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Free vibration analysis of plates using least-square-based finite difference method

机译：最小二乘有限差分法分析板的自由振动

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摘要

In this paper, we apply the two-dimensional least-square-based finite difference (LSFD) method for solving free vibration problems of isotropic, thin, arbitrarily shaped plates with simply supported and clamped edges. Using the chain rule, we show how the fourth-order derivatives of the plate governing equation can be discretized in two or three steps as well as how the boundary conditions can be implemented directly into the governing equation. By analyzing vibrating plates of various shapes and comparing the solutions obtained against existing results, we clearly demonstrate the effectiveness of LSFD as a mesh-free method for computing vibration frequencies of generally shaped plates accurately.
机译：在本文中，我们采用二维最小二乘有限差分法（LSFD）来解决各向同性，薄且任意形状的板的简单振动问题，这些板具有简单的支撑和夹紧边缘。使用链规则，我们展示了如何以两步或三步离散化板控制方程的四阶导数，以及如何将边界条件直接实现到控制方程中。通过分析各种形状的振动板并将所获得的解决方案与现有结果进行比较，我们清楚地证明了LSFD作为无网格方法准确计算一般形状的板的振动频率的有效性。

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