应用大挠度薄板功的互等定理求解一对边固定一对边自由的矩形薄板

应用大挠度弯曲薄板的第二类功的互等定理，求解均载一对边固定一对边自由大挠度弯曲矩形板的挠曲面方程。     

变厚度矩形薄板弯曲问题的DQ法研究

针对矩形薄板的线性挠曲控制微分方程及其边界条件,在空间域采用DQ法离散,得到以板各节点弯曲挠度为全部待定参数的线性方程组,只需一次求解该方程组即得到各节点的弯曲挠度,再由高阶Lagrange插值得到薄板全域内的任意点挠度。     

对边固支另两边简支矩形薄板弯曲问题的哈密顿方法

利用哈密顿体系以及辛几何中的分离变量和本征函数展开的方法,给出了求解对边固支另两边简支的矩形薄板弯曲问题的方法,并通过实例计算和分析说明了该方法的正确性.     

弹性地基上四边自由矩形大挠度薄板的自由振动

考虑具有粘滞阻尼的Winkler地基上四边自由受简谐激励的矩形板的偏微分方程组,找到了满足所有边界条件的近似挠度函数,利用Galerkin方法把偏微分方程表示的非线性动力学方程转化为用常微分方程表示的非线性动力学方程。在KBM法的基础上,引入谐波平衡的观点研究了弹性地基上四边自由无阻尼矩形板自由振动,应用Hamiltonion函数研究了系统能量与周期的关系。     

弹性地基上四边自由矩形大挠度薄板复杂运动研究

考虑具有粘滞阻尼的Winkler地基上四边自由受简谐激励的矩形板的偏微分方程组,找到了满足所有边界条件的近似挠度函数,利用Galerkin方法把偏微分方程表示的非线性动力学方程转化为用常微分方程表示的非线性动力学方程。应用多尺度法求得了系统的主共振解,并对主共振解的静态分岔方程进行了奇异性分析。应用Floquet理论和Melnikov方法分析了系统的全局特性。     

纵横载荷联合作用下弯曲薄板的功的互等定理

本文将功的互等定理应用于形状、大小和材料均相同又处于真实状态的两个薄板系统之间，得出了纵横载荷联合作用下弯曲薄板的功的互等定理，并给出了简洁的数学表达式。该式既可以用于横向载荷作用下弯曲薄板问题的求解，又可以用于薄板稳定问题的求解。定理推导过程中没有对薄板的形状和边界条件加以限制，因而使该定理具有较广的适用范围。     

矩形薄板混合边界条件受迫振动分析

本文将试函数方法和模态分析方法结合，给出矩形薄板在混合边界条件下受迫振动问题的分析方法．虽然我们仅就矩形薄板一条边界上具有两种边界条件的混合边界问题进行分析，但实际上本文方法对一条边界上具有多种混合边界条件问题，乃至一组边界上具有多种混合边界条件问题同样有效．作为算例，我们计算了在瞬时脉冲均布栽荷作用下，矩形薄板受迫振动的混合边界问题的挠度响应．     

磁场中矩形薄板的非线性内共振响应

给出了横向磁场作用下矩形薄板的磁弹性振动方程,针对一边固定、三边简支的矩形薄板,通过位移模态展开,并利用Galerkin法得到两自由度内共振非线性振动微分方程组。算例分析中,利用数值方法得到了系统内共振时两阶模态的时间历程响应图和相平面图,并分别讨论了系统初值及磁场强度对系统振动的影响。结果表明,系统呈现明显的非线性内共振特征。     

多孔超弹性矩形板中微孔的增长

The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.     

利用功的互等法求解集中载荷作用下简支矩形厚板的弯曲问题

在本文中，功的互等法（RTM）被推广应用于求解基于Reissner理论的厚矩形板的弯曲问题，得到了在任意一点作用集中荷载矩形厚板弯曲问题的解析解，并给出了具有实价的计算结果。     

均布载荷作用下厚矩形板的弯曲

推广应用功的互等定理法(RTM)于求解基于Reissner理论的厚矩形板的弯曲问题，给出了二对边简支另两边固定厚矩形板在均布载荷作用下弯曲的精确解析解，并分析了解的数值结果．     

Stochastic Optimal Control of First-Passage Failure for Rectangular Thin Plate Vibration Model under Gaussian White-Noise Excitations

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 Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation

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.     

温度场中非线性弹性地基上矩形薄板的1/3次亚谐共振

为了研究温度场中非线性地基上矩形薄板受简谐激励的1/3次亚谐共振问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程。利用非线性振动的多尺度分析方法求得系统1/3次亚谐共振的近似解,并进行数值计算。分析温度、地基系数、阻尼、几何参数、激励等对系统3次超谐共振的影响。得到了随参数变化响应曲线的变化规律。     

Winkler地基上四边自由矩形薄板的1/3次亚谐共振与混沌分析

研究Winkler地基上四边自由矩形薄板的复杂运动,按照弹性力学理论建立Winkler地基上四边自由受简谐激励作用矩形薄板的动力学方程;利用Galerkin方法将其转化为非线性振动方程;应用非线性振动的多尺度法求得了系统满足1/3次亚谐共振情况时的一次近似解,并进行数值计算;分析激励、调谐值、阻尼等对系统响应曲线的影响;应用Floquet理论分析了系统的稳定性问题;应用Melnikov方法得到了系统可能产生混沌运动的条件。