周边夹紧圆板在横向激振力作用下的4倍超谐波共振分析

Analysis of a 4 Superharmonic Resonances of Edge-clamped Circular Plate Subjected to Transverse Excitation Load

基于von Kármán薄板理论及Hamilton原理,得到了横向周期载荷作用下周边不可移夹紧圆板轴对称非线性强迫振动运动方程组,应用Kantorovich时间平均法将运动方程组简化为非线性常微分方程组.通过打靶法得到了4倍超谐波共振数值解,并考察了静载荷、激振力力幅、激振频率以及自振振幅对超谐波共振响应的影响.

On the basis of von Karman＇s thin plate theory and Hamilton＇s law,a group of motion governing equations of a circular plate with immovably clamped edge subjected to the transverse periodical load are obtained. The governing equations are converted into a set of nonlinear ordinary differential equations by employing the Ritz-Kantorovich averaging method. A numerical solution of 4 superharmonic resonances is obtained by using the shooting method. The influences of static and dynamic loads, forced frequencies and free vibration amplitudes on the superharmonic resonances are investigated in details.