受简谐激励弹性地基不可伸长梁的主共振响应

Primary Resonance of Inextensional Beam on Elastic Foundation Subjected to Harmonic Excitation

基于弹性地基不可伸长梁的非线性动力学模型,对简谐激励下梁的主共振响应进行了研究。利用多尺度方法,求得弹性地基不可伸长梁的主共振幅频响应方程及其横向位移的二次近似表达式,进而运用梁主共振的幅频响应曲线,分析了弹性地基模型、Winkler参数、外激励幅值和边界条件等对梁非线性动力响应的影响。数值分析结果表明:Winkler参数在弹性地基梁的主共振响应中起控制性作用,而剪切参数的引入有利于更精确地展现弹性地基梁的非线性动力学特性,外激励幅值对弹性地基梁的动力学特性基本无影响。

Based on the nonlinear dynamics model of inextensional beam on elastic foundation,the primary resonance of the beam subjected to harmonic excitation was investigated. Through the method of multiple scales,the frequency-response equation and the second-order approximate solution of the primary resonance of the beam were obtained. Then,by means of the frequency-response curve,the effects of foundation model,Winkler parameter,excitation amplitude and boundary condition on the primary resonance of the beam were analyzed. The numerical results show that the Winkler parameter dominates the primary resonance of the beam,and the introduction of shear parameter in the foundation model may be conducive to accurately reveal the nonlinear dynamic nature of the beam. However,the dynamic nature of the primary resonance of the elastic foundation beam is independent of the excitation amplitude.