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Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates 认领 引用 被引量：10
1
作者 WANG Hua Alatancang HUANG Jun-Jie 《Communications in Theoretical Physics》 SCIE CAS 2009年第12期1087-1092,共6页
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia... The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method. 展开更多
关键词 free vibration of rectangular thin plate double symplectic eigenfunction expansion method upper triangular matrix differential system general solution
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Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field 认领 引用 被引量：20
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作者 胡宇达 张金志 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第11期1405-1420,共16页
Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying ... Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated. 展开更多
关键词 magneto-elastic axially moving rectangular thin plate principalparametric resonance stability
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Bifurcation and chaos of a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields 认领 引用 被引量：5
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作者 Wei-guo ZHU Xiang-zhong BAI 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS 2009年第1期62-71,共10页
We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and me-chanical fields.Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangula... We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and me-chanical fields.Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the ex-pressions of electromagnetic forces,the vibration equations are derived for the mechanical loading in a steady transverse magnetic field.Using the Melnikov function method,the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping.The vibration equations are solved numerically by a fourth-order Runge-Kutta method.Its bifurcation dia-gram,Lyapunov exponent diagram,displacement wave diagram,phase diagram and Poincare section diagram are obtained. 展开更多
关键词 Rectangular thin plate Electromagnetic-mechanical coupling Melnikov function method Runge-Kutta method Bifurcation Chaos
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Stochastic Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation 认领 引用 被引量：1
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作者 葛根 王洪礼 许佳 《Transactions of Tianjin University》 EI CAS 2011年第1期13-19,共7页
A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under axial inplane excitation considering the influence of random environment factors. Firstly, the model is simp... A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under axial inplane excitation considering the influence of random environment factors. Firstly, the model is simplified by applying the stochastic averaging method of quasi-nonintegrable Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process are utilized to analyze the stochastic stability of the trivial solution of the system. Thirdly, the stochastic Hopf bifurcation of the vibration model is explored according to the qualitative changes in stationary probability density of system response, showing that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simple way on the potential applications of stochastic stability and bifurcation analysis. 展开更多
关键词 rectangular thin plate stochastic stability stochastic Hopf bifurcation
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THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD 认领 引用 被引量：1
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作者 钟阳 张永山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第6期833-839,共7页
The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firs... The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution. 展开更多
关键词 elastic foundation rectangular thin plate symplectic geometry method theoretic solution
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Stochastic Optimal Control of First-Passage Failure for Rectangular Thin Plate Vibration Model under Gaussian White-Noise Excitations 认领 引用 被引量：1
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作者 葛根 王洪礼 《Transactions of Tianjin University》 EI CAS 2011年第6期431-434,共4页
A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito stochastic... A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method. 展开更多
关键词 rectangular thin plate first-passage failure stochastic optimal control
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AN EXACT SOLUTION FOR THE BENDING OF POINT-SUPPORTED ORTHOTROPIC RECTANGULAR THIN PLATES 认领 引用 被引量：1
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作者 姜稚清 刘金喜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第6期547-557,共11页
A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simpl... A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past. 展开更多
关键词 exact solution point supports orthotropic rectangular thin plate
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Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance 认领 引用
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作者 李双宝 张伟 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第9期1115-1128,共14页
Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitat... Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-to- one internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate. 展开更多
关键词 rectangular thin plate global bifurcation multi-pulse chaotic dynamics extended Melnikov method
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BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS 认领 引用
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作者 黄家寅 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第7期812-816,共5页
Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bendin... Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given. 展开更多
关键词 orthotropic rectangular thin plate with variable thickness nonlinear unsymmetrical bending equilibrium equation compatibility equation basic equation dimensionless equation
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UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS 认领 引用
10
作者 黄家寅 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第7期817-826,共10页
By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate wi... By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained. 展开更多
关键词 orthotropic rectangular thin plate with variable thickness four clampled edge nonlinear unsymmetrical bending method of modified two-variable method of mixing perturbation uniformly valid asymptotic solution
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THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE 认领 引用 被引量：5
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作者 Wen Jihong Yu Dianlong Wang Gang Zhao Hongang Liu Yaozong 《Chinese Journal of Mechanical Engineering》 EI CAS 2005年第3期385-388,共4页
