考虑横向剪切变形厚板弯曲的位移型方程及简支矩形板的一般解

基于考虑横向剪切变形厚板的几何方程、本构关系及平衡方程,建立关于一个中面位移和两个中面转角为独立变量的厚板振动的位移型基本方程.该方程退化为薄板振动的位移性方程的正确性说明推导过程的正确性及一般性.文中将双重三角级数作为广义坐标,应用MATLAB工具对简支矩形板的双重三角级数进行求解,求解过程简便,且挠度的收敛性较快.

Displacement fundamental equations of the thick plates bending and the general solution to simply supported rectangular plates by transvers shearing defomation

The paper establishs the displacemental fundamental equations of the vibration with middle-thick plates by transvers shearing deformation, based on the geometric equations, inner fundamental relations and mechanical relations, concerning three independent variables, i.e. one middle surface displacements and two middle surface corners.The displacemental fundamental equations degenerate to the displacemental fundamental equations of thin plates vibration, which demonstrate the generality of derived equations. Using double trigonometric series as generalized coordinates ,and analyzing the double trigonometric series of simply supported rectangular plates based on MATLAB,the simple method can be applied to bending of thick plates in elastic foundations which is uniform in calculation and convenient for application,and convergence rate of deflections is high.