弹性地基上加热梁受简谐激励的主共振响应

The main resonance response of a heating beam on elastic foundation under simple harmonic energizing

基于Hamilton原理,得到了弹性地基上加热梁受简谐激励作用的非线性强迫振动控制方程。运用Kantorovich平均法将非线性偏微分方程转化成一组常微分方程,考虑不可移夹紧边界条件,采用打靶法得到了主共振的数值结果。考察了不同参数对主共振响应的影响。

Based on the Hamilton principle,the governing equations of the nonlinear forced vibration of a heated beam on an elestic foundation under simple harmonic energization were obtained in this paper and the nonlinear partial differential equations were converted into a set of ordinary ones by using Kantorovich average methed.Considering immovable clamped boundary conditions,the numerical results of the main resonance were obtained by employing a shooting method.At last,the influence of different parameters on the main resonance is examined too in details.