With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane... With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion （PWE） method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates. 展开更多
关键词 Phononic crystals Flexural wave band gaps Thin rectangular plate
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Chaotic Motion Analysis for a Coupled Magnetic-Flow-Mechanical Model of the Rectangular Conductive Thin Plate 认领 引用 被引量：1
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作者 Xinzong Wang Xiaofang Kang Qingguan Lei 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第11期1749-1771,共23页
The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin pl... The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow. 展开更多
关键词 Rectangular conductive thin plate chaotic airflow magnetic field Melnikov function Galerkin’s method
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Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges 认领 引用 被引量：1
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作者 王砚 王忠民 阮苗 《Journal of Shanghai University(English Edition)》 2010年第3期187-195,共9页
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t... The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed. 展开更多
关键词 element free method rectangular thin plates interior elastic point supports elastically restrained edges free vibration
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COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE 认领 引用
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作者 Jiusheng Ren Hanhai Li +1 位作者 Changjun Cheng Xuegang Yuan 《Acta Mechanica Solida Sinica》 SCIE EI 2012年第3期312-320,共9页
The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite el... The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared. 展开更多
关键词 fiber reinforced hyper-elastic material rectangular thin plate with void void shapeand void size potential energy principle growth of void
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ANALYSIS OF GLOBAL DYNAMICS IN A PARAMETRICALLY EXCITED THIN PLATE 认领 引用
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作者 张伟 《Acta Mechanica Sinica》 SCIE EI CAS 2001年第1期71-85,共15页
The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The formulas of the thin plate are derived by von Karman type equation and Galerkin's approac... The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The formulas of the thin plate are derived by von Karman type equation and Galerkin's approach. The method of multiple scales is used to obtain the averaged equations. Based on the averaged equations, the theory of the normal form is used to give the explicit expressions of the normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple program. On the basis of the normal form, a global bifurcation analysis of the parametrically excited rectangular thin plate is given by the global perturbation method developed by Kovacic and Wiggins. The chaotic motion of thin plate is also found by numerical simulation. 展开更多
关键词 rectangular thin plate global bifurcations normal form chaos
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A FREE RECTANGULAR PLATE ON ELASTIC FOUNDATION 认领 引用
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作者 成祥生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第10期977-982,共6页
This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the ... This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively. We select a flexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces. We apply the variational method meanwhile and then obtain better approximate solutions. 展开更多
关键词 rectangular thin plate bending problem Galerkin's variational method flexural function
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基于假设振型法对驾驶室顶板的振动分析 认领 引用
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作者 孟杰 马孝昌 史尚昆 《太原科技大学学报》 2026年第4期336-341,347,共6页
工程车辆驾驶室的动态振动响应会严重影响乘坐舒适性,分析驾驶室壁板的振动特性具有重要意义。提出了一种研究薄板振动特性的有效解析方法,将假设振型法应用到工程车辆驾驶室板件的运动方程中,通过建立结构体系的拉格朗日运动方程,推导... 工程车辆驾驶室的动态振动响应会严重影响乘坐舒适性,分析驾驶室壁板的振动特性具有重要意义。提出了一种研究薄板振动特性的有效解析方法,将假设振型法应用到工程车辆驾驶室板件的运动方程中,通过建立结构体系的拉格朗日运动方程,推导出用广义坐标表示的系统动力学方程,确定了结构的质量矩阵与刚度矩阵,最后根据特征值来计算系统的固有频率和振型函数,并与有限元计算结果进行了比较。随后进行了受迫振动分析,计算了矩形薄板在外部激励下的振动特性,并通过试验进行了验证。结果表明理论计算的数值结果与有限元分析结果以及试验结果吻合较好,并且计算效率比有限元高53.4%,其研究结果可对其他任意边界的不同类型薄板的振动特性分析提供参考,同时也为工程车辆驾驶室的减振提供思路。 展开更多
关键词 假设振型法 矩形薄板 拉格朗日方程 有限元分析
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Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions 认领 引用 被引量：8
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作者 闫红梅 崔维成 刘应中 《海洋工程：英文版》 2003年第2期151-162,共12页
Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is signific... Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied. 展开更多
关键词 hydroelastic response very large floating structure fluid Green function plate Green function thin plate theory free-free rectangular plate
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An extended high-dimensional Melnikov analysis for global and chaotic dynamics of a non-autonomous rectangular buckled thin plate 认领 引用 被引量：1
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作者 ZHANG JunHua ZHANG Wei 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2012年第9期1679-1690,共12页
By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectan... By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectangular buckled thin plate.The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation.The two cases of the buckling for the rectangular thin plate are considered.With the aid of Galerkin's approach,a two-degree-of-freedom nonautonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate.The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate.Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate.The results obtained here indicate that the chaotic motions can occur in the parametrically excited,simply supported rectangular buckled thin plate. 展开更多
关键词 extended high-dimensional Melnikov method rectangular buckled thin plate non-autonomous nonlinear system chaotic motions
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基于约束等效的背栓式石材幕墙自振频率解及裂缝损伤识别 认领 引用 被引量：5
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作者 杨煌涛 朱元臣 +1 位作者 丛浩楠 王建民 《工业建筑》 2025年第7期30-38,共9页
针对背栓式石材幕墙面板所具有的四边外伸、四点局部背栓(面)约束的相对复杂的构造特征,目前没有相关自振频率理论解用以验证数值模拟和指导试验测试分析。综合考虑实际背栓式石材幕墙面板的约束特征,首先简化等效为沿面板某一方向的线... 针对背栓式石材幕墙面板所具有的四边外伸、四点局部背栓(面)约束的相对复杂的构造特征,目前没有相关自振频率理论解用以验证数值模拟和指导试验测试分析。综合考虑实际背栓式石材幕墙面板的约束特征,首先简化等效为沿面板某一方向的线性约束,再等同于两端外伸简支梁,最后根据无限自由度振动理论得到两端外伸梁自振频率理论解。背栓式石材幕墙模态试验结果表明:试验值与理论解较为接近,并通过数值模拟进行辅助验证;考虑幕墙面板裂缝缺陷,背栓式石材幕墙面板简化模型的相应自振频率与带裂缝的理论解整体也能得到吻合验证。背栓式石材幕墙面板(包括部分带裂缝的面板)所得到的部分振型自振频率理论解可用于验证模拟分析及试验测试结果。 展开更多
关键词 背栓式石材幕墙 自振频率 理论解 数值模拟 矩形薄板
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