摘要
研究了一类参数激励和外激励联合作用下四边简支薄板在1:1内共振下的周期解分叉.首先,根据von Karman方程推导出四边简支薄板的运动控制方程,利用Galerkin方法得到参数激励和外激励联合作用下的两个自由度的运动方程.然后,通过引入周期变换和相应的Poincaré映射推广了次谐Melnikov方法.最后,对系统进行数值模拟验证了理论的正确性.
The bifurcations of periodic solutions for a parametrically and externally excited rectangular thin plate with 1 ： 1 internal resonance were investigated. First, the equations of motion with two-degree-of- freedom of the rectangular thin plate were derived from the von Karman equation and Galerkin＇s method. Then, based on periodic transformations and Poincare map, the subharmonic Melnikov function was improved to analyze the periodic solutions of four-dimensional non-autonomous systems. Numerical simulations verified the analytical predictions.
出处
《动力学与控制学报》
2013年第2期149-152,共4页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(11072008
10732020)~~
关键词
周期解
次谐Melnikov函数
周期变换
薄板
periodic solution
subharmonic Melnikov function
periodic transformation
rectangular thinplate
