弹性地基上多孔功能梯度材料矩形板的自由振动与临界屈曲载荷分析

多孔功能梯度材料(FGM)构件的特性与孔隙率和孔隙分布形式有密切关系。本文基于经典板理论,考虑不同孔隙分布形式时修正的混合率模型,研究Winkler弹性地基上四边受压多孔FGM矩形板的自由振动与临界屈曲载荷特性。首先利用Hamilton原理和物理中面的定义推导Winkler弹性地基上四边受压多孔FGM矩形板自由振动的控制微分方程并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程和边界条件进行变换,得到计算无量纲固有频率和临界屈曲载荷的代数特征方程。将问题退化为孔隙率为零时的FGM矩形板并与已有文献进行对比以验证其有效性。最后计算并分析了梯度指数、孔隙率、地基刚度系数、长宽比、四边受压载荷及边界条件对多孔FGM矩形板无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。

Analysis of free vibrations and critical buckling loads of a porous functionally graded materials rectangular plate resting on elastic foundation

The properties of porous functionally graded materials (FGM) components are closely related to porosity and distribution form of the pores.Based on the classical plate theory,considering the modified mixing rate model with different pore distribution,the free vibration and critical buckling load of a porous FGM rectangular plate with four sides compression on Winkler elastic foundation are studied.Firstly,the Hamilton principle and the definition of the physical middle surface are used to derive the governing differential equation of the free vibration of the four-side compressed porous FGM rectangular plate on Winkler elastic foundation.Then the dimensionless form of the governing differential equation is also derived.The dimensionless governing differential equation and the boundary conditions are transformed by differential transformation method (DTM),and the algebraic characteristic equations for calculating the dimensionless natural frequencies and critical buckling loads are obtained.The problem is reduced to a FGM rectangular plate with zero porosity and compared with the existing literature to verify its effectiveness.Finally,the effects of gradient index,porosity,foundation stiffness coefficient,aspect ratio,compression load with four sides,boundary conditions on the dimensionless natural frequencies and all parameters on the dimensionless critical buckling loads of the porous FGM rectangular plate are calculated and analyzed.