Closed form solutions for free vibrations of rectangular Mindlin plates

作     者：Yufeng Xing Bo Liu The Solid Mechanics Research Center, Beihang University,100191 Beijing, China 

作者机构：The Solid Mechanics Research Center Beihang University Beijing China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2009年第25卷第5期

页      面：689-698页

核心收录：

学科分类：08[工学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China (10772014) 

主　　题：Mindlin plate Free vibration Closed form solution Separation of variable 

摘      要：A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate.