温度场中桥面矩形薄板的主共振—主参数共振

PRIMARY RESONANCE AND PRIMARY PARAMETRIC RESONANCE OF A DECK THIN RECTANGULAR PLATE IN TEMPERATURE FIELD

为了研究温度场中桥面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、激励等对系统主共振—主参数共振的影响。指出系统主共振—主参数共振幅频响应曲线具有双峰特点并呈M形状。

In order to study the primary resonance and primary parametric resonance of a rectangular deck plate subject to harmonic disturbances in temperature field, by applying elastic theory, a nonlinear dynamical equation in partial differential form for the plate is established first. Then the nonlinear vibration equation in ordinary differential form is obtained based on Galerkin＇ s method. By means of the method of multiple scales for nonlinear vibrations analysis, the approximation solution of primary resonance and primary parametric resonance of the system is acquired. Numerical analysis of the influence of temperature and excitations on the system is carried out. The results show that amplitude frequency response curve of primary resonance and primary paremetric resonance has double peaks in the form of M.