摘要
基于von Kármán薄板理论,讨论了滑动固定基础上周边面内压力作用下夹层圆板的非线性振动问题,应用变分法导出了该问题的非线性特征方程和边界条件,给出了其精确静态解,并使用修正迭代法求解了该方程,导出了夹层圆板振幅和非线性振频的解析关系式.当周边面力使夹层圆板的最低固有频率为零时,就可获得临界载荷的值.
Based on yon Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circtmjacent load with the loosely clanoed boundary condition is researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.
出处
《应用数学和力学》
CSCD
北大核心
2006年第10期1243-1249,共7页
Applied Mathematics and Mechanics
关键词
夹层圆板
非线性振动
临界载荷
屈曲
幅频-载荷特征关系
sandwich plate
nonlinear vibration
critical load
buckling
amplitude frequency-load characteristic relalion
