos" and nonlinear coherent states (2D solitons) are predicted.
Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan
2016-09-01
In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.
Beam-Based Nonlinear Optics Corrections in Colliders
Pilat, Fulvia Caterina; Malitsky, Nikolay; Ptitsyn, Vadim
2005-01-01
A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, which gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 3 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non linear correction techniques.
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
Sorokin, Vladislav S; Thomsen, Jon Juel
2016-02-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation.
Implementation of a strain energy-based nonlinear finite element in the object-oriented environment
Wegner, Tadeusz; Pęczak, Andrzej
2010-03-01
The objective of the paper is to describe a novel finite element computational method based on a strain energy density function and to implement it in the object-oriented environment. The original energy-based finite element was put into the known standard framework of classes and handled in a different manner. The nonlinear properties of material are defined with a modified strain energy density function. The local relaxation procedure proposed as a method used to resolve a nonlinear problem is implemented in C++ language. The hexahedral element with eight nodes as well as the adaptation of the nonlinear finite element is introduced. The chosen numerical model is made of nearly incompressible hyperelastic material. The application of the proposed element is shown on the example of a rectangular parallelepiped with a hollow port.
A sandwich bar element for geometric nonlinear thermo-elastic analysis
Murín J.
2008-11-01
Full Text Available This contribution deals with a two-node straight sandwich composite bar element with constant double symmetric rectangular cross-sectional area. This new bar element (based on the non-linear second-order theory is intended to perform the non-incremental full geometric non-linear analysis. Stiffness matrix of this composite bar contains transfer constants, which accurately describe polynomial uniaxial variation of the material thermo-physical properties.In the numerical experiments the weak coupled thermo-structural geometric non-linear problem was solved. Obtained results were compared with several analyses made by ANSYS programme. Findings show good accuracy of this new finite element. The results obtained with this element do not depend on the element mesh density.
Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.
2016-07-01
In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.
Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma
R K Khanna; K Baheti
2001-06-01
In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.
Evaluation of a Nonlinear Finite Element Program - ABAQUS.
1983-03-15
shell elements) - Pipe elements with the effect of internal pressure Materials - A hypoelastic model for soils - Modified Cam Clay model - ORNL creep...is a lack of representation of different elements or material models . Furthermore, the manual that the reviewer has is in a rough draft form which... models (or routines) can be called to generate the material stiffness matrix D: • MATELA - Linearly elastic materials with isotropic, orthotropic and
Nonlinear Dynamical analysis of an AFM tapping mode microcantilever beam
Choura S.
2012-07-01
Full Text Available We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM microcantilever beam. This latter is subjected to a harmonic excitation of its base displacement and to Van der Waals and DMT contact forces at its free end. For AFM design purposes, we derive a mathematical model for accurate description of the AFM microbeam dynamics. We solve the resulting equations of motions and associated boundary conditions using the Galerkin method. We find that using one-mode approximation in tapping mode operating in the neighborhood of the contact region one-mode approximation may lead to erroneous results.
Finite Element Models for Electron Beam Freeform Fabrication Process
Chandra, Umesh
2012-01-01
Electron beam freeform fabrication (EBF3) is a member of an emerging class of direct manufacturing processes known as solid freeform fabrication (SFF); another member of the class is the laser deposition process. Successful application of the EBF3 process requires precise control of a number of process parameters such as the EB power, speed, and metal feed rate in order to ensure thermal management; good fusion between the substrate and the first layer and between successive layers; minimize part distortion and residual stresses; and control the microstructure of the finished product. This is the only effort thus far that has addressed computer simulation of the EBF3 process. The models developed in this effort can assist in reducing the number of trials in the laboratory or on the shop floor while making high-quality parts. With some modifications, their use can be further extended to the simulation of laser, TIG (tungsten inert gas), and other deposition processes. A solid mechanics-based finite element code, ABAQUS, was chosen as the primary engine in developing these models whereas a computational fluid dynamics (CFD) code, Fluent, was used in a support role. Several innovative concepts were developed, some of which are highlighted below. These concepts were implemented in a number of new computer models either in the form of stand-alone programs or as user subroutines for ABAQUS and Fluent codes. A database of thermo-physical, mechanical, fluid, and metallurgical properties of stainless steel 304 was developed. Computing models for Gaussian and raster modes of the electron beam heat input were developed. Also, new schemes were devised to account for the heat sink effect during the deposition process. These innovations, and others, lead to improved models for thermal management and prediction of transient/residual stresses and distortions. Two approaches for the prediction of microstructure were pursued. The first was an empirical approach involving the
Nonlinear dynamics of planetary gears using analytical and finite element models
Ambarisha, Vijaya Kumar; Parker, Robert G.
2007-05-01
Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.
Efficient Finite Element Methods for Transient Nonlinear Analysis of Shells.
1983-08-01
governing equations for a beam based on shallow shell theory and the variational formulations which pertain in this context to displacement, hybrid, and...functions, respectively. Because the curvature is treated by shallow - shell theory , cf. Eqs. (1), all terms were integrated over the straight x-axis. Only
Nonlinear dynamics of a sliding beam on two supports under sinusoidal excitation
R J Somnay; R A Ibrahim
2006-08-01
This study deals with the nonlinear dynamics associated with large deformation of a beam sliding on two-knife edge supports under external excitation. The beam is referred to as a Gospodnetic–Frisch-Fay beam, after the researchers who reported its static deformation in closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deﬂection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll-restoring moment of ships. The Gospodnetic–Frisch-Fay exact solution is given in terms of elliptic functions. A curve ﬁt of the exact solution up to eleventh-order is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the value of the initial conditions. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitude and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases.
Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity
Bekhoucha, F.; Rechak, S.; Duigou, L.; Cadou, J. M.
2016-09-01
In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and rotations associated with small strains. Based on the Timoshenko beam model, these equations are derived from Hamilton's principle, in which the warping is considered. All coupling terms are considered including Coriolis terms. The studied beams are isotropic with clamped-free boundary conditions. By combining the Galerkin method with the harmonic balance method, the equations of motion are converted into a quadratic function treated with a continuation method: the Asymptotic Numerical Method, where the generalized displacement vector is presented as a series expansion. While analysing the effect of the angular velocity, we determine the amplitude versus frequency variations which are plotted as backbone curves. Considering the first lagging and flapping modes, the changes in beam behaviour from hardening to softening are investigated and identified as a function of the angular velocity and the effect of shear. Particular attention is paid to high angular velocities for both Euler-Bernoulli and Timoshenko beams and the natural frequencies so obtained are compared with the results available in the literature.
Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan
2016-06-27
We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.
Reliability-based design optimization of a nonlinear elastic plastic thin-walled T-section beam
Ba-Abbad, Mazen A.
A two part study is performed to investigate the application of reliability-based design optimization (RBDO) approach to design elastic-plastic stiffener beams with T-section. The objectives of this study are to evaluate the benefits of reliability-based optimization over deterministic optimization, and to illustrate through a practical design example some of the difficulties that a design engineer may encounter while performing reliability-based optimization. Other objectives are to search for a computationally economic RBDO method and to utilize that method to perform RBDO to design an elastic-plastic T-stiffener under combined loads and with flexural-torsional buckling and local buckling failure modes. First, a nonlinear elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear beam element. To address the problems of RBDO, such as the high non-linearity and derivative discontinuity of the reliability function, and to illustrate a situation where RBDO fails to produce a significant improvement over the deterministic optimization, a graphical method was developed. The method started by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor (SF), and based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost for the same level of reliability as the deterministic design. Three failure modes were considered for an elastic-plastic beam of T cross-section under combined axial and bending loads. The failure modes are based on the total plastic failure in a beam section, buckling, and maximum allowable deflection. The results of the first part show that it is possible to get improved optimum designs (more reliable or lighter weight) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly non-linear with respect to
H. Vázquez-Leal
2013-01-01
Full Text Available In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to 179.99999999∘ yielding a relative error of 0.01222747.
Advance elements of optoisolation circuits nonlinearity applications in engineering
Aluf, Ofer
2017-01-01
This book on advanced optoisolation circuits for nonlinearity applications in engineering addresses two separate engineering and scientific areas, and presents advanced analysis methods for optoisolation circuits that cover a broad range of engineering applications. The book analyzes optoisolation circuits as linear and nonlinear dynamical systems and their limit cycles, bifurcation, and limit cycle stability by using Floquet theory. Further, it discusses a broad range of bifurcations related to optoisolation systems: cusp-catastrophe, Bautin bifurcation, Andronov-Hopf bifurcation, Bogdanov-Takens (BT) bifurcation, fold Hopf bifurcation, Hopf-Hopf bifurcation, Torus bifurcation (Neimark-Sacker bifurcation), and Saddle-loop or Homoclinic bifurcation. Floquet theory helps as to analyze advance optoisolation systems. Floquet theory is the study of the stability of linear periodic systems in continuous time. Another way to describe Floquet theory, it is the study of linear systems of differential equations with p...
Elements of nonlinear time series analysis and forecasting
De Gooijer, Jan G
2017-01-01
This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible...
Wolz, Michael; Blöcher, Ullrich; Dross, Gerhard; Schmitt, Jana; Bischoff, Christian; Umhofer, Udo
2015-03-01
Laser beam shaping elements can be used e.g. for material processing. The results of these processes can be improved when the usually Gaussian profile of the laser is transformed into a top hat profile, which can be circular or rectangular in shape. Another frequently used type of beam-forming devices are beam splitters for parallel processing using only one laser. These types of beam formers can be implemented as diffractive or refractive elements. So far these optics are produced either directly by means of lithography e.g. in glass or in plastic using a hot embossing process or nanoimprint technology. Elements produced in this way have either the disadvantage of high costs or they are limited in temperature range, laser power or wavelength. A newly developed molding process for glass allows the manufacture of larger numbers of optics with reduced cost. The production of molds for refractive top hat beam shaping devices requires very high precision of the applied grinding process. Form deviations below 100 nm are necessary to obtain a homogeneous illumination. Measurements of the surface topography of gauss to top hat beam shaping elements using white light interferometry are presented as well as results of optical measurements of the beam profile using a camera. Continuous diffractive beam shaping elements for beam splitting applications are designed to generate several sub-beams each carrying the same energy. In order to achieve this, form deviations of less than 50 nm are required. Measurements of the surface of a 1 x 5 beam splitter are compared with ideal beam splitter profiles. The resulting beam intensity distribution of a molded element is presented.
Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.
2017-08-01
We have proposed an algorithm for the sequential construction of nonisotropic matrix elements of the collision integral, which are required to solve the nonlinear Boltzmann equation using the moments method. The starting elements of the matrix are isotropic and assumed to be known. The algorithm can be used for an arbitrary law of interactions for any ratio of the masses of colliding particles.
A stabilised nodal spectral element method for fully nonlinear water waves
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
Wu, Shen R
2012-01-01
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Liao, F; Huang, Z.
2015-01-01
Open Access funded by Engineering and Physical Sciences Research Council under a Creative Commons license. A robust finite element procedure for modelling the localised fracture of reinforced concrete beams at elevated temperatures is developed. In this model a reinforced concrete beam is represented as an assembly of 4-node quadrilateral plain concrete, 3-node main reinforcing steel bar, and 2-node bond-link elements. The concrete element is subdivided into layers for considering the temp...
Lee, S. Y.
2014-04-07
We had carried out a design of an ultimate storage ring with beam emittance less than 10 picometer for the feasibility of coherent light source at X-ray wavelength. The accelerator has an inherent small dynamic aperture. We study method to improve the dynamic aperture and collective instability for an ultimate storage ring. Beam measurement and accelerator modeling are an integral part of accelerator physics. We develop the independent component analysis (ICA) and the orbit response matrix method for improving accelerator reliability and performance. In collaboration with scientists in National Laboratories, we also carry out experimental and theoretical studies on beam dynamics. Our proposed research topics are relevant to nuclear and particle physics using high brightness particle and photon beams.
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
Carlevaro, Nakia; Montani, Giovanni; Zonca, Fulvio
2015-01-01
In this paper, we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analyzed.
The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities
Chang, Philip; Lamberts, Astrid
2014-01-01
Very-high energy gamma-rays from extragalactic sources pair-produce off of the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here, we show with numerical calculations that the effective damping rate is $8\\times 10^{-4}$ of the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wavenumber and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to ap...
Nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode
Frolov, Nikita S.; Kurkin, Semen A.; Koronovskii, Alexey A.; Hramov, Alexander E.
2017-07-01
In this paper we report on the results of investigations of nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode in micrometer-scaled source of sub-THz electromagnetic radiation. The numerical analysis is provided by means of 3D electromagnetic particle-in-cell (PIC) simulation. We have studied evolution of the system dynamics with the change of beam current value by means of Fourier and bifurcation analysis. The bifurcation diagram has identified a number of the alternating regions of beam current with regular or chaotic regimes of system dynamics. The study of spatiotemporal dynamics of formed electron structures in the beam has revealed the physical mechanisms responsible for the regimes switchings in the system.
