摘要
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稳定性问题,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的影响。幅频响应曲线存在跳跃现象。随着阻尼、板厚、地积系数的增加,主共振振幅减小;随着激励幅值的增加,主共振振幅增大。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。
In order to study the primary resonance system of a thin rectangular plate on nonlinear foundation subject to harmonic excitation in temperature field, the nonlinear dynamical equation of the system is derived at first by applying elastic theory, which is then reduced into a nonlinear vibration one by Galerkin＇ s method. By means of the method of multiple scales, the first order approximate solution for primary resonance of the system are obtained. Numerical methods are used to further analyze the influence of temperature, foundation coefficient, damping, geometric parameter, or excitation on the system in detail. The numerical results show that the amplitude of resonant response reduces with the increasing of damping, thickness of plate, or foundation coefficient. Specifically the response amplitude increases with the increasing of temperature coefficient T1 or amplitudes of excitation. While the response amplitude reduces with the increasing of temperature coefficient T0.
出处
《机械强度》
CAS
CSCD
北大核心
2008年第5期744-748,共5页
Journal of Mechanical Strength
关键词
温度场
非线性地基
矩形薄板
多尺度法
主共振
Temperature field
Nonlinear foundation
Thin rectangular plate
The method of multiple scales
Primaryresonance
