摘要
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.
The paper establishs the dispiacementai 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 disptacemental fundamentaI 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.
出处
《西安建筑科技大学学报(自然科学版)》
CSCD
北大核心
2009年第6期780-784,共5页
Journal of Xi'an University of Architecture & Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(50878181)
关键词
横向剪切变形
厚板
振动
位移型基本方程
简支矩形板
双重三角级数
transvers shearing deformation
thick plates
vibration
displacemental fundamental equations
simply supported rectangular plates
double trigonometric series