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Free vibration analysis of laminated composite plates by the meshless natural neighbour Petrov-Galerkin method

DOI：

 作者 单位 E-mail 陈莘莘 华东交通大学土木建筑学院 chenshenshen@tsinghua.org.cn

基于一阶剪切变形理论，本文提出了复合材料层合板自由振动分析的无网格自然邻接点Petrov-Galerkin法。计算时在层合板中面上仅需要布置一系列的离散节点，并利用这些节点构建插值函数。在板中面上的局部多边形子域上采用加权余量法建立层合板自由振动的离散化控制方程，并且这些子域可由Delaunay三角形方便地创建。自然邻接点插值构造的试函数具有Kronecker delta函数性质，可以直接准确地施加本质边界条件。采用本文给出的方法，对不同边界条件、不同跨厚比、不同材料参数和铺设角度的层合板进行自由振动分析，均得到满意的结果。数值算例结果表明，所提出的方法求解层合板的自由振动问题是行之有效的。

Based on the first-order shear deformation theory, a meshless natural neighbour Petrov-Galerkin method has been developed for free vibration analysis of laminated composite plates in this paper. In the computation, only a set of randomly distributed nodes over the middle plane of the considered plate are required and the interpolation functions are constructed through these nodes. The discretized governing equations for free vibration analysis of laminated composite plates are derived by using the weighted residual method over local polygonal sub-domains in the mean surface of the plate. These polygonal sub-domains can be conveniently constructed with Delaunay tessellations. Because the constructed shape functions from the natural neighbour interpolation possess the Kronecker delta function property, the essential boundary conditions can be imposed directly and accurately. The natural frequencies computed by the present method for the laminated composite plates with various boundary conditions, side-to-thickness ratios, material parameters and laying angles are all well, which demonstrate that the proposed method for free vibration analysis of laminated composite plates is effective.
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