Refined theory for vibration of thick plates with the lateral and tangential loads

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• 作者：Chao Hu ; Hanxiong Hu ; Xiaowei Zhang ; Fai Ma
• 关键词：Refined dynamic theory of plates ; Spectral decomposition of operators ; Typical low ; dimensional structure ; Dynamic equations of plate bending and stretching ; Lateral and tangential loads
• 刊名：Archive of Applied Mechanics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：87
• 期：3
• 页码：439-455
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics; Classical Mechanics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0681
• 卷排序：87

文摘

Based on the three-dimensional elastodynamics, without using the classical assumption, an operator method is established to refine the dynamic theory of an infinite homogenous isotropic plate by using the spectral decomposition of operators. By this method, the governing equations of the bending and stretching vibrations of plates with the lateral and tangential loads on the surface are derived from the Boussinesq–Galerkin solution of the three-dimensional elasticity, respectively. To effectively deduce the governing equations, a complex differential operator is introduced. Dispersion relations based on the refined equations and the three-dimensional elastodynamics are compared to verify the refined theory of plates. It is shown that the dispersion relation of the refined theory of plates agrees more with the result based on the three-dimensional elastodynamics than Mindlin’s theory. Therefore, the refined equations are accurate that can be used to solve the vibration of thick plates and determine high-order vibration modes of plates. The applicable conditions of the refined plate theory are analyzed and discussed.