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By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation
method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions
can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate
theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons
between the three theories are made.
The project is supported by the National Natural Science Foundation of China (No. 19872060). 相似文献
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横观各向同性介质中弹性波的吸收边界条件 总被引:2,自引:0,他引:2
在数值求解固体中的弹性波动问题时,常需引入吸收边界条件来限制大范围或无边界的求解区域,使数值计算得以顺利进行。本文通过合成简单的一阶偏微分算子,给出了横观各向同性介质中弹性波的吸收边界条件,其中每个单一的算子均可完全吸收沿某一角度出射的平面波。文中还基于弹性波的势函数理论,导出了准P波和准S波在吸收边界处的反射系数公式,用以检验其吸收能力。本文所给出的吸收条件,形式简单,且算例表明吸收效果良好,因 相似文献
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横观各向同性层状场地对入射SH波的响应分析 总被引:11,自引:0,他引:11
本文采用横观各向同性层状弹性模型模拟半空间之上的层状了,推导了在SH波入射时这种场地土的动力刚度矩阵及基岩输入运动时场地呼应的计算公式,算例表明,横观各向同性层状场地与各向同性层状了频谱特性有明显的区别,应当引起重视。 相似文献
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圆截面弹性细杆的平面振动 总被引:1,自引:1,他引:0
基于Kirchhoff理论讨论圆截面弹性细杆的平面振动.以杆中心线的Frenet坐标系为参考系建立动力学方程.杆作平面运动时,其扭转振动与弯曲振动解耦.讨论任意形状杆的扭转振动和轴向受压直杆在无扭转条件下的弯曲振动,证明直杆平衡的静态Lyapunov稳定性与欧拉稳定性条件为动态稳定性的必要条件.考虑轴向力和截面转动惯性效应的影响,导出弯曲振动的固有频率. 相似文献
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非惯性参考系中弹性薄板动力系统在纵横振动相互耦合时的全局分岔及混沌性质 总被引:3,自引:0,他引:3
讨论非惯性参考系中弹性薄板动力系统1∶1内共振时的全局分岔及其混沌性质.首先对系统的奇点进行了分析,进而得到了奇点附近同宿轨的参数方程,再用Melnikov方法研究了系统的同宿轨分岔及其混沌运动.研究表明,对各种不同共振情形,系统将由同宿轨分岔过渡到混沌运动.最后用数值仿真证实了理论分析的结果. 相似文献
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Jiang Aimin Ding Haojiang 《Acta Mechanica Solida Sinica》1995,8(2):163-170
In this paper a stochastic boundary element method(SBEM)isdeveloped to analyze moderately thick plates with random material parameters andrandom thickness.Based on the Taylor series expansion,the boundary integrationequations concerning the mean and deviation of the generalized displacements arederived,respectively.It is found that the randomness of material parameters isequivalent to a random load,so the mean and covariance matrices of unknowngeneralized boundary displacements and tractions can be obtained.Furthermore,themean and covariance of generalized displacements and forces at internal points can alsobe obtained.A numerical example has been worked out with the method proposed andnecessary analysis is made for the results. 相似文献
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薄板统计分析的随机边界元法 总被引:1,自引:1,他引:1
本文建立了分析含随机材料参数的薄板弯曲问题的随机边界元法。基于Taylor级数展开技术,分别得到了位移的均值和一阶偏差的边界积分方程,发现材料参数的随机性可作为一个等效的随机荷载处理,从而得到边界位移或边界力的均值和协方差,并进一步求出内点位移和力矩的均值和协方差,最后用本文方法计算了两个算例,并对结果进行了必要的分析。 相似文献
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We study shear-horizontal (SH) waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elast... 相似文献
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基于Biot动力控制方程,运用Fourier积分变换技术,并按照混合边值条件和连续条件建立了上覆单相弹性层饱和地基上弹性基础竖向振动的对偶积分方程.利用正交多项式将对偶积分方程化简,得到了动力柔度系数随无量纲频率b0的变化关系曲线,从而得到了上覆单相弹性层饱和地基上弹性基础的竖向振动规律.数值分析结果表明,对于弹性基础,当弹性基础的挠曲刚度较大时,发现弹性基础的竖向振动特性与刚性基础的类同,可忽略挠曲刚度对竖向振动的影响,且当无量纲频率较小的时候,动力柔度系数Cv随着无量纲频率b0的变化而发生显著的变化,但当无量纲频率b0较大的时候,动力柔度系数Cv受无量纲频率的影响较小,甚至基本上不受影响.当弹性基础的挠曲刚度较小时,随着挠曲刚度的减小,弹性基础的竖向振动将发生显著的变化,动力柔度系数Cv的实部和虚部的绝对值均变大. 相似文献
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含孔平板弹性波散射问题的复变函数方法 总被引:1,自引:0,他引:1
本文采用平板弯曲波动理论及复变函数方法,对平板开孔弹性波的散射及动应力集中问题进行了分析研究,得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术,就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例,本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果,并对其进行了讨论。 相似文献
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基于遗传算法及一阶剪切理论, 提出一种弹性地基上加肋板肋条位置优化的无网格方法. 首先, 通过一系列点来离散平板及肋条, 并用弹簧模拟弹性地基, 从而得到加肋板的无网格模型; 其次, 基于一阶剪切理论及移动最小二乘近似原理导出位移场, 求出弹性地基加肋板总势能; 再次, 根据哈密顿原理导出结构的弯曲控制方程, 并通过完全转换法处理边界条件; 最后, 引入遗传算法和改进遗传算法, 以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数, 对肋条位置进行优化达到地基板控制点挠度最小的目的. 以不同参数、载荷布置形式的弹性地基加肋板为例, 与ABAQUS有限元结果及文献解进行比较. 研究表明, 采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题, 结果易收敛, 同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置, 后者计算效率相对较高, 只进行了三次迭代便可获得稳定的最优解, 此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵, 又避免了网格重构. 相似文献
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This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation.Governing equations are obtained based on the first order shear deformation theory(FSDT) with the assumption that the mechanical properties of plate materials vary continuously in the thickness direction.A semi-analytical approach named differential transform method is adopted to transform the differential governing equations into algebraic recurrence equations.And eigenvalue equation for free vibration analysis is solved for arbitrary boundary conditions.Comparison between the obtained results and the results from analytical method confirms an excellent accuracy of the present approach.Afterwards,comprehensive studies on the FG plates rested on elastic foundation are presented.The effects of parameters,such as thickness-to-radius,material distribution,foundation stiffness parameters,different combinations of constraints at edges on the frequency,mode shape and modal stress are also investigated. 相似文献
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首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程,得到传递矩阵.进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题. 相似文献
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We design an artificial boundary condition for the steady incompressible Navier–Stokes equations in streamfunction–vorticity formulation in a flat channel with slip boundary conditions on the wall. The new boundary condition is derived from the Oseen equations and the method of lines. A numerical experiment for the non-linear Navier–Stokes equations is presented. The artificial boundary condition is compared with Dirichlet and Neumann boundary conditions for the flow past a rectangular cylinder in a flat channel. The numerical results show that our boundary condition is more accurate. 相似文献