温度场中非线性弹性地基上矩形薄板的3次超谐共振

3rd Super Harmonic Resonance 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3次超谐共振问题,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3次超谐共振的近似解,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3次超谐共振的影响.发现随着阻尼的增加,幅频响应曲线的振幅减小;随着温度系数T1的增加,共振曲线的振幅增大;随着温度系数T0的增加,共振曲线的振幅减小.图8,参13.

Applying elastic theory, nonlinear dynamical equation of the system was established. Nonlinear vibration equation was obtained based on Galerkin＇s method. By means of the method of multiple scales for nonlinear vibrations the approximation solution of 3rd super harmonic resonance of the system was acquired. Numerical analysis of the influence of temperature, foundation eoeflqeient, damping, geometric parameter, and excitation on the system was carried out. It is pointed out that with the increasing of damping, the amplitude reduces, with the increasing of temperature coefficient T0, the amplitude increases, with the increasing of temperature eoefficient To, the amplitude reduces.