摘要
基于von Karman薄板理论,建立了均布载荷和周边面内载荷联合作用下夹层圆板非线性振动问题的控制方程和滑动固定边界条件,给出了相应静力问题的精确解及其数值结果.基于时间模态假设和变分法,得到了空间模态的控制方程,并使用修正迭代法求解该方程,得到夹层圆板幅频-载荷特征关系.讨论了两种载荷对夹层圆板振动特性的影响规律.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.
The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condition were established by yon plate theory, and then accordingly exact solution of static load and its numerical results is given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude fi-equency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule which the two kinds of load affected the vibration character of the circular sandwich plate was investigated. When circurnjacent 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
2007年第8期967-975,共9页
Applied Mathematics and Mechanics