Seismic analysis of the APR1400 nuclear reactor system using a verified beam element model
Park, Jong-beom [Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722 (Korea, Republic of); Park, No-Cheol, E-mail: pnch@yonsei.ac.kr [Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722 (Korea, Republic of); Lee, Sang-Jeong; Park, Young-Pil [Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722 (Korea, Republic of); Choi, Youngin [Korea Institute of Nuclear Safety, 62 Gwahak-ro, Yuseong-gu, Daejeon 34142 (Korea, Republic of)
2017-03-15
Highlights: • A simplified beam element model is constructed based on the real dynamic characteristics of the APR1400. • Time history analysis is performed to calculate the seismic responses of the structures. • Large deformations can be observed at the in-phase mode of reactor vessel and core support barrel. - Abstract: Structural integrity is the first priority in the design of nuclear reactor internal structures. In particular, nuclear reactor internals should be designed to endure external forces, such as those due to earthquakes. Many researchers have performed finite element analyses to meet these design requirements. Generally, a seismic analysis model should reflect the dynamic characteristics of the target system. However, seismic analysis based on the finite element method requires long computation times as well as huge storage space. In this research, a beam element model was developed and confirmed based on the real dynamic characteristics of an advanced pressurized water nuclear reactor 1400 (APR1400) system. That verification process enhances the accuracy of the finite element analysis using the beam elements, remarkably. Also, the beam element model reduces seismic analysis costs. Therefore, the beam element model was used to perform the seismic analysis. Then, the safety of the APR1400 was assessed based on a seismic analysis of the time history responses of its structures. Thus, efficient, accurate seismic analysis was demonstrated using the proposed beam element model.
In-beam spectroscopy of the heaviest elements
Herzberg, Rolf-Dietmar
2016-12-01
In-beam spectroscopy provides many powerful tools for the detailed study of nuclear structure. Over the past two decades the coupling of sensitive in-beam spectrometers to recoil separators has allowed the study of weakly populated reaction channels, such as the fusion-evaporation reactions leading to nuclei beyond fermium (Z = 100). The methods, observables, and limitations of this approach are discussed.
Kriging-Based Timoshenko Beam Element for Static and Free Vibration Analyses
Syamsoeyadi H.
2011-01-01
Full Text Available An enhancement of the finite element method using Kriging interpolation (K-FEM has been recently proposed and applied to solve one- and two- dimensional linear elasticity problems. The key advantage of this innovative method is that the polynomial refinement can be performed without adding nodes or changing the element connectivity. This paper presents the development of the K-FEM for static and free vibration analyses of Timoshenko beams. The transverse displacement and the rotation of the beam are independently approximated using Kriging interpolation. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. In an attempt to eliminate the shear locking, the selective-reduced integration technique is utilized. The developed beam element is tested to several static and free vibration problems. The results demonstrate the excellent performance of the developed element.
Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions
Ahmad Shahba
2012-01-01
Full Text Available The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.
Beam Shape Sensing Using Inverse Finite Element Method: Theory and Experimental Validation
2011-09-01
within a simple inverse beam-frame element. The element is based on Timoshenko beam theory which includes the axial, bending, torsional and...moment of inertia P y zI I I= + . Consistent with the hypotheses of Timoshenko beam theory (each cross-section remains flat and rigid with respect to...equilibrium equations of Timoshenko beam theory which relate the bending moments ( yM , zM ) to the transverse shear forces ( yQ , zQ ) 2 23, 5 2
Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel
Sonu Sen
2014-01-01
Full Text Available In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have numerical appreciation of the results the propagation equation for plasma is solved using the fourth order Runge-Kutta method for the initial plane wave front of the beam, using boundary conditions. The spot size of the laser beam decreases as the beam penetrates into the plasma and significantly adds self-focusing in plasma. This causes the laser beam to become more focused by reduction of diffraction effect, which is an important phenomenon in inertial confinement fusion and also for the understanding of self-focusing of laser pulses. Numerical computations are presented and discussed in the form of graphs for typical parameters of laser-plasma interaction.
A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams
无
2007-01-01
Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Galerkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.
1992-12-01
Dugundji (12) have developed a theory to predict large deflections of laminated beams. Minguet and Dugundji assume transverse shear strains are constant...nine elements as shown in figure 3.3. 3.2 Cantilevered Composite Beam The next problem considered is one considered by Minguet and Dugundji (12) in...in figure 3.4. Minguet and Dugundji (M&D) formulated an updated Lagrangian displacement scheme based on Euler angles which track the rigid body motion
Hu Ding; Li-Qun Chen
2011-01-01
Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation.It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same, but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.
Spoorthi, K.; Pramodini, S.; Kityk, I. V.; Abd-Lefdil, M.; Sekkati, M.; El Fakir, A.; Rao, Ashok; Sanjeev, Ganesh; Poornesh, P.
2017-06-01
In this article, we report the third-order nonlinear optical properties of electron beam irradiated gadolinium-doped zinc oxide (GZO) thin films prepared using the spray pyrolysis deposition technique. GZO thin films were treated with an electron beam from a variable energy microtron accelerator at dose rates ranging from 1-5 kGy. Nonlinear optical measurements were conducted by employing the single beam Z-scan technique. A continuous wave He-Ne laser operating at 633 nm was used as the source of excitation. Closed aperture Z-scan results reveal that the films exhibit self-defocusing nonlinearity. Open aperture Z-scan results exhibit a switching over phenomena of reverse saturable absorption to saturable absorption for thin film irradiated at 3 kGy, indicating the influence of electron beams on optical nonlinearity. The significant change in third-order nonlinear optical susceptibility χ (3) ranging from 2.14 × 10-3 to 3.12 × 10-3 esu is attributed to the effect of electron beam irradiation. The study shows that the nonlinear coefficients of GZO films can be tuned by electron beams for use in nonlinear optical device applications.
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.
Rahman, Md. Saifur; Lee, Yiu-Yin
2017-10-01
In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Chang, Philip; Lamberts, Astrid [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Broderick, Avery E.; Shalaby, Mohamad [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Pfrommer, Christoph [Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg (Germany); Puchwein, Ewald, E-mail: chang65@uwm.edu [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA (United Kingdom)
2014-12-20
Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10{sup –4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.
Numerical Simulations of Nonlinear Dynamics of Electron Cyclotron Maser with a Straight Beam
KONG Ling-Bao; HOU Zhi-Ling
2011-01-01
An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered,and the nonlinear equation of beam-wave interaction is presented.With the numerical methods,the nonlinear dynamics of the ADECM is investigated.It is shown that the saturated interaction efficiency of the ADECM approaches 90％ and the interaction length for the saturated efficiency spans about 5-20cm.The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.In the late 1950s,the theoretical studies on the instability of electron cyclotron maser based on normal Doppler effect (NDECM) were performed almost simultaneously by Gaponov,[1] Twiss,[2] and Schneider.[3] Their discoveries have resulted in the most successful fast-wave devices such as the gyrotron and variants.[4,5] The possible applications of microwaves span a wide range of technologies such as in thermonuclear fusion energy,charged particle accelerations,radar systems,and processing of advanced ceramics.[6-16]%An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered, and the nonlinear equation of beam-wave interaction is presented. With the numerical methods, the nonlinear dynamics of the ADECM is investigated. It is shown that the saturated interaction efficiency of the ADECM approaches 90% and the interaction length for the saturated efficiency spans about 5-20 cm. The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.
Advances in nonlinear vibration analysis of structures. Part-I. Beams
Sudhakar R Marur
2001-06-01
The development of nonlinear vibration formulations for beams in the literature can be seen to have gone through distinct phases — earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.
Non-linearity of Beam Halo-Chaos in the ADS
2001-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applicationsin industry, medicine, and national defense. This latter reviews some general features of complexities and their expressions in accelerator-driven clean nuclear power system (ADS).Complexity has become an important subject for study, especially in the field of nonlinear
A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures
SZE; K; Y
2009-01-01
This paper presents eight-node solid-shell elements for geometric non-linear analyze of piezoelectric structures. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid ele- ment, a hybrid-stress solid-shell element is formulated. The presented finite shell element is able to model arbitrary curved shell structures. Non-linear numerical examples demonstrate the ability of the proposed model to analyze nonlinear piezoelectric devices.
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Quadratic solid-shell elements for nonlinear structural analysis and sheet metal forming simulation
Wang, Peng; Chalal, Hocine; Abed-Meraim, Farid
2017-01-01
In this paper, two quadratic solid-shell (SHB) elements are proposed for the three-dimensional modeling of thin structures. These consist of a 20-node hexahedral solid-shell element, denoted SHB20, and its 15-node prismatic counterpart, denoted SHB15. The formulation of these elements is extended in this work to include geometric and material nonlinearities, for application to problems involving large displacements and rotations as well as plasticity. For this purpose, the SHB elements are coupled with large-strain anisotropic elasto-plastic constitutive equations for metallic materials. Although based on a purely three-dimensional approach, several modifications are introduced in the formulation of these elements to provide them with interesting shell features. In particular, a special direction is chosen to represent the thickness, along which a user-defined number of integration points are located. Furthermore, for efficiency requirements and for alleviating locking phenomena, an in-plane reduced-integration scheme is adopted. The resulting formulations are implemented into the finite element software ABAQUS/Standard and, to assess their performance, a variety of nonlinear benchmark problems are investigated. Attention is then focused on the simulation of various complex sheet metal forming processes, involving large strain, anisotropic plasticity, and double-sided contact. From all simulation results, it appears that the SHB elements represent an interesting alternative to traditional shell and solid elements, due to their versatility and capability of accurately modeling selective nonlinear benchmark problems as well as complex sheet metal forming processes.
Quadratic solid-shell elements for nonlinear structural analysis and sheet metal forming simulation
Wang, Peng; Chalal, Hocine; Abed-Meraim, Farid
2016-10-01
In this paper, two quadratic solid-shell (SHB) elements are proposed for the three-dimensional modeling of thin structures. These consist of a 20-node hexahedral solid-shell element, denoted SHB20, and its 15-node prismatic counterpart, denoted SHB15. The formulation of these elements is extended in this work to include geometric and material nonlinearities, for application to problems involving large displacements and rotations as well as plasticity. For this purpose, the SHB elements are coupled with large-strain anisotropic elasto-plastic constitutive equations for metallic materials. Although based on a purely three-dimensional approach, several modifications are introduced in the formulation of these elements to provide them with interesting shell features. In particular, a special direction is chosen to represent the thickness, along which a user-defined number of integration points are located. Furthermore, for efficiency requirements and for alleviating locking phenomena, an in-plane reduced-integration scheme is adopted. The resulting formulations are implemented into the finite element software ABAQUS/Standard and, to assess their performance, a variety of nonlinear benchmark problems are investigated. Attention is then focused on the simulation of various complex sheet metal forming processes, involving large strain, anisotropic plasticity, and double-sided contact. From all simulation results, it appears that the SHB elements represent an interesting alternative to traditional shell and solid elements, due to their versatility and capability of accurately modeling selective nonlinear benchmark problems as well as complex sheet metal forming processes.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
陈立群; 程昌; 张能辉
2000-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
陈立群; 程昌; 张能辉
2001-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged
Material nonlinear analysis via mixed-iterative finite element method
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.
Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor
2013-08-01
The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Stimulated Raman Scattering and Nonlinear Focusing of High-Power Laser Beams Propagating in Water
Hafizi, B; Penano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-01-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. While discussed here in the context of propagation in water, the gain-focusing phenomenon is general to any medium supporting nonlinear focusing and stimulated forward Raman scattering.
Extreme events induced by self-action of laser beams in dynamic nonlinear liquid crystal cells
Bugaychuk, S.; Iljin, A.; Chunikhina, K.
2017-06-01
Optical extreme events represent a feature of nonlinear systems where there may emerge individual pulses possessing very high (or very low) intensity hardly probable statistically. Such property is being connected with the generation of solitons in the nonlinear systems. We carry out the first experiments for detection of extreme events during two-wave mixing with nonlinear dynamical liquid crystal (LC) cells. We investigate the statistics of the extreme events in dependence on relation between the duration of a laser pulse and the time characteristic of dynamic grating relaxation in LC cell. Our research shows that the self-diffraction of laser beams with a dynamical grating support the generation of envelope solitons in this system.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks.
Mangussi, Franco; Zanette, Damián H
2016-01-01
In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks
Mangussi, Franco
2016-01-01
In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829
Rodrigues Ribeiro, R. S.; Guerreiro, A.; Viegas, J.; Jorge, P. A. S.
2016-05-01
In this work, spiral phase lenses and Fresnel zone lenses for beam tailoring, fabricated on the tip of optical fibers, are reported. The spiral phase lenses allow tailoring the fundamental guided mode, a Gaussian beam, into a Laguerre - Gaussian profile without using additional optical elements. Whereas, the Fresnel lenses are used as focusing systems. The lenses are fabricated using Focused Ion Beam milling, enabling high resolution in the manufacturing process. The output optical intensity profiles matching the numerical simulations are presented and analyzed.
Nonlinear Finite Element Analysis of Pull-Out Test
Saabye Ottesen, N
1981-01-01
A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region......, respectively. The aim is to attain a clear insight into structural behavior. Special attention is given to the failure mode. Severe cracking occurs and the stress distribution is very inhomogeneous. However, large compressive forces run from the disc in a rather narrow band towards the support...
