Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method

This paper describes a method for free vibration analysis of rectangular plates with any thicknesses, which range from thin, moderately thick to very thick plates. It utilises admissible functions comprising the Chebyshev polynomials multiplied by a boundary function. The analysis is based on a linear, small-strain, three-dimensional elasticity theory. The proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions. A very simple and general programme has been compiled for the purpose. For a plate with geometric symmetry, the vibration modes can be classified into symmetric and antisymmetric ones in that direction. In such a case, the computational cost can be greatly reduced while maintaining the same level of accuracy. Convergence studies and comparison have been carried out taking square plates with four simply-supported edges as examples. It is shown that the present method enables rapid convergence, stable numerical operation and very high computational accuracy. Parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail, with respect to different thickness-side ratios, aspect ratios and Poisson’s ratios. These results may serve as benchmark solutions for validating approximate two-dimensional theories and new computational techniques in future.     

广义协调元的变分基础及几何不变性

本文根据修正的势能原理推出了广义协调元列式。从而为广义协调元提供了一种变分依据。同时讨论了广义协调元的几何不变性,即单元与其节点号编序的相关性问题。在此基础上推导了一个任意四边形薄板弯曲单元,数值结果表明该单元能保证收敛,具有与单元节点号编序无关性,与现有的同类单元相比,具有较高的精度。     

自由正交异性矩形厚板的动态稳定

对在一条边上作用着均匀分布的非保守跟随力的四边自由正交异性矩形厚板的动态稳定进行了分析，通过把位移和剪力展成重傅立叶级数解，把微分方程简化成了代数方程。计算表明厚度的微小变化会引起颤振载荷明显的减小。这个明显减小是因为存在剪切变形。     

On consistent plate theories

Summary  Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction. Received 10 January 2002; accepted for publication 16 April 2002     

变温环境对压电圆板频率主动控制的影响

定量研究了具有几何非线性热弹性压电圆板的频率压电控制特征，考察了环境温度改变引起的热弹性效应和非线性大振幅振动对其控制特性的影响等．研究结果表明：环境温度的变化使压电控制的固有频率受到影响，而在压电电压较大时，振幅对振动频率影响不大．     

簧片阀三种力学模型的建立及比较

一端固定一端自由的簧片阀片按其运动特征及不同的简化条件，可视为单质点力学系统，连续梁力学系统及平板振动力学系统，并分别给出其数学模型，建立相应的仿真软件系统。最后以管状直流阀为例比较了这三种力学模型的仿真结果，给出了它们的应用场合     

Design of a Laminated Plate Possessing the Required Stiffnesses Using the Minimum Number of Materials and Layers

This paper deals with the problem of the design of a laminated plate possessing the required set of stiffnesses under the condition of using the minimum number of layers and minimum number of materials. It is shown that the minimum number of layers is not more than four and the minimum number of materials is not more than two. We consider the case when three types of stiffness (bending, in-plane and out-of-plane) are prescribed and the case when two types of stiffness (physical bending and in-plane) are prescribed. It is proved that for both cases the sets of the possible values of physical stiffnesses are the same but the sets of designs can be different. A design algorithm is developed.      

单层5A06铝合金板高速撞击实验研究

采用非火药驱动二级轻气炮发射球形弹丸,对单层5A06铝合金板进行高速撞击实验研究,从而模拟空间碎片对航天器防护结构的高速撞击作用。实验得到了该铝合金板在不同的速度区间的损伤模式。结果表明,弹丸撞击速度一定时,弹坑深度和弹坑直径均与弹丸直径呈线性关系。当撞击速度在4km/s至5km/s时,靶板上的弹坑深度和弹坑直径随撞击速度的增大而减小,在其它速度范围内,弹坑深度和弹坑直径随撞击速度的增大而增大。通过固定弹丸直径,变化撞击速度,寻找临界撞击速度的方法获得了该铝合金板在弹丸撞击速度为1.0km/s至4.2km/s时的撞击极限曲线,并将实验弹坑深度与由Cour-Palais方程得到的预测弹坑深度进行了比较,实验弹坑深度大于预测值。     

Tension of a nonthin transversely isotropic plate with a noncircular cylindrical cavity

The three-dimensional stress state of a transversely isotropic plate with a nearly circular cylindrical cavity is examined. The cavity surface is subject to normal and tangential stresses and the plate is subject at infinity to tensile and shear forces. The problem is solved by expanding unknown functions into Fourier-Legendre series in the thickness coordinate and using the boundary-shape perturbation method. The equations and recurrence formulas needed to solve the problem in an arbitrary approximation are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 101–113, November 2006.     

Unsteady Free Convection along an Infinite Vertical Flat Plate Embedded in a Stably Stratified Fluid-Saturated Porous Medium

The problem of unsteady free convection heat transfer from a one-dimensional (parallel) flow along an infinite vertical flat plate embedded in a thermally stratified fluid-saturated porous medium is considered. Flows are induced by a sudden change in the arbitrary temporal plate temperature. By a formal reduction of the corresponding boundary value problems to well-known Fourier heat conduction problems, analytical solutions of the Darcy and energy equations are obtained. Several special cases are discussed in detail.