Arbitrary precision frequencies of a free rectangular thin plate
Arbitrary precision frequencies of a free rectangular thin plate
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DOI：
10.1006/jsvi.1999.2629
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发表时间：
2000-02
影响因子：
4.7
通讯作者：
C. Filipich;M. B. Rosales
中科院分区：
文献类型：
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作者：
C. Filipich;M. B. Rosales
本文用作者发展的整体单元法(WEM)求出了四边无约束矩形薄板的任意精度频率。WEM包括提出一个适当的泛函和一个表示板横向位移w(x，y)的序列。这样的序列是由属于L2中的完备集的函数的线性组合组成的。序列，而不是每个坐标函数，需要满足基本或几何条件。序列的生成是系统的，不需要对板的经典固有模式进行分析。具体地说，在本分析中使用了先验属于域中完备集的三角函数。涉及非常简单和的求解方程源于泛函的最小化。WEM是基于证明问题的特征值的最终正确性和本质函数的一致收敛的定理。据作者所知，这个问题没有经典解。
Abstract A variational method developed by the authors and named whole element method (WEM) is used to find the arbitrary precision frequencies of a rectangular thin plate (within the Germain–Lagrange theory) having its four borders free of constraint. WEM consists is proposing an adequate functional and a sequence representing the plate transversal displacementw (x, y). Such a sequence is made of a linear combination of functions belonging to a complete set inL2 . The sequence, and not each co-ordinate function, is required to satisfy the essential or geometric conditions. The sequence generation is systematic and no analysis of the classical natural modes of the plate is needed. In particular, trigonometric functions which a priori belong to a complete set in the domain are used in the present analysis. The solving equations involving very simple sums arise from the minimization of the functional. WEM is based on theorems which show the ultimate exactness of the eigenvalues and the uniform convergence of the essential functions of the problem. To the authors knowledge this problem has no classical solution.