Winkler地基上有限长梁的组合共振响应分析

Combination resonance of finite-length beam on Winkler foundation

基于Winkler地基模型及Euler-Bernoulli梁理论,建立了两个横向激励共同作用下Winkler地基上有限长梁的组合共振模型,运用Galerkin方法和多尺度方法求得组合共振幅频响应方程,进而研究地基刚度、弹性模量、黏滞阻尼、外激励幅值等主要参数对其幅频响应曲线的影响。研究结果表明:增大地基刚度、弹性模量、黏滞阻尼或减小外激励幅值均可减小梁的响应幅值。黏滞阻尼的变化对影响的共振区域并无影响。

In this paper, based on Winkler foundation model and Euler-Bernoulli beam theory,the combination resonance model of the finitelength beam on Winkler foundation under two excitation forces is built. Then, amplitude-frequcncy response equation is derived by using Galerkin method and multi-scale method. Finally, various amplitude-frequency response curves are given to show the effect of kinds of parameters on response amplitude, such asstiffness coefficient of foundation, modulus of elasticity, damping coefficient, excitation amplitude and so on. The numerical results show that the amplitude of vibration decreases as the strength of stiffness coefficient of foundation,modulus of elasticity or damping coefficient increases. Nevertheless, decreasing the excitation amplitude will decrease the vibration amplitude of the beam. In addition, damping coefficient has little effect on the resonance field.