Taylor, Z A; Cheng, M; Ourselin, S
2008-05-01
The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16,000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.
Nonlinear dynamics of beam-plasma instability in a finite magnetic field
Bogdankevich, I. L.; Goncharov, P. Yu.; Gusein-zade, N. G.; Ignatov, A. M.
2017-06-01
The nonlinear dynamics of beam-plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam-plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B 0 = 4.5 kG (Ω ω B p ) and 20 kG (Ω B ≫ ωp). For B 0 = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.
Olarte, Omar E.; Licea-Rodriguez, Jacob; Palero, Jonathan A.; Gualda, Emilio J.; Artigas, David; Mayer, Jürgen; Swoger, Jim; Sharpe, James; Rocha-Mendoza, Israel; Rangel-Rojo, Raul; Loza-Alvarez, Pablo
2012-01-01
We present the implementation of a combined digital scanned light-sheet microscope (DSLM) able to work in the linear and nonlinear regimes under either Gaussian or Bessel beam excitation schemes. A complete characterization of the setup is performed and a comparison of the performance of each DSLM imaging modality is presented using in vivo Caenorhabditis elegans samples. We found that the use of Bessel beam nonlinear excitation results in better image contrast over a wider field of view. PMID:22808423
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
A New Integrated Slot Element Feed Array for Multi-beam Systems
Yngvesson, K. S.; Johansson, J. F.; Kollberg, E. L.
1985-01-01
A feed array consisting of constant width slot antennas (CWSA's), fed from a block containing fin-line transitions, has been developed. The array has a two-dimensional configuration, with five elements each on five parallel substrates. Beam-widths are compatible with use in f/D-1.0 multi-beam systems, with optimum taper. Array element spacings are close to a factor of two smaller than for other typical arrays, and spill-over efficiency is about 65%.
Antony, Albin; Pramodini, S.; Kityk, I. V.; Abd-Lefdil, M.; Douayar, A.; Cherkaoui El Moursli, F.; Sanjeev, Ganesh; Manjunatha, K. B.; Poornesh, P.
2017-10-01
Electron beam induced effects on Fluorine doped ZnO thin films (FZO) grown by chemical spray pyrolysis deposition technique were studied. The samples were exposed to 8 MeV electron beam at different dose rate ranging from 1 kGy to 4 kGy. All films exhibit a polycrystalline nature which shows an increase in crystallanity with irradiation dosages. The electron beam irradiation effectively controls the films surface morphology and its linear optical characteristics. Z-Scan technique was employed to evaluate the sign and magnitude of nonlinear refractive index and nonlinear absorption coefficient using a continuous wave laser at 632.8 nm as light source. Enhancement in the third order nonlinear optical properties was were noted due to electron beam irradiation. Tailoring the physical and NLO properties by electron beam, the FZO thin films becomes a promising candidate for various optoelectronic applications such as phase change memory devices, optical pulse compression, optical switching and laser pulse narrowing.
Duan, M.
2004-12-01
In this paper, a geometrically nonlinear hybrid/mixed curved quadrilateral shell element (HMSHEL4N) with four nodes is developed based on the modified Hellinger/Reissner variational principles. The performance of element is investigated and tested using some benchmark problems. A number of numerical examples of plate and shell nonlinear deflection problems are included. The results are compared with theoretical solutions and other numerical results. It is shown that HMSHEL4N does not possess spurious zero energy modes and any locking phenomenon, and is convergent and insensitive to the distorted mesh. A good agreement of the results with theoretical solutions, and better performance compared with displacement finite element method, are observed. It is seen that an efficient shell element based on stress and displacement field assumptions in solution and time is obtained.
A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves
Engsig-Karup, Allan Peter; Bigoni, Daniele
2015-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) \\cite{CaiEtAl1998}, although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global $L^2$ projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical...
Esfandiar, Habib; KoraYem, Moharam Habibnejad [Islamic Azad University, Tehran (Iran, Islamic Republic of)
2015-09-15
In this study, the researchers try to examine nonlinear dynamic analysis and determine Dynamic load carrying capacity (DLCC) in flexible manipulators. Manipulator modeling is based on Timoshenko beam theory (TBT) considering the effects of shear and rotational inertia. To get rid of the risk of shear locking, a new procedure is presented based on mixed finite element formulation. In the method proposed, shear deformation is free from the risk of shear locking and independent of the number of integration points along the element axis. Dynamic modeling of manipulators will be done by taking into account small and large deformation models and using extended Hamilton method. System motion equations are obtained by using nonlinear relationship between displacements-strain and 2nd PiolaKirchoff stress tensor. In addition, a comprehensive formulation will be developed to calculate DLCC of the flexible manipulators during the path determined considering the constraints end effector accuracy, maximum torque in motors and maximum stress in manipulators. Simulation studies are conducted to evaluate the efficiency of the method proposed taking two-link flexible and fixed base manipulators for linear and circular paths into consideration. Experimental results are also provided to validate the theoretical model. The findings represent the efficiency and appropriate performance of the method proposed.
Zhigang Zhang
2015-01-01
Full Text Available A two-node spatial beam element with the Euler-Bernoulli assumption is developed for the nonlinear dynamic analysis of slender beams undergoing arbitrary rigid motions and large deformations. During the analysis, the global displacement and rotation vectors with six degrees of freedom are selected as the nodal coordinates. In addition, the “shear locking” problem is avoided successfully since the beam cross-sections are always perpendicular to the current neutral axes by employing a special coupled interpolation of the centroid position and the cross-section orientation. Then a scheme is presented where the original transient strains representing the nodal forces are replaced by proposed average strains over a small time interval. Thus all the high frequencies can be filtered out and a corresponding equivalent internal damping will be produced in this new formulation, which can improve the computation performance of the proposed element for solving the stiff problem and evaluate the governing equations even by using the nonstiff ordinary differential equation solver. Finally, several numerical examples are carried out to verify the validation and efficiency of this proposed formulation by comparison with the analytical solutions and other research works.
Kacem, N; Hentz, S; Pinto, D; Reig, B; Nguyen, V [CEA/LETI-MINATEC, Grenoble (France)
2009-07-08
In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.
Kacem, N; Hentz, S; Pinto, D; Reig, B; Nguyen, V
2009-07-08
In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.
Sorokin, Vladislav S.; Thomsen, Jon Juel
2016-01-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli– Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature...
Vismara, S. O.; Ricci, S.; Bellini, M.; Trittoni, L.
2016-06-01
The objective of the present paper is to describe a procedure to identify and model the non-linear behaviour of structural elements. The procedure herein applied can be divided into two main steps: the system identification and the finite element model updating. The application of the restoring force surface method as a strategy to characterize and identify localized non-linearities has been investigated. This method, which works in the time domain, has been chosen because it has `built-in' characterization capabilities, it allows a direct non-parametric identification of non-linear single-degree-of-freedom systems and it can easily deal with sine-sweep excitations. Two different application examples are reported. At first, a numerical test case has been carried out to investigate the modelling techniques in the case of non-linear behaviour based on the presence of a free-play in the model. The second example concerns the flap of the Intermediate eXperimental Vehicle that successfully completed its 100-min mission on 11 February 2015. The flap was developed under the responsibility of Thales Alenia Space Italia, the prime contractor, which provided the experimental data needed to accomplish the investigation. The procedure here presented has been applied to the results of modal testing performed on the article. Once the non-linear parameters were identified, they were used to update the finite element model in order to prove its capability of predicting the flap behaviour for different load levels.
Dongyang Shi; Haihong Wang; Yuepeng Du
2009-01-01
An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.
Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems
Plasser René
2014-12-01
Full Text Available An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.
On high-continuity transfinite element formulations for linear-nonlinear transient thermal problems
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
This paper describes recent developments in the applicability of a hybrid transfinite element methodology with emphasis on high-continuity formulations for linear/nonlinear transient thermal problems. The proposed concepts furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom; and the methodology is applicable to linear/nonlinear thermal problems. Characteristic features of the formulations are described in technical detail as the proposed hybrid approach combines the major advantages and modeling features of high-continuity thermal finite elements in conjunction with transform methods and classical Galerkin schemes. Several numerical test problems are evaluated and the results obtained validate the proposed concepts for linear/nonlinear thermal problems.
A SIMPLE FINITE ELEMENT FOR NON-LINEAR ANALYSIS OF COMPOSITE PLATES
V.B. Tungikar
2011-06-01
Full Text Available Finite Element Analysis for geometrically nonlinear behaviour of laminated composite plates is presented andcompared with the reported investigations. However structural non-linearity is encountered in certain cases andneeds attention. A higher order displacement field that accounts for transverse shear effects under geometricnonlinear condition is employed in the formulation of a four node, rectangular, element with thirteen degrees offreedom per node. First order Zigzag terms have been included in displacement field for improvement in theresponse. Von Karman strain approach is considered in the present analysis. Incremental Pica iterative scheme isused to solve resulting nonlinear equilibrium equations. The formulation demonstrates its excellence in theperformance for predicting response at various lay ups and plies conditions.
Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model
Yue-bao Deng
2016-01-01
Full Text Available A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
Thornton, E. A.; Dechaumphai, P.
1986-01-01
A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.
Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....
Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe...
THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS
N＇guimbi; Germain
2001-01-01
Abstract. The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal Lz and H1 estimates for the error and its time derivative are established.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
YanpingCHEN; YunqingHUANG
1998-01-01
Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine
Wong, Christian; Gehrchen, P Martin; Darvann, Tron;
2003-01-01
A finite-element analysis (FEA) model of an intact lumbar disc-body unit was generated. The vertebral body of the FEA model consisted of a solid tetrahedral core of trabecular bone surrounded by a cortical shell. The disc consisted of an incompressible nucleus surrounded by nonlinear annulus fibers...
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Song, Huimin
In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and
Generation of Bessel Beams at mm- and Sub mm-wavelengths by Binary Optical Elements
Yu, Y. Z.; Dou, W. B.
2008-07-01
In this paper, binary optical elements (BOE’s) are designed for generating Bessel beams at mm- and sub mm- wavelengths. The design tool is to combine a genetic algorithm (GA) for global optimization with a two-dimension finite-difference time-domain (2-D FDTD) method for rigorous electromagnetic computation. The design process for converting a normally incident Gaussian beam into a Bessel beam is described in detail. Numerical results demonstrate that the designed BOE’s can not only successfully produce arbitrary order Bessel beams, but also have higher diffraction efficiencies when compared with amplitude holograms.
Dynamic modeling and analysis of the PZT-bonded composite Timoshenko beams: Spectral element method
Lee, Usik; Kim, Daehwan; Park, Ilwook
2013-03-01
The health of thin laminated composite beams is often monitored using the ultrasonic guided waves excited by wafer-type piezoelectric transducers (PZTs). Thus, for the smart composite beams which consist of a laminated composite base beam and PZT layers, it is very important to develop a very reliable mathematical model and to use a very accurate computational method to predict accurate dynamic characteristics at very high ultrasonic frequency. In this paper, the axial-bending-shear-lateral contraction coupled differential equations of motion are derived first by the Hamilton's principle with Lagrange multipliers. The smart composite beam is represented by a Timoshenko beam model by adopting the first-order shear deformation theory (FSDT) for the laminated composite base beam. The axial deformation of smart composite beam is improved by taking into account the effects of lateral contraction by adopting the concept of Mindlin-Herrmann rod theory. The spectral element model is then formulated by the variation approach from coupled differential equations of motion transformed into the frequency domain via the discrete Fourier transform. The high accuracy of the present spectral element model is verified by comparing with other solution methods: the finite element model developed in this paper and the commercial FEA package ANSYS. Finally the dynamics and wave characteristics of some example smart composite beams are investigated through the numerical studies.
Mixed finite element models for free vibrations of thin-walled beams
Noor, Ahmed K.; Peters, Jeanne M.; Min, Byung-Jin
1989-01-01
Simple, mixed finite element models are developed for the free vibration analysis of curved thin-walled beams with arbitrary open cross section. The analytical formulation is based on a Vlasov's type thin-walled beam theory with the effects of flexural-torsional coupling, transverse shear deformation and rotary inertia included. The fundamental unknowns consist of seven internal forces and seven generalized displacements of the beam. The element characteristic arrays are obtained by using a perturbed Lagrangian-mixed variational principle. Only C(sup o) continuity is required for the generalized displacements. The internal forces and the Lagrange multiplier are allowed to be discontinuous at interelement boundaries. Numerical results are presented to demonstrate the high accuracy and effectiveness of the elements developed. The standard of comparison is taken to be the solutions obtained by using 2-D plate/shell models for the beams.
Nonlinear flexural waves and chaos behavior in finite-deflection Timoshenko beam
Shan-yuan ZHANG; Zhi-fang LIU
2010-01-01
Based on the Timoshenko beam theory,the finite-deflection and the axial inertia are taken into account,and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills,the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case,a shock wave solution is given. The small perturbations are further introduced,arising from the damping and the external load to an original Hamilton system,and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research Phase II proposal offers to develop a comprehensive computer simulation methodology based on the finite element method for...
