温度场中非线性弹性地基上矩形薄板的主共振-主参数共振

Primary Resonance and Primary Parametric Resonance of 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-主参数共振问题,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。利用非线性振动的多尺度分析方法求得系统主共振-主参数共振的近似解,并进行数值计算。分析温度、地基系数、阻尼、几何参数、激励等对系统主共振-主参数共振的影响。得到了随参数变化响应曲线的变化规律。

The primary resonance and primary parametric resonance of a thin rectangular plate on nonlinear foundation in temperature field,are discussed.By means of the method of multiple scales for nonlinear vibrations,the approximation solution of primary resonance and primary parametric resonance of the system is acquired.The numerical analysis of the influence of temperature,foundation coefficient,damping,geometric parameter,and excitation on the system is carried out.The change laws of response curve with varying parameters are obtained.