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An improved separation-of-variable method for the free vibration of orthotropic rectangular thin plates

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摘要

A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567-74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh's variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling.
机译：通过本作者和同事提出了一种可变的方法，通过本作者和同官员（兴yf，刘B.薄的正交矩形板的自由振动新的精确解决方案。Compos Struct 2009; 89：567-74），但这种传统的可变方法是无法自由边界条件。因此，这项工作是改善传统的可变方法，使其能够处理自由边界条件。这种新方法称为改进的可变分离方法，其中直接解决了特征差分控制方程，并且自由边界条件也具有可分离的形式，其利用瑞利的变分原理实现。此外，空间特征值与时间特征值之间的关系非常简洁。对于没有自由边缘的板，所提出的方法减少了传统的可变方法。数值实验验证改进的方法。处理自由边缘条件的本技术是针对特征值问题的一般方法，例如自由振动和特征。

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