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research proposal offers to develop the most accurate, comprehensive and efficient finite element models to date for simulation of the...
What is the primary beam response of an interferometer with unequal elements?
Strom, R.G.; Bachiller, R.; Colomer, F.; Desmurs, J.F.; de Vicente, P.
2004-01-01
The EVN stations encompass elements with a range of diameters, even including an interferometer (the Westerbork Telescope, with up to 14 elements used together as a tied array). In combination, the various station pairs will each produce their own primary beam envelopes, with which the interferomete
Semina Yuliya Anatol'evna
2015-09-01
Full Text Available The behavior of reinforced concrete elements under some types of cyclic loads is described in the paper. The main aim of the investigations is research of the stress-strain state and strength of the inclined sections of reinforced concrete beam elements in conditions of systemic impact of constructive factors and the factor of external influence. To spotlight the problem of cyclic loadings three series of tests were conducted by the author. Firstly, the analysis of the tests showed that especially cyclic alternating loading reduces the bearing capacity of reinforced concrete beams and their crack resistance by 20 % due to the fatigue of concrete and reinforcement. Thus the change of load sign creates serious changes of stress-strain state of reinforced concrete beam elements. Low cycle loads of constant sign effect the behavior of the constructions not so adversely. Secondly, based on the experimental data mathematical models of elements’ strength were obtained. These models allow evaluating the impact of each factor on the output parameter not only separately, but also in interaction with each other. Furthermore, the material spotlighted by the author describes stress-strain state of the investigated elements, cracking mechanism, changes of deflection values, the influence of mode cyclic loading during the tests. Since the data on the subject are useful and important to building practice, the ultimate aim of the tests will be working out for improvement of nonlinear calculation models of span reinforced concrete constructions taking into account the impact of these loads, and also there will be the development of engineering calculation techniques of their strength, crack resistance and deformability.
Nonlinear and long-term beam dynamics in low energy storage rings
Papash, A. I.; Smirnov, A. V.; Welsch, C. P.
2013-06-01
Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF+ ions at 93keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3-30 keV ions with a gas jet target are summarized.
Nonlinear and long-term beam dynamics in low energy storage rings
A. I. Papash
2013-06-01
Full Text Available Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF^{+} ions at 93 keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3–30 keV ions with a gas jet target are summarized.
Silva, Clodoaldo J.; Daqaq, Mohammed F.
2017-02-01
Despite the shear amount of research studies on nonlinear flexural dynamics of cantilever beams, very few efforts address the practical geometry involving a constant thickness and linearly-varying width. This stems from the nature of the associated linear eigenvalue problem which cannot be easily solved in closed form. In this paper, we present a closed-form solution to this particular linear eigenvalue problem in the form of a general Meijer-G differential equation for which a solution is readily available in the shape of the Meijer-G functions. Using this approach, the exact linear modal frequencies and shapes are obtained and used in the discretization of the nonlinear partial-differential equation describing the dynamics of the system. The discretized system of ordinary-differential equations is then solved using the method of multiple scales to obtain an approximate analytical solution describing the primary resonance behavior of a given vibration mode. An analytical expression for the modal effective nonlinearity is obtained and used to analyze the influence of the beam's tapering on the nonlinear primary resonance behavior of the response (softening/hardening). Results are then compared to a finite element (FE) solution of the linear eigenvalue problem in which the modal shapes obtained using the FE method are fit into a set of orthogonal polynomial functions and used to discretize the nonlinear problem. It is shown that, while the modal frequencies obtained using the FE method approximate those obtained analytically with negligible error (less than 1%), there is a substantial error in the resulting estimates of the modal effective nonlinearity. This indicates that, even negligible errors in the approximate solution of the linear problem, can propagate to become significant when analyzing the nonlinear problem further reinforcing the importance of the exact solution.
Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams
Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.
2015-04-01
In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized
Joglekar, D. M.; Mitra, M.
2015-11-01
A breathing crack, due to its bilinear stiffness characteristics, modifies the frequency spectrum of a propagating dual-frequency elastic wave, and gives rise to sidebands around the probing frequency. This paper presents an analytical-numerical method to investigate such nonlinear frequency mixing resulting from the modulation effects induced by a breathing crack in 1D waveguides, such as axial rods and the Euler-Bernoulli beams. A transverse edge-crack is assumed to be present in both the waveguides, and the local flexibility caused by the crack is modeled using an equivalent spring approach. A simultaneous treatment of both the waveguides, in the framework of the Fourier transform based spectral finite element method, is presented for analyzing their response to a dual frequency excitation applied in the form of a tone-burst signal. The intermittent contact between the crack surfaces is accounted for by introducing bilinear contact forces acting at the nodes of the damage spectral element. Subsequently, an iterative approach is outlined for solving the resulting system of nonlinear simultaneous equations. Applicability of the proposed method is demonstrated by considering several test cases. The existence of sidebands and the higher order harmonics is confirmed in the frequency domain response of both the waveguides under investigation. A qualitative comparison with the previous experimental observations accentuates the utility of the proposed solution method. Additionally, the influence of the two constituent frequencies in the dual frequency excitation is assessed by varying the relative strengths of their amplitudes. A brief parametric study is performed for bringing out the effects of the relative crack depth and crack location on the degree of modulation, which is quantified in terms of the modulation parameter. Results of the present investigation can find their potential use in providing an analytical-numerical support to the studies geared towards the
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.
Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com [Department of Physics, National Institute of Technology Jalandhar (India); Singh, Navpreet, E-mail: navpreet.nit@gmail.com [Guru Nanak Dev University College, Kapurthala, Punjab (India)
2015-11-15
This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.
Laursen, Tod A
2003-01-01
This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.
Jinhua Xie
2012-01-01
Full Text Available Based on the transmission and equilibrium relationship of vibration energy in beam-like structures, the Galerkin weighted residual method was applied to equation discretization. An equivalent transformation of feedback element was suggested to develop the Energy Finite Element model of a composite piezoelectric cantilever beam driven by harmonic excitation on lateral direction, with both systems with and without time delay being studied and the power input estimation of harmonic excitation was discussed for the resolution of Energy Finite Element function. Then the energy density solutions of the piezoelectric coupling beam through Energy Finite Element Method (EFEM and classical wave theory were compared to verify the EFEM model, which presented a good accordance. Further investigation was undertaken about the influence of control parameters including the feedback gain and arrangement of piezoelectric patches on characteristics of system energy density distribution.
Rodrigues Ribeiro, R. S.; Dahal, P.; Guerreiro, A.; Jorge, P. A. S.; Viegas, J.
2016-03-01
In this work, spiral phase lenses fabricated on the tip of single mode optical fibers are reported. This allows tailoring the fundamental guided mode, a Gaussian beam, into a Laguerre - Gaussian profile without using additional optical elements. The lenses are fabricated using Focused Ion Beam milling, enabling high resolution in the manufacturing process. The phase profiles are evaluated and validated using an implementation of the Finite Differences Time Domain. The output optical intensity profiles matching the numerical simulations are presented and analyzed. Finally, results on cell trapping and manipulation are briefly described.
QIN Xinqiang; MA Yichen; GONG Chunqiong
2004-01-01
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
Non-Linear Beam Dynamics Studies of the Diamond Storage Ring
Bartolini, Riccardo; Belgroune, Mahdia; Henry Rowland, James; Jones, James; Martin, Ian; Singh, Beni
2005-01-01
The non-linear beam dynamics have been investigated for the non-zero dispersion lattice of the Diamond storage ring. Effects in realistic lattice configurations such as the introduction of coupling errors, beta beating, closed orbit correction, quadrupole fringe field and in-vacuum and helical insertion devices have been studied in the presence of realistic physical aperture limitations. Frequency map analysis together with 6D tracking allows identification of the limiting resonances as well as the loss locations and calculation of the influence of non-linear longitudinal motion on the Touschek lifetime. The sensitivity of the lattice to some of these effects leads to the identification of a better working point for the machine.
(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material
Hu Yong-Hua; Fu Xi-Quan; Wen Shuang-Chun; Su Wen-Hua; Fan Dian-Yuan
2006-01-01
In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized (3+1)-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material (RHM) and left-handed material (LHM) is derived. By the commonly used Drude dispersive model for LHM, a (3+1)-dimensional nonlinear Schr(o)dinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
Passian, Ali; Siopsis, George
2016-08-01
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.
Ming Hsu Tsai
2011-01-01
Full Text Available A corotational finite element method combined with floating frame method and a numerical procedure is proposed to investigate large steady-state deformation and infinitesimal-free vibrationaround the steady-state deformation of a rotating-inclined Euler beam at constant angular velocity. The element nodal forces are derived using the consistent second-order linearization of the nonlinear beam theory, the d'Alembert principle, and the virtual work principle in a current inertia element coordinates, which is coincident with a rotating element coordinate system constructed at the current configuration of the beam element. The governing equations for linear vibration are obtained by the first-order Taylor series expansion of the equation of motion at the position of steady-state deformation. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady-state deformation and natural frequency of the rotating beam with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.
E. Carrera
2011-01-01
Full Text Available This paper presents hierarchical finite elements on the basis of the Carrera Unified Formulation for free vibrations analysis of beam with arbitrary section geometries. The displacement components are expanded in terms of the section coordinates, (x, y, using a set of 1-D generalized displacement variables. N-order Taylor type expansions are employed. N is a free parameter of the formulation, it is supposed to be as high as 4. Linear (2 nodes, quadratic (3 nodes and cubic (4 nodes approximations along the beam axis, (z, are introduced to develop finite element matrices. These are obtained in terms of a few fundamental nuclei whose form is independent of both N and the number of element nodes. Natural frequencies and vibration modes are computed. Convergence and assessment with available results is first made considering different type of beam elements and expansion orders. Additional analyses consider different beam sections (square, annular and airfoil shaped as well as boundary conditions (simply supported and cantilever beams. It has mainly been concluded that the proposed model is capable of detecting 3-D effects on the vibration modes as well as predicting shell-type vibration modes in case of thin walled beam sections.
Overall Buckling and Wringkling of Debonded Sandwich Beams: Finite Element and Experimental Results
Bambang K. Hadi
2006-05-01
Full Text Available Overall buckling and wrinkling of debonded sandwich beams under compressive loads were analyzed by both finite element and experimental methods. In the finite element method, a quarter and a half models of the specimens were analyzed. It shows that a quarter model is not adequate to analyze buckling of debonded sandwich beams, since it will disregard overall buckling mode that may occur in sandwich beams having compressive loads. At least a half model should be used to analyze buckling of sandwich beams. A finite element program UNA was used extensively to analyze the buckling loads. Experimental buckling of sandwich beams was carried out using a compression testing machine. Two LVDTs were used to measure deflections of the specimen during experimental loading. The loads were measured using load cells available in the machine. Specimens having core thickness of 45 and 75 mm were tested to represent overall and wrinkling modes respectively. The delamination lengths were 20, 60 and 80 mm, which represent 10, 30 and 40% of the beam length. The results show that the differences between experimental and finite element methods were less than 10%. Both overall buckling and wrinkling modes were shown in these specimens.
A URI 4-NODE QUADRILATERAL ELEMENT BY ASSUMED STRAIN METHOD FOR NONLINEAR PROBLEMS
WANG Jinyan; CHEN Jun; LI Minghui
2004-01-01
In this paper one-point quadrature "assumed strain" mixed element formulation based on the Hu-Washizu variational principle is presented. Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking. The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection, while the implementation of the proposed URI scheme is straightforward to suppress hourglass modes. In order to treat geometric nonlinearities simply and efficiently, a corotational coordinate system is used. Several numerical examples are given to demonstrate the performance of the suggested formulation, including nonlinear static/dynamic mechanical problems.
An axisymmetrical non-linear finite element model for induction heating in injection molding tools
Guerrier, Patrick; Nielsen, Kaspar Kirstein; Menotti, Stefano;
2016-01-01
To analyze the heating and cooling phase of an induction heated injection molding tool accurately, the temperature dependent magnetic properties, namely the non-linear B-H curves, need to be accounted for in an induction heating simulation. Hence, a finite element model has been developed...... in to the injection molding tool. The model shows very good agreement with the experimental temperature measurements. It is also shown that the non-linearity can be used without the temperature dependency in some cases, and a proposed method is presented of how to estimate an effective linear permeability to use...
Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements
Clausen, Johan; Damkilde, Lars
2006-01-01
The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...
Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements
Clausen, Johan Christian; Damkilde, Lars
2006-01-01
The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design....
Guermond, Jean-Luc
2014-01-01
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements
Clausen, Johan Christian; Damkilde, Lars
2006-01-01
The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design....
Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements
Clausen, Johan; Damkilde, Lars
2006-01-01
The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...... are carried out at much higher stress levels than present in a slope failure, this leads to the conclusion that the use of the non-linear criterion leads to a safer slope design...
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo;
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which ...... is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....
