论文部分内容阅读
基于Winkler地基模型和Euler-Bernoulli梁理论,建立了Winkler地基上有限长梁的非线性运动方程。运用Galerkin方法对运动方程进行一阶模态截断,得到了离散的非线性振动方程,然后利用多尺度法求得了该系统3次超谐共振的幅频响应方程及其位移的一阶近似解。为揭示弹性地基上有限长梁的3次超谐共振响应的特性,分别分析了长细比、弹性模量、基床系数、阻尼、密度等主要参数对该系统3次超谐共振幅频响应曲线的影响,并通过与非共振硬激励情况的对比分析了3次超谐共振对系统实际动力反应的影响。研究结果表明:3次超谐共振响应曲线有跳跃和滞后现象;增大阻尼和基床系数均对3次超谐共振的发生有抑制作用;增大外激励幅值,系统3次超谐共振区域增大;3次超谐共振将增大系统的稳态动力响应幅值和加速度。
Based on the Winkler foundation model and the Euler-Bernoulli beam theory, a nonlinear motion equation of a finite length beam on the Winkler foundation is established. First-order modal truncation of the equations of motion was performed using the Galerkin method. Discrete nonlinear vibration equations were obtained. The amplitude-frequency response equation of the third-order superharmonic resonance of the system and the first-order approximate solution of the displacement were obtained by using the multi-scale method. In order to reveal the characteristics of the third superharmonic resonance of a finite length beam on an elastic foundation, the effects of the main parameters of slenderness ratio, elastic modulus, bed coefficient, damping and density on the superharmonic resonance frequency response The influence of the third superharmonic resonance on the actual dynamic response of the system was analyzed by comparison with the non-resonant hard excitation. The results show that the third superharmonic resonance response curve has the phenomenon of jump and hysteresis. Increasing the damping and the bed coefficient all inhibit the occurrence of the third superharmonic resonance. Increasing the amplitude of the external excitation, the third superharmonic resonance of the system Area increases; 3 super-harmonic resonance will increase the system steady-state dynamic response amplitude and acceleration.