温度场中矩形地基薄板主共振系统稳定性

Dynamical Stability of Primary Resonance System of a Thin Rectangular Plate on Nonlinear Foundation in Temperature Field

为了研究温度场中非线性地基上矩形薄板受简谐激励的主共振稳定性问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程.利用稳定性理论分析主共振系统平衡点类型及稳定性.选择激励参数F作为控制参数进行数值计算.分析主共振系统时间历程和相图结果表明:随着控制参数的变化,主共振运动稳定性发生变化;随着控制参数F的增大,主共振系统的振幅增加;当控制参数F取值较小时,主共振系统存在拍振现象.

In order to study the dynamical stability of primary resonance system of a thin rectangular plate on nonlinear foundation subject to harmonic excitation in temperature field, the nonlinear dynamical equation of the system is established according to elastic theory. A nonlinear vibration equation is obtained based on Galerkin＇s method. The type of equilibrium point and the stability of the system are analyzed by means of stability theory. By using the amplitude of excitation F as the control parameter, the results of numerical analysis are as follows ： from the analyzing results of history diagram and phase diagram, the stability of the system varies with changing the control parameter of the system; the amplitude of the primary resonance system increases with the control parameter F increasing; and the amplitude of the primary resonance system exists beating phenomenon when the control parameter F is small.