Lie algebraic analysis for the nonlinear transport of intense pulsed beams in electrostatics lenses
Lu Jian-Qin; Li Jin-Hai
2004-01-01
The Lie algebraic method is applied to the analysis of the nonlinear transport of an intense pulsed beam in cylindrically symmetrical electrostatic lenses, and particle orbits in a six-dimensional phase space (x, px, y, py, τ, pτ)are obtained in the second order approximation. They can also be acquired in the third or higher order approximation if needed. In the analysis, we divide the electrostatic lenses into several segments. Each segment is considered as a uniform accelerating field, and each dividing point is treated as a thin lens. The particle distribution in a three-dimensional ellipsoid is of Gaussian type.
Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution
Martins, Weliton Soares; de Silans, Thierry Passerat; Oriá, Marcos; Chevrollier, Martine; 10.1364/AO.51.005080
2012-01-01
Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses non-linear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersive-like lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.
Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies
Chang, Jing [College of Information Technology, Jilin Agricultural University, Changchun 130118 (China); Gao, Yixian, E-mail: gaoyx643@nenu.edu.cn; Li, Yong [School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)
2015-05-15
Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .
Calibration of a Non-Linear Beam Position Monitor Electronics by Switching Electrode Signals
Gasior, M
2013-01-01
Button electrode signals from beam position monitors embedded into new LHC collimators will be individually processed with front-end electronics based on compensated diode detectors and digitized with 24-bit audio-range ADCs. This scheme allows sub-micrometre beam orbit resolution to be achieved with simple hardware and no external timing. As the diode detectors only operate in a linear regime with large amplitude signals, offset errors of the electronics cannot be calibrated in the classical way with no input. This paper describes the algorithms developed to calibrate the offset and gain asymmetry of these nonlinear electronic channels. Presented algorithm application examples are based on measurements performed with prototype diode orbit systems installed on the CERN SPS and LHC machines.
Non-Linear Optical Flow Cytometry Using a Scanned, Bessel Beam Light-Sheet
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-01-01
Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers. PMID:26021750
Nonlinear effects in optical pumping of a cold and slow atomic beam
Porfido, N.
2015-10-12
By photoionizing hyperfine (HF) levels of the Cs state 62P3/2 in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around 180μs) spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of “dark” and “bright” resonances leading to power-dependent branching coefficients.
Nonlinear Breit-Wheeler pair production in a tightly focused laser beam
Di Piazza, A
2016-01-01
The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.
Nonlinear Breit-Wheeler Pair Production in a Tightly Focused Laser Beam
Di Piazza, A.
2016-11-01
The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field in the realistic assumption that the energy of the incoming photon is the largest dynamical energy in the problem. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.
Modeling Gun Dynamics with Three-Dimensional Beam Elements
1990-11-01
34 Sixth U.S. Army Symposium on Gun Dynamics, 14-17 May, 1990. Shames, Irving, and Clive Dym. Energy and Finite Element Methods in Structural Mechanics. New...Group ATIN: Mr. G. Barker Mr. A. E. Chambers Mr. J. Hoyle Mr. N. D. Manners Mr. S. E. Powell Dr. D. N. Bulman Shrivenham, Swindon, Wilts SN6 8LA
High speed, high power one-dimensional beam steering from a 6-element optical phased array.
Huang, W Ronny; Montoya, Juan; Kansky, Jan E; Redmond, Shawn M; Turner, George W; Sanchez-Rubio, Antonio
2012-07-30
Beam steering at high speed and high power is demonstrated from a 6-element optical phased array using coherent beam combining (CBC) techniques. The steering speed, defined as the inverse of the time to required to sweep the beam across the steering range, is 40 MHz and the total power is 396 mW. The measured central lobe FWHM width is 565 μrad. High on-axis intensity is maintained periodically by phase-locking the array via a stochastic-parallel-gradient-descent (SPGD) algorithm. A master-oscillator-power-amplifier (MOPA) configuration is used where the amplifier array elements are semiconductor slab-coupled-optical-waveguide-amplifiers (SCOWAs). The beam steering is achieved by LiNbO(3) phase modulators; the phase-locking occurs by current adjustment of the SCOWAs. The system can be readily scaled to GHz steering speed and multiwatt-class output.
Concept for ELENA Extraction and Beam Transfer Elements
Borburgh, J; Balhan, B; Barna, D; Bartmann, W; Fowler, T; Pricop, V; Sermeus, L; Vanbavinckhove, G
2013-01-01
In 2011 the ELENA decelerator was approved as a CERN project. Initially one extraction was foreseen, which should use a kicker and a magnetic septum which can be recuperated from an earlier installation. Since then a second extraction has been approved and a new solution was studied using only electric fields to extract the beam. This will be achieved by fast pulsing a separator, allowing single-bunch but also a full single-turn extraction from ELENA towards the experiments. The extraction and transfer requirements of ELENA are described, followed by the principal differences between the magnetic and electric field concepts. The design of electrostatic focussing and bending devices for the transfer lines will be presented. Finally the field quality which can be achieved with the separator and the concept of its power supply will be discussed.
Ramos, D
2008-01-01
The short interconnect length between the LHC superconducting magnets required the development of an optimised RF shielded bellows module, with a low impedance combined with compensation for large thermal displacements and alignment lateral offsets. Each bellows is shielded by slender copper-beryllium fingers working as preloaded beams in order to provide a constant force at the sliding contact. Unless the sliding friction and some geometrical parameters of the fingers are kept within a limited range, a large irreversible lateral deflection towards the vacuum chamber axis may occur and eventually block the beam aperture. The finite element analysis presented here simulates this failure mechanism, providing a complete understanding of the finger behaviour as well as the influence of the various design parameters. An implicit nonlinear two-dimensional model integrating friction on the sliding contacts, geometrical non-linearity and plasticity was implemented in a first stage. The design was then verified throug...
The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method
Zhibo Yang
2014-01-01
Full Text Available A B-spline wavelet on interval (BSWI finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.
Wang, X.; Zheng, G. T.
2016-02-01
A simple and general Equivalent Dynamic Stiffness Mapping technique is proposed for identifying the parameters or the mathematical model of a nonlinear structural element with steady-state primary harmonic frequency response functions (FRFs). The Equivalent Dynamic Stiffness is defined as the complex ratio between the internal force and the displacement response of unknown element. Obtained with the test data of responses' frequencies and amplitudes, the real and imaginary part of Equivalent Dynamic Stiffness are plotted as discrete points in a three dimensional space over the displacement amplitude and the frequency, which are called the real and the imaginary Equivalent Dynamic Stiffness map, respectively. These points will form a repeatable surface as the Equivalent Dynamic stiffness is only a function of the corresponding data as derived in the paper. The mathematical model of the unknown element can then be obtained by surface-fitting these points with special functions selected by priori knowledge of the nonlinear type or with ordinary polynomials if the type of nonlinearity is not pre-known. An important merit of this technique is its capability of dealing with strong nonlinearities owning complicated frequency response behaviors such as jumps and breaks in resonance curves. In addition, this technique could also greatly simplify the test procedure. Besides there is no need to pre-identify the underlying linear parameters, the method uses the measured data of excitation forces and responses without requiring a strict control of the excitation force during the test. The proposed technique is demonstrated and validated with four classical single-degree-of-freedom (SDOF) numerical examples and one experimental example. An application of this technique for identification of nonlinearity from multiple-degree-of-freedom (MDOF) systems is also illustrated.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Ruilan Tian
2016-06-01
Full Text Available The coupled system of smooth and discontinuous absorber and beam bridge under moving loads is constructed in order to detect the effectiveness of smooth and discontinuous absorber. It is worth pointing out that the coupled system contains an irrational restoring force which is a barrier for conventional nonlinear techniques. Hence, the harmonic balance method and Fourier expansion are used to obtain the approximate solutions of the system. The first and the second kind of generalized complete elliptic integrals are introduced. Furthermore, using power flow approach, the performance of smooth and discontinuous absorber in vibration reduction is estimated through the input energy, the dissipated energy, and the damping efficiency. It is interesting that only depending on the value of the smoothness parameter, the efficiency parameter of vibration reduction is optimized. Therefore, smooth and discontinuous absorber can adapt itself to effectively reducing the amplitude of the vibration of the beam bridge, which provides an insight to the understanding of the applications of smooth and discontinuous oscillator in engineering and power flow characteristics in nonlinear system.
Qi Song
2013-01-01
Full Text Available This paper proposes a partial refactorization for faster nonlinear analysis based on sparse matrix solution, which is nowadays the default solution choice in finite element analysis and can solve finite element models up to millions degrees of freedom. Among various fill-in’s reducing strategies for sparse matrix solution, the graph partition is in general the best in terms of resultant fill-ins and floating-point operations and furthermore produces a particular graph of sparse matrix that prevents local change of entries from wide spreading in factorization. Based on this feature, an explicit partial triangular refactorization with local change is efficiently constructed with limited additional storage requirement in row-sparse storage scheme. The partial refactorization of the changed stiffness matrix inherits a big percentage of the original factor and is carried out only on partial factor entries. The proposed method provides a new possibility for faster nonlinear analysis and is mainly suitable for material nonlinear problems and optimization problems. Compared to full factorization, it can significantly reduce the factorization time and can make nonlinear analysis more efficient.
Tamma, Kumar K.; Railkar, Sudhir B.
1988-01-01
The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...
Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2010-12-15
Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.
A modified beam stiffness matrix for superconductor elements
Gori, R.; Schrefler, B.A. (Padua Univ. (Italy). Ist. di Scienza e Tecnica delle Costruzioni)
1989-10-01
The components of the stiffness matrix of superconductor elements are derived taking into account the effects of the wrapping of superconductor strands around the internal insulating strip and of possible stabilizing profiles around conductor core. It is already known that the inclination of the strands referred to the longitudinal axis of the superconductor produces a reduction of the axial stiffness and a considerable increase in torsional stiffness. Here also the effects of bending are taken into account, completing hence the previous investigation. Examples relating to superconductors proposed for the Toroidal Field Coil of the Next European Torus are shown. In that instance the strand transposition is carried out by roebling. (orig.).
Non-linear shape functions over time in the space-time finite element method
Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements
Høgsberg, Jan Becker; Krenk, Steen
2014-01-01
numerically by introducing a cubic-linear two-dimensional isoparametric element. The cubic interpolation of this element accurately represents quadratic shear stress variations along cross-section walls, and thus moderately thin-walled cross-sections are effectively discretized by these elements. The ability......In technical beam theory the six equilibrium states associated with homogeneous tension, bending, shear and torsion are treated as individual load cases. This enables the formulation of weak form equations governing the warping from shear and torsion. These weak form equations are solved...... of this element to represent curved geometries, and to accurately determine cross-section parameters and shear stress distributions is demonstrated....
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously
A new higher-order shear deformation theory and refined beam element of composite laminates
Wanji Chen; Zhen Wu
2005-01-01
A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.
Fractal Two-Level Finite Element Method For Free Vibration of Cracked Beams
A.Y.T. Leung
1998-01-01
Full Text Available The fractal two-level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial program.
A finite element beam propagation method for simulation of liquid crystal devices.
Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal
2009-06-22
An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.
On the development of hierarchical solution strategies for nonlinear finite element formulations
Padovan, J.; Lackney, J.
1984-01-01
This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.
Padovan, Joe
1987-01-01
In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.
A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates
Putcha, N. S.; Reddy, J. N.
1986-01-01
The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.
Sun, Young; Shang, Dashan; Chai, Yisheng; Cao, Zexian; Lu, Jun
2015-09-01
From the viewpoint of electric circuit theory, the three fundamental two-terminal passive circuit elements, resistor R , capacitor C, and inductor L, are defined in terms of a relationship between two of the four basic circuit variables, charge q, current i, voltage v, and magnetic flux φ. From a symmetry concern, there should be a fourth fundamental element defined from the relationship between charge q and magnetic flux φ. Here we present both theoretical analysis and experimental evidences to demonstrate that a two-terminal passive device employing the magnetoelectric (ME) effects can exhibit a direct relationship between charge q and magnetic flux φ, and thus is able to act as the fourth fundamental circuit element. The ME effects refer to the induction of electric polarization by a magnetic field or magnetization by an electric field, and have attracted enormous interests due to their promise in many applications. However, no one has linked the ME effects with fundamental circuit theory. Both the linear and nonlinear-memory devices, termed transtor and memtranstor, respectively, have been experimentally realized using multiferroic materials showing strong ME effects. Based on our work, a full map of fundamental two-terminal circuit elements is constructed, which consists of four linear and four nonlinear-memory elements. This full map provides an invaluable guide to developing novel circuit functionalities in the future.
Misra, Nilanjal; Rapolu, Mounika; Venugopal Rao, S.; Varshney, Lalit; Kumar, Virendra
2016-05-01
The optical nonlinearity of metal nanoparticles in dielectrics is of special interest because of their high polarizability and ultrafast response that can be utilized in potential device applications. In this study nanocomposite thin films containing in situ generated Ag nanoparticles dispersed in an aliphatic urethane acrylate (AUA) matrix were synthesized using electron beam curing technique, in presence of an optimized concentration of diluent Trimethylolpropanetriacrylate (TMPTA). The metal nanocomposite films were characterized using UV-visible spectrophotometry, transmission electron microscope (TEM) and field emission scanning electron microscope (FE-SEM) techniques. Ag nanoparticle impregnated films demonstrated an absorption peak at ∼420 nm whose intensity increased with increase in the Ag concentration. The optical limiting property of the coatings was tested using a nanosecond Nd-YAG laser operated at third harmonic wavelength of 355 nm. For a 25 ns pulse and 10 Hz cycle, Ag-polymer coatings showed good optical limiting property and the threshold fluence for optical limiting was found to be ∼3.8×10-2 J/cm2 while the transmission decreased to 82%. The nonlinear optical coefficients were also determined using the standard Z-scan technique with picosecond (∼2 ps, 1 kHz) and femtosecond (∼150 fs, 100 MHz) pulses. Open aperture Z-scan data clearly suggested two-photon absorption as the dominant nonlinear absorption mechanism. Our detailed studies suggest these composites are potential candidates for optical limiting applications.
