Winkler地基梁在温度场中受简谐激励作用下的主共振和主参数共振分析

ANALYSIS ON PRIMARY RESONANT AND PRIMARY PARAMETRIC RESONANT OF HARMONICALLY DRIVEN ON WINKLER FOUNDATION IN TEMPERATURE FIELD

研究在温度场中受简谐激励作用的Winkler地基梁的响应问题。为考虑温度场中Winkler地基上受简谐激励梁的响应问题,应用弹性理论和伽辽金方法,导出温度场Winkler地基上受横向、纵向激励的梁的非线性动力学方程。通过多尺度法得到系统主共振和主参数共振的近似解,并进行数值计算,分析各种参数对共振系统的影响。

The response problem of a harmonically driven beam with respect to the influence of Winkler foundation in temperature field is considered. By applying elastic theory and Galerkin＇s method, the nonlinear dynamical equation is derived for a beam on Winkler foundation in temperature field, driven by vertical and horizontal harmonic excitations. By the method of multiple scales, the first approximation solutions for primary resonance and primary parametric resonance of the system are obtained. Then, it is followed by a detailed numerical analysis on influence of all kinds of parameters on the resonant responses of the system.