Winkler地基上材料非线性矩形薄板主参数共振-主共振研究

研究Winkler地基上材料非线性矩形薄板的参数共振-主共振问题。建立Winkler地基上材料非线性矩形薄板的动力学方程。利用Galerkin方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足主参数共振-主共振条件的近似解，并进行数值计算。分析激励、调谐值、阻尼系数、非线性参数、几何参数对共振响应曲线的影响。

Study on primary parametric resonance with primary resonance of thin rectangular plate on Winkler foundation considering material nonlinearity

In order to study on primary parametric resonance with primary resonance of thin rectangular plate on Winkler foundation subjected to harmonic excitation considering material nonlinearity, its nonlinear dynamical equation is established and transformed to nonlinear vibration equation based on Galerkin’s method. By using the method of multiple scales for nonlinear vibration, the approximate solution of primary parametric resonance and primary resonance of the system is acquired. Numerical computation is carried out to analyze the influences of excitation, detuning, damping, nonlinear parameters and geometric parameters on the system.