Torsional inertia moment of beam element with complex section analysis based on FEM
Zhao An; Huang Jun; Lu Jianming
2012-01-01
Currently, for the analysis of complex bridge based on beam element, the calculation of cross-section torsional inertia moment is still an unresolved technical problem. Most current calculation of section torsional inertia moment is an approximate analytic method for two-dimensional cross-section, which is not fully consistent with the actual situation, and do not consider the effects of diaphragm in bridge. In order to analyze accurately cable-stayed bridge, suspension bridge and other complex bridge structures based on beam element, the calculation method of section torsional inertia moment based on finite element method （FEM） is invented in this paper. Firstly, setting up local cantilever fine model with solid element or shell element and applying torsion on the end of cantilever. Secondly, calculating the torsion angle of cantilever by FEM method and then the torsional moment through equivalent beam method. Finally, the examples of the section torsional moment calculation of concrete model with solid element with diaphragm and steel girder box model with shell element with diaphragm are used to verify the calculation method, which is applied to the suspension bridge design and construction control special software SBNA developed by Research Institute of Highway Ministry of Transport. Taizhou Bridge under construction is one of the examples.
Puso, M; Maker, B N; Ferencz, R M; Hallquist, J O
2000-03-24
This report provides the NIKE3D user's manual update summary for changes made from version 3.0.0 April 24, 1995 to version 3.3.6 March 24,2000. The updates are excerpted directly from the code printed output file (hence the Courier font and formatting), are presented in chronological order and delineated by NIKE3D version number. NIKE3D is a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Thirty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a direct factorization method.
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing
2017-02-01
In this work, we employ a focused beam theory to modify the phase reversal at the stress-free boundary, and consequently enhance the second harmonic generation during its back-propagation toward the initial source position. We first confirmed this concept through experiment by using a spherically focused beam at the water-air interface, and measuring the reflected second harmonic and comparing with a planar wave reflected from the same stress-free or a rigid boundary. In order to test the feasibility of this idea for measuring the nonlinearity parameter of solids in a reflection mode, a focused nonlinear ultrasonic beam is modeled for focusing at and reflection from a stress-free boundary. A nonlinearity parameter expression is then defined together with diffraction and attenuation corrections.
Vibration Analysis of Rotating Tapered Timoshenko Beams by a New Finite Element Model
Bulent Yardimoglu
2006-01-01
Full Text Available A new finite element model is developed and subsequently used for transverse vibrations of tapered Timoshenko beams with rectangular cross-section. The displacement functions of the finite element are derived from the coupled displacement field (the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium approach by considering the tapering functions of breadth and depth of the beam. This procedure reduces the number of nodal variables. The new model can also be used for uniform beams. The stiffness and mass matrices of the finite element model are expressed by using the energy equations. To confirm the accuracy, efficiency, and versatility of the new model, a semi-symbolic computer program in MATLAB® is developed. As illustrative examples, the bending natural frequencies of non-rotating/rotating uniform and tapered Timoshenko beams are obtained and compared with previously published results and the results obtained from the finite element models of solids created in ABAQUS. Excellent agreement is found between the results of new finite element model and the other results.
Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams
Phadte, D. S.; Patidar, C. B.
2013-07-01
Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Mass flow prediction of the coriolis meter using C0 continuous beam elements
Binulal, B. R.; Rajan, Akash; Abhilash, Suryan R.; Kochupillai, Jayaraj; Kim, Heuy Dong
2015-06-01
A three node C0 continuous isoparametric beam element is formulated to model the curved pipe conveying fluid in three dimensional configuration. The equations of motion for the combined structure and fluid domain including added mass effect, Coriolis effect, centrifugal effect and the effect of pressure on the walls of pipe have been developed by Paidoussis. This equation is converted to finite element formulation using Galerkin technique and is validated with the results available from literature.
Dávila Pintle, José A; Lara, Edmundo Reynoso; Iturbe Castillo, Marcelo D
2013-07-01
It is presented a criteria for selecting the optimum aperture radius for the one beam Z-scan technique (OBZT), based on the analysis of the transmittance of the aperture. It is also presented a modification to the OBZT by directly measuring the beam radius in the far field with a rotating disk, which allows to determine simultaneously the non-linear absorptive coefficient and non-linear refractive index, much less sensitive to wave front distortions caused by inhomogeneities of the sample with a negligible loss of signal to noise ratio. It is demonstrated its equivalence to the OBZT.
无
2001-01-01
The physical mechanism of the halo-chaos formation for a high intensity proton beam in a periodic-fo cusing channel is analyzed using the transfer mahix theory and a qualiative analysis method.Particles-in-cell simula tims are further used to explore the mechanism of the beam halo-chaos fomation, which concerns not only with thc non linear effect of the beam space charge but also with the lransverse energy exchange belween the particles and the particle core. as well as the chaos generated by the nonlinear resonance ovcrlap. A nonlinear control method is proposed for con trolling tie haho-chaos. Simulation results show lhal the melhod is efhclivc. Somc potemlial applications of the halo chaos conlrol in experimenls are discussed.
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
Nonlinear Steady-State Vibration Analysis of a Beam with Breathing Cracks
Kamiya, Keisuke; Yoshinaga, Terumitsu
This paper presents a method for analysis of steady-state vibration of a beam with breathing cracks, which open and close during vibration. There are several papers treating problems of vibration analysis of a beam with breathing cracks. However, due to their treatments of the condition which determines the switch between the open and closed states of the crack, it is difficult for one to obtain steady-state vibration efficiently by methods such as the incremental harmonic balance method. Since opening and closing of a breathing crack depends on the sign of the bending moment, or the curvature, of the beam, the key point to this problem is explicit treatment of the bending moment. The mixed variational principle allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper a governing equation of a beam with breathing cracks is derived by a finite element procedure based on the mixed variational principle. Then, the derived governing equations are solved by combining the iteration method and the harmonic balance method. Finally, examples of analysis by the presented method are given.
Mereghetti, A; Cerutti, F; Versaci, R; Vlachoudis, V
2012-01-01
Extended FLUKA models of accelerator beam lines can be extremely complex: heavy to manipulate, poorly versatile and prone to mismatched positioning. We developed a framework capable of creating the FLUKA model of an arbitrary portion of a given accelerator, starting from the optics configuration and a few other information provided by the user. The framework includes a builder (LineBuilder), an element database and a series of configuration and analysis scripts. The LineBuilder is a Python program aimed at dynamically assembling complex FLUKA models of accelerator beam lines: positions, magnetic fields and scorings are automatically set up, and geometry details such as apertures of collimators, tilting and misalignment of elements, beam pipes and tunnel geometries can be entered at user’s will. The element database (FEDB) is a collection of detailed FLUKA geometry models of machine elements. This framework has been widely used for recent LHC and SPS beam-machine interaction studies at CERN, and led to a dra...
Composite Beam Cross-Section Analysis by a Single High-Order Element Layer
Couturier, Philippe; Krenk, Steen
2015-01-01
An analysis procedure of general cross-section properties is presented. The formulation is based on the stress-strain states in the classic six equilibrium modes of a beam by considering a finite thickness slice modelled by a single layer of 3D finite elements. The theory is illustrated by applic...
Chioran, Doina; Nicoarǎ, Adrian; Roşu, Şerban; Cǎrligeriu, Virgil; Ianeş, Emilia
2013-10-01
Digital processing of two-dimensional cone beam computer tomography slicesstarts by identification of the contour of elements within. This paper deals with the collective work of specialists in medicine and applied mathematics in computer science on elaborating and implementation of algorithms in dental 2D imagery.
The Use of Sprint Interface Element Delamination Simulation of Sandwich Composite Beam
Xu, Geng; Yan, Renjun
2016-12-01
Sandwich composite beams have been more and more used in various industries because of their excellent mechanical properties. However, the mismatched performance between face sheet and foam core always lead to such as cracks and damages in the core or face/core interface during the processes of manufacturing or service. Delamination damage at the adhesive interface is the most dangerous and could be one main source that the mechanical capability of the structure is serous degenerated. In this paper, a simple and natural model to evaluate the stiffness of the spring interface elements, which is based on the physics and the geometry of the adhesive layers, is proposed. In order to validate the model, cantilever beam bending test were conducted for marine sandwich composite I-beam. A good comparison has been found between predictions and experimental results, and results indicate that the spring interface element can provide an efficient model for the delamination simulation of sandwich composite structures.
BEAM 1.7: development for modelling fuel element and bundle buckling strength
Cheng, G.; Xu, S.; Xu, Z.; Paul, U.K. [Atomic Energy of Canada, Mississauga, Ontario (Canada)
2010-07-01
This paper describes BEAM, an AECL developed computer program, used to assess mechanical integrity of CANDU fuel bundles. The BEAM code has been developed to satisfy the need for buckling strength analysis of fuel bundles. Buckling refers to the phenomenon where a compressive axial load is large enough that a small lateral load can cause large lateral deflections. The buckling strength refers to the critical compressive axial load at which lateral instability is reached. The buckling strength analysis has practical significance for the design of fuel bundles, where the buckling strength of a fuel element/bundle is assessed so that the conditions leading to bundle jamming in the pressure tube are excluded. This paper presents the development and qualification of the BEAM code, with emphasis on the theoretical background and code implementation of the newly developed fuel element/bundle buckling strength model. (author)
Pusterla, M.; Servizi, G.; Turchetti, G.
1985-10-01
Theoretical models, suitable for description of the long behaviour of bunched and unbunched beams of particles in accelerators and storage rings, are becoming more and more appreciated by physicists that want a high luminosity joined with the stability of the beams. Such a point is going to be particulary important for the next generation machines as L.E.P., S.S.C. and L.H.C. In this note we are giving a simplified analysis of the beam-beam non-linear effects for proton colliders on the basis of the latest designs (we think of S.S.C. and L.H.C.). Before doing that, however, we like to consider the general features of the dynamical approaches that describe the beam-beam forces both for the proton proton rings (fixed angle collision) and for proton-antiproton or electronpositron rings (head-on collisions): they follow directly from the recent developments of non-linear classical mechanics, namely the K.A.M. theorem and the transition to a chaotic motion in deterministic mechanical systems.
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.
A HIGH ORDER ADAPTIVE FINITE ELEMENT METHOD FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS
Zhengfu Xu; Jinchao Xu; Chi-Wang Shu
2011-01-01
In this note,we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations,with the objective of achieving high order accuracy and mesh efficiency.We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem.The computational results verify that,by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al.,an order of N-3/2 accuracy can be obtained when continuous piecewise linear elements are used,where N is the number of elements.
A stabilised nodal spectral element method for fully nonlinear water waves
Engsig-Karup, A. P.; Eskilsson, C.; Bigoni, D.
2016-08-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order - possibly adapted - spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.
Ahad Zeinali
2007-12-01
Full Text Available Introduction: Because of the importance of vertebral compressive fracture (VCF role in increasing the patients’ death rate and reducing their quality of life, many studies have been conducted for a noninvasive prediction of vertebral compressive strength based on bone mineral density (BMD determination and recently finite element analysis. In this study, QCT-voxel based nonlinear finite element method is used for predicting vertebral compressive strength. Material and Methods: Four thoracolumbar vertebrae were excised from 3 cadavers with an average age of 42 years. They were then put in a water phantom and were scanned using the QCT. Using a computer program prepared in MATLAB, detailed voxel based geometry and mechanical characteristics of the vertebra were extracted from the CT images. The three dimensional finite element models of the samples were created using ANSYS computer program. The compressive strength of each vertebra body was calculated based on a linearly elastic-linearly plastic model and large deformation analysis in ANSYS and was compared to the value measured experimentally for that sample. Results: Based on the obtained results the QCT-voxel based nonlinear finite element method (FEM can predict vertebral compressive strength more effectively and accurately than the common QCT-voxel based linear FEM. The difference between the predicted strength values using this method and the measured ones was less than 1 kN for all the samples. Discussion and Conclusion: It seems that the QCT-voxel based nonlinear FEM used in this study can predict more effectively and accurately the vertebral strengths based on every vertebrae specification by considering their detailed geometric and densitometric characteristics.
James Sae Siew
2015-01-01
Full Text Available Rail turnouts are built to enable flexibility in the rail network as they allow for vehicles to switch between various tracks, therefore maximizing the utilisation of existing rail infrastructure. In general, railway turnouts are a safety-critical and expensive feature to a rail system as they suffer aggressive operational loads, in comparison to a plain rail track, and thus require frequent monitoring and maintenance. In practice, great consideration is given to the dynamic interaction between the turnouts components as a failed component may have adverse effects on the performance of neighbouring components. This paper presents a nonlinear 3D finite element (FE model, taking into account the nonlinearities of materials, in order to evaluate the interaction and behaviour of turnout components. Using ABAQUS, the finite element model was developed to simulate standard concrete bearers with 60 kg/m rail and with a tangential turnout radius of 250 m. The turnout structure is supported by a ballast layer, which is represented by a nonlinearly deformable tensionless solid. The numerical studies firstly demonstrate the importance of load transfer mechanisms in the failure modes of the turnout components. The outcome will lead to a better design and maintenance of railway turnouts, improving public safety and operational reliability.
Enhanced focus steering abilities of multi-element therapeutic arrays operating in nonlinear regimes
Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Ilyin, S. [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation); Gavrilov, L. [Andreyev Acoustics Institute, 4 Schvernik Str., 117036 Moscow (Russian Federation); Sapozhnikov, O.; Khokhlova, V. [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation); Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40" t" h, Street, Seattle, WA 98105 (United States); Kreider, W. [Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40" t" h, Street, Seattle, WA 98105 (United States)
2015-10-28
Steering abilities of a typical HIFU therapeutic array operated in linear and nonlinear regimes were compared using numerical simulation with the 3D Westervelt equation. The array included 256 elements of 1.2 MHz frequency and 6.6 mm diameter distributed in a quasi-random pattern over a spherical shell with a 130 mm aperture and a focal length of 120 mm. In the case of linear focusing, thermal effects are proportional to the intensity level and the criterion for safe array operation is that the intensity in the grating lobes should be less than 10% of the intensity in the main focus. In the case of nonlinear focusing, the heating effect is no longer proportional to intensity; therefore the heat deposition rate was chosen as the relevant metric, using the same 10% threshold for the secondary lobe in comparison with the focal maximum. When steering the focus, the same linearly predicted intensity level at the main focus was maintained by increasing the array power. Numerical simulations of the acoustic field were performed for nonlinear propagation both in water and in tissue. It was shown that for shock-forming conditions in the main focus, the steering range of safe electronic focusing is larger than that for linear propagation conditions. Nonlinear sonication regimes therefore can be used to enlarge tissue volumes that can be sonicated using electronic steering of the focus of HIFU arrays.
Nonlinear simulation of arch dam cracking with mixed finite element method
Ren Hao
2008-06-01
Full Text Available This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts: external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.
Enhanced focus steering abilities of multi-element therapeutic arrays operating in nonlinear regimes
Yuldashev, P.; Ilyin, S.; Gavrilov, L.; Sapozhnikov, O.; Kreider, W.; Khokhlova, V.
2015-10-01
Steering abilities of a typical HIFU therapeutic array operated in linear and nonlinear regimes were compared using numerical simulation with the 3D Westervelt equation. The array included 256 elements of 1.2 MHz frequency and 6.6 mm diameter distributed in a quasi-random pattern over a spherical shell with a 130 mm aperture and a focal length of 120 mm. In the case of linear focusing, thermal effects are proportional to the intensity level and the criterion for safe array operation is that the intensity in the grating lobes should be less than 10% of the intensity in the main focus. In the case of nonlinear focusing, the heating effect is no longer proportional to intensity; therefore the heat deposition rate was chosen as the relevant metric, using the same 10% threshold for the secondary lobe in comparison with the focal maximum. When steering the focus, the same linearly predicted intensity level at the main focus was maintained by increasing the array power. Numerical simulations of the acoustic field were performed for nonlinear propagation both in water and in tissue. It was shown that for shock-forming conditions in the main focus, the steering range of safe electronic focusing is larger than that for linear propagation conditions. Nonlinear sonication regimes therefore can be used to enlarge tissue volumes that can be sonicated using electronic steering of the focus of HIFU arrays.
Application of Cu-Al-Mn superelastic alloy bars as reinforcement elements in concrete beams
Shrestha, Kshitij C.; Araki, Yoshikazu; Nagae, Takuya; Yano, Hayato; Koetaka, Yuji; Omori, Toshihiro; Sutou, Yuji; Kainuma, Ryosuke; Ishida, Kiyohito
2012-04-01
Experimental works are done to assess the seismic behavior of concrete beams reinforced with superelastic alloy (SEA) bars. Applicability of newly developed Cu-Al-Mn SEA bars, characterized by large recovery strain, low material cost, and high machinability, have been proposed as partial replacements for conventional steel bars in order to reduce residual deformations in structures during and after intense earthquakes. Four-point reverse-cyclic bending tests were done on 1/3 scale concrete beams comprising three different types of specimens - conventional steel reinforced concrete (ST-RC), SEA reinforced concrete (SEA-RC), and SEA reinforced concrete with pre-tensioning (SEA-PC). The results showed that SEA reinforced concrete beams demonstrated significant enhancement in crack recovery capacity in comparison to steel reinforced beam. Average recovery of cracks for each of the specimens was 21% for ST-RC, 84% for SEA-RC, and 86% for SEA-PC. In addition, SEA-RC and SEA-PC beams demonstrated strong capability of recentering with comparable normalized strength and ductility relative to conventional ST-RC beam specimen. ST-RC beam, on the other hand, showed large residual cracks due to progressive reduction in its re-centering capability with each cycle. Both the SEA-RC and SEA-PC specimens demonstrated superiority of Cu-Al-Mn SEA bars to conventional steel reinforcing bars as reinforcement elements.
Cichalewski, w
2010-01-01
The high power amplifiers transfer characteristics nonlinearities can have a negative influence on the overall system performance. This is also true for the TESLA superconducting cavities accelerating field parameters control systems. This Low Level Radio Frequency control systems uses microwave high power amplifiers (like 10 MW klystrons) as actuators in the mentioned feedback loops. The amplitude compression and phase deviations phenomena introduced to the control signals can reduce the feedback performance and cause electron beam energy instabilities. The transfer characteristics deviations in the Free Electron Laser in Hamburg experiment have been investigated. The outcome of this study together with the description of the developed linearization method based on the digital predistortion approach have been described in this paper. Additionally, the results from the linearization tool performance tests in the FLASH's RF systems have been placed.
Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila
2016-09-01
In the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.
Measurement of the Beam Longitudinal Profile in a Storage Ring by Non-Linear Laser Mixing
Beche, J.-F.; Byrd, J.; De Santis, S.; Denes, P.; Placidi, M.; Turner, W.; Zolotorev, M.
2004-11-01
We report on the development of a new technique for the measurement of the longitudinal beam profile in storage rings. This technique, which has been successfully demonstrated at the Advanced Light Source, mixes the synchrotron radiation with the light from a mode-locked solid-state laser oscillator in a non-linear crystal. The up-converted radiation is then detected with a photomultiplier and processed to extract, store, and display the required information. The available choices of laser repetition frequency, pulse width, and phase modulation give a wide range of options for matching the bunch configuration of a particular storage ring. Besides the dynamic measurement of the longitudinal profile of each bunch, the instrument can monitor the evolution of the bunch tails, the presence of un trapped particles, and their diffusion into nominally empty RF buckets ("ghost bunches").
Tran Hy, J
1998-01-01
This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed amplitude but appropriate sign were shown to provide linear damping and no coherent tune shift, though the rate predicted analytically was somewhat higher than that observed in simulations. This algorithm gave much faster damping (for equal power) than conventional proportional kicks, which damp exponentially. Two single-particle effects of the image-change force were investigated: distortion of the momentum dispersion function and amplitude dependence of the betatron tunes (resulting in tune spread). The former is calculated using transfer maps and the method of undetermined coefficients, the latter by solving the cubic ...
A Beam-Fourier Technique for the Numerical Investigation of 2D Nonlinear Convective Flows
Papanicolaou, N. C.
2011-11-01
In the current work, we develop a numerical method suitable for treating the problem of nonlinear two-dimensional flows in rectangular domains. For the spatial approximation we employ the Fourier-Galerkin approach. More specifically, our basis functions are products of trigonometric and Beam functions. This choice means that the solutions automatically satisfy the boundary and periodic conditions in the x and y directions respectively. The accuracy of the method is assessed by applying it to model problems which admit exact analytical solutions. The numerical and analytic solutions are found to be in good agreement. The convergence rate of the spectral coefficients is found to be fifth-order algebraic in the x-direction and y-direction, confirming the efficiency and speed of our technique.
Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.
Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent
2015-11-01
Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions.
Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method
Syngellakis, S.; Arnold, M. A.; Rassoulian, H.
2000-01-01
The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element progr...
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
Y. J. Choi
2012-01-01
Full Text Available We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as O(k+hγ˜, where γ˜ is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.
LI YaoChen
2007-01-01
The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated.Some assumptions are presented based on the published experimental data.The electrical yielding criterion,mechanical yielding criterion and isotropic hardening model are established.The flow theory in incremental forms in polarization procedure is presented.The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically.Finally,the nonlinear constitutive law expressed in a form of matrices and vectors,which is immediately associated with finite element analysis,is formulated.In the example problem of a rectangular specimen subjected to a uniaxial electric field,the procedure from virgin state to fully polarized state is simulated.Afterward,a uniaxial compressive loading is applied to depolarizing the specimen.Results are in agreement with the experimental data.
2007-01-01
The hysteresis phenomena of ferroelectric/ferroelastic material in polarization procedure are investigated. Some assumptions are presented based on the published experimental data. The electrical yielding criterion, mechanical yielding criterion and isotropic hardening model are established. The flow theory in incremental forms in polarization procedure is presented. The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically. Finally, the nonlinear constitutive law expressed in a form of matrices and vectors, which is immediately associated with finite element analysis, is formulated. In the example problem of a rectangular specimen subjected to a uniaxial electric field, the procedure from virgin state to fully polarized state is simulated. Afterward, a uniaxial compressive loading is applied to depolarizing the specimen. Results are in agreement with the experimental data.
Hu, Y. J.; Yang, J.; Kitipornchai, S.
2013-07-01
This paper presents a geometrically nonlinear micro-beam model for the electro-dynamic analysis of an initially curved micro-beam under an applied voltage, with an emphasis on its snap-through and pull-in behaviors. The governing equations of motion and the associated boundary conditions are derived in an arc coordinate system without involving any assumptions on the nonlinear deformation. Differential quadrature method (DQM) and Petzold-Gear Backward Differentiation Formulas (BDF) are employed to solve the governing equations in the space and time domains respectively to obtain the nonlinear fundamental frequency, snap-through voltage, pull-in voltage and the corresponding mode shapes of a micro-beam clamped at both ends. The present analysis is validated through a direct comparison with the published experimental and numerical results. A parametric study is conducted to investigate the influences of the initial gap, base length, arc rise, and initial curved configuration on the snap-through and pull-in behaviors of the micro-beam.
Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance
Liu-Yang Xiong
2014-01-01
Full Text Available Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time. For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance. The ordinary differential equations of the two mode shapes are established using the Galerkin method. The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities. The multiple scales method is applied to derive the modulation-phase equations. Steady-state solutions of the system as well as their stability are examined. The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction. The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance. The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method. The unstable regions in the internal resonance are explored via numerical simulations.
Sedighi, H. M.; Shirazi, K. H.
2014-11-01
This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.
Analysis and Application of Advanced Control Strategies to a Heating Element Nonlinear Model
Turhan, C.; Simani, S.; Zajic, I.; Gokcen Akkurt, G.
2017-01-01
This paper presents the design of different control strategies applied to a heating element nonlinear model. The description of this heating element was obtained exploiting a data-driven and physically meaningful nonlinear continuous-time model, which represents a test-bed used in passive air conditioning for sustainable housing applications. This model has low complexity while achieving high simulation performance. The physical meaningfulness of the model provides an enhanced insight into the performance and functionality of the system. In return, this information can be used during the system simulation and improved model- based and data-driven control designs for tight temperature regulation. The main purpose of this study is thus to give several examples of viable and practical designs of control schemes with application to this heating element model. Moreover, extensive simulations and Monte- Carlo analysis are the tools for assessing experimentally the main features of the proposed control schemes, in the presence of modelling and measurement errors. These developed control methods are also compared in order to evaluate advantages and drawbacks of the considered solutions. Finally, the exploited simulation tools can serve to highlight the potential application of the proposed control strategies to real air conditioning systems.
Romanas Karkauskas
2011-04-01
Full Text Available The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained.Article in Lithuanian
Calculation of benchmarks with a shear beam model
Ferreira, D.
2015-01-01
Fiber models for beam and shell elements allow for relatively rapid finite element analysis of concrete structures and structural elements. This project aims at the development of the formulation of such elements and a pilot implementation. Standard nonlinear fiber beam formulations do not account
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
Romanchenko, I. V., E-mail: riv@lfe.hcei.tsc.ru; Rostov, V. V.; Gunin, A. V.; Konev, V. Yu. [Institute of high current electronics SB RAS, Akademichesky 2/3, 634055, Tomsk (Russian Federation)
2015-06-07
We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700 MW (6% standard deviation) at frequencies from 0.5 to 1.7 GHz (1% standard deviation) with 100 Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350 MW maximum peak power, which corresponds to 350 kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within ±15° in the horizontal plane by coherent RF pulses with circular polarization at 1.0 GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.
Experimental nonlinear beam dynamics studies with turn- by-turn phase space monitors
Terebilo, Andrei Gennadyevich
1999-10-01
This thesis presents an experimental study of single particle and collective beam dynamics undertaken by the author in SPEAR electron storage ring. The technique used for measurement consists of exciting transverse oscillations of a bunch circulating in the ring with a fast kicker and observing the center of mass oscillations every turn for several thousand turns. The goal of this study was to develop new applications of the turn-by-turn technique to accelerator diagnostics. One innovation introduced is the use of a collective mode of the beam motion as a phase space probe. When in this mode the bunch behaves similar to a macroparticle and oscillates coherently. It is possible to control the growth/damping rate of this oscillation by adjusting the accelerator parameters. Another new tool proposed is the analysis of phase space trajectories in the time-frequency domain. This technique makes it possible to conduct nonlinear dynamics experiments such as observation of high order resonances in the frequency map and single-kick measurement of the tune dependence on the amplitude of oscillations.
Cross-sectional mapping for refined beam elements with applications to shell-like structures
Pagani, A.; de Miguel, A. G.; Carrera, E.
2017-02-01
This paper discusses the use of higher-order mapping functions for enhancing the physical representation of refined beam theories. Based on the Carrera unified formulation (CUF), advanced one-dimensional models are formulated by expressing the displacement field as a generic expansion of the generalized unknowns. According to CUF, a novel physically/geometrically consistent model is devised by employing Legendre-like polynomial sets to approximate the generalized unknowns at the cross-sectional level, whereas a local mapping technique based on the blending functions method is used to describe the exact physical boundaries of the cross-section domain. Classical and innovative finite element methods, including hierarchical p-elements and locking-free integration schemes, are utilized to solve the governing equations of the unified beam theory. Several numerical applications accounting for small displacements/rotations and strains are discussed, including beam structures with cross-sectional curved edges, cylindrical shells, and thin-walled aeronautical wing structures with reinforcements. The results from the proposed methodology are widely assessed by comparisons with solutions from the literature and commercial finite element software tools. The attention is focussed on the high computational efficiency and the marked capabilities of the present beam model, which can deal with a broad spectrum of structural problems with unveiled accuracy in terms of geometrical representation of the domain boundaries.
Meier, Christoph; Wall, Wolfgang A; Popp, Alexander
2016-01-01
Recently, the authors have proposed a novel all-angle beam contact (ABC) formulation that combines the advantages of existing point and line contact models in a variationally consistent manner. However, the ABC formulation has so far only been applied in combination with a special torsion-free beam model, which yields a very simple and efficient finite element formulation, but which is restricted to initially straight beams with isotropic cross-sections. In order to abstain from these restrictions, the current work combines the ABC formulation with a geometrically exact Kirchhoff-Love beam element formulation that is capable of treating even the most general cases of slender beam problems in terms of initial geometry and external loads. While the neglect of shear deformation that is inherent to this formulation has been shown to provide considerable numerical advantages in the range of high beam slenderness ratios, alternative shear-deformable beam models are required for examples with thick beams. The curren...
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
Damping of rotating beams with particle dampers: Discrete element method analysis
Els, D. N. J.
2013-06-01
The performance of particle dampers (PDs) under centrifugal loads was investigated. A test bench consisting of a rotating cantilever beam with a particle damper at the tip was developed (D. N. J. Els, AIAA Journal 49, 2228-2238 (2011)). Equal mass containers with different depths, filled with a range of uniform-sized steel ball bearings, were used as particle dampers. The experiments were duplicated numerically with a discrete element method (DEM) model, calibrated against the experimental data. The DEM model of the rotating beam with a PD at the tip captured the performance of the PD very well over a wide range of tests with different configurations and rotation velocities.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem
无
2006-01-01
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
Solution of Nonlinear Coupled Heat and Moisture Transport Using Finite Element Method
T. Krejčí
2004-01-01
Full Text Available This paper deals with a numerical solution of coupled of heat and moisture transfer using the finite element method. The mathematical model consists of balance equations of mass, energy and linear momentum and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressures, gas pressure and displacement. In contrast with pure mechanical problems, there are several difficulties which require special attention. Systems of algebraic equations arising from coupled problems are generally nonlinear, and the matrices of such systems are nonsymmetric and indefinite. The first experiences of solving complicated coupled problems are mentioned in this paper.
Tang, Yao-Zong; Li, Xiao-Lin
2017-03-01
We first give a stabilized improved moving least squares (IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. Project supported by the National Natural Science Foundation of China (Grant No. 11471063), the Chongqing Research Program of Basic Research and Frontier Technology, China (Grant No. cstc2015jcyjBX0083), and the Educational Commission Foundation of Chongqing City, China (Grant No. KJ1600330).
Yan-ping Chen; Yun-qing Huang
2001-01-01
Improved L2-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higherorder spaces. A second paper will present the analysis of a fully discrete scheme (Numer.Math. J. Chinese Univ. vol.9, no.2, 2000, 181-192).
Second-Order Nonlinear Analysis of Steel Tapered Beams Subjected to Span Loading
Ali Hadidi
2014-03-01
Full Text Available A second-order elastic analysis of tapered steel members with I-shaped sections subjected to span distributed and concentrated loadings is developed. Fixed end forces and moments as well as exact stiffness matrix of tapered Timoshenko-Euler beam are obtained with exact geometrical properties of sections. The simultaneous action of bending moment, shear, and axial force including P−δ effects is also considered in the analysis. A computer code has been developed in MATLAB software using a power series method to solve governing second-order differential equation of equilibrium with variable coefficients for beams with distributed span loading. A generalized matrix condensation technique is then utilized for analysis of beams with concentrated span loadings. The accuracy and efficiency of the results of the proposed method are verified through comparing them to those obtained from other approaches such as finite element methods, which indicates the robustness and time saving of this method even for large scale frames with tapered members.
Almeida, EDGARD S.; Spilker, ROBERT L.
1998-01-01
This two-part paper addresses finite element-based computational models for the three-dimensional (3-D) nonlinear analysis of soft hydrated tissues, such as articular cartilage in diarthrodial joints, under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible inviscid fluid and a hyperelastic, transversely isotropic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order, nonlinear system of equations is discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. Details of the formulations were presented in Part I [1]. In Part II, the two formulations are used to develop two-dimensional (2-D) quadrilateral and triangular elements and three-dimensional (3-D) hexahedral and tetrahedral elements. Numerical examples, including those representative of soft tissue material testing and simple human joints, are used to validate the formulations and to illustrate their applications. A focus of this work is the comparison of the alternate formulations for nonlinear problems. While it is demonstrated that both formulations produce a range of converging elements, the velocity-pressure formulation is found to be more efficient computationally.
Ibrahim Dauda Muhammad
2015-01-01
Full Text Available The single-walled zirconia nanotube is structurally modeled and its Young’s modulus is valued by using the finite element approach. The nanotube was assumed to be a frame-like structure with bonds between atoms regarded as beam elements. The properties of the beam required for input into the finite element analysis were computed by connecting energy equivalence between molecular and continuum mechanics. Simulation was conducted by applying axial tensile strain on one end of the nanotube while the other end was fixed and the corresponding reaction force recorded to compute Young’s modulus. It was found out that Young’s modulus of zirconia nanotubes is significantly affected by some geometrical parameters such as chirality, diameter, thickness, and length. The obtained values of Young’s modulus for a certain range of diameters are in agreement with what was obtained in the few experiments that have been conducted so far. This study was conducted on the cubic phase of zirconia having armchair and zigzag configuration. The optimal diameter and thickness were obtained, which will assist in designing and fabricating bulk nanostructured components containing zirconia nanotubes for various applications.
Padovan, Joe
1986-01-01
In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.
Yong Zhao
1996-01-01
Full Text Available The large strain ratcheting in cyclic plasticity of a typical pressurized pipe elbow in a realistic nuclear piping system was investigated in a more quantitative manner than previously. The elbow was modeled using a fine mesh of shell elements that can provide the completed information of detailed time varying strain distributions in the whole elbow area. The nonlinear time history stress analyses performed were based on a pseudostatic concept using the vector-valued stochastic displacement response time series loaded at the elbow ends. The response time series were synthesized using a simulation approach based on the random vibration analyses of the piping system and its supporting building. After a finite element mesh convergence study, parametric analyses were conducted that included the effects due to the magnitude changes in excitation level, internal pressure, material yield stress, and material strain hardening.
leMesurier, Brenton John; Christiansen, Peter Leth; Gaididei, Yuri B; Rasmussen, Jens Juul
2004-10-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
Non-linear beam dynamics tests in the LHC: LHC dynamic aperture MD on Beam 2 (24th of June 2012)
Maclean, E H; Persson, T H B; Redaelli, S; Schmidt, F; Tomas, R; Uythoven, J
2013-01-01
This MD note summarizes measurements performed on LHC Beam 2 during the non-linear machine development (MD) of 24 June 2012. The aim of the measurement was to observe the dynamic aperture of LHC Beam 2, and obtain turn-by-turn (TbT) betatron oscillation data, enabling the study of amplitude detuning and resonance driving terms (RDTs). The regular injections required by the MD also represented an opportunity to test a new coupling feedback routine based on the analysis of injection oscillation data. Initial measurements were performed on the nominal state of the LHC at injection. On completion of this study the Landau octupoles were turned off and corrections for higher-order chromaticities were implemented to reduce the non-linearity of the machine as far as possible. A second set of measurements were then performed. All studies were performed using the LHC aperture kicker (MKA).
Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method
Hui Li
2014-01-01
Full Text Available This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM to theoretically calculate its nature frequency and vibration response. First of all, strain dependent mechanical property of hard coating is briefly introduced and polynomial method is adopted to characterize the storage and loss modulus of coating material. Then, the principle formulas of inherent and dynamic response characteristics of the hard coating composite plate are derived. And consequently specific analysis procedure is proposed by combining ANSYS APDL and self-designed MATLAB program. Finally, a composite plate coated with MgO + Al2O3 is taken as a study object and both nonlinear vibration test and analysis are conducted on the plate specimen with considering strain dependent mechanical parameters of hard coating. Through comparing the resulting frequency and response results, the practicability and reliability of FEIM have been verified and the corresponding analysis results can provide an important reference for further study on nonlinear vibration mechanism of hard coating composite structure.
Guangsong Chen
2014-01-01
Full Text Available This paper presents formulations for a Timoshenko beam subjected to an accelerating mass using spectral element method in time domain (TSEM. Vertical displacement and bending rotation of the beam were interpolated by Lagrange polynomials supported on the Gauss-Lobatto-Legendre (GLL points. By using GLL integration rule, the mass matrix was diagonal and the dynamic responses can be obtained efficiently and accurately. The results were compared with those obtained in the literature to verify the correctness. The variation of the vibration frequencies of the Timoshenko and moving mass system was researched. The effects of inertial force, centrifugal force, Coriolis force, and tangential force on a Timoshenko beam subjected to an accelerating mass were investigated.
Evaluation of Flanking Noise Transmission within Periodically Distributed Lightweight Beam Elements
Domadiya, Parthkumar Gandalal; Andersen, Lars Vabbersgaard; Sorokin, Sergey
2012-01-01
Wooden frame structures are highly preferred as lightweight building systems nowadays. Lightweight building structures have gained more interest due to lower cost of production. However, there is a growing concern regarding noise and vibration issues within lightweight structures. Sound may pass...... from one room to another as indirect or flanking noise via joints or as direct transmission between adjacent rooms. The present analysis concerns flanking transmission within two-dimensional infinite periodic beam structures. The beam is comprised of two different materials placed in a periodic manner....... Two different theoretical methods are taken into consideration to evaluate flanking noise transmission within the beam structure: The finite-element method (FEM) and a Floquet theory approach. Research is carried out regarding the effects of periodicity in a wide range of frequencies from 0 to 300 Hz...
Haitao Che
2011-01-01
Full Text Available We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.
Zhiguang Xiong; Chuanmiao Chen
2007-01-01
In this paper,n-degree continuous finite element method with interpolated coefficients for nonlinear initial value problem of ordinary differential equation is introduced and analyzed. An optimal superconvergence u - uh = O(hn+2),n ≥ 2,at (n + 1)-order Lobatto points in each element respectively is proved. Finally the theoretical results are tested by a numerical example.
Iman Eshraghi
2016-09-01
Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.
COMPUTATION OF SUPER-CONVERGENT NODAL STRESSES OF TIMOSHENKO BEAM ELEMENTS BY EEP METHOD
王枚; 袁驷
2004-01-01
The newly proposed element energy projection (EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements. General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given. Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions. The EEP method gives super-convergent nodal stresses, which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude. And in addition, it can overcome the "shear locking" difficulty for stresses even when the displacements are badly affected. This research paves the way for application of the EEP method to general onedimensional systems of ordinary differential equations.
Maquer, Ghislain; Laurent, Marc; Brandejsky, Vaclav; Pretterklieber, Michael L; Zysset, Philippe K
2014-06-01
Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently