【摘要】 基于已建立的弹性地基上不可伸长梁的非线性动力学模型,本文针对简谐横向荷载作用下梁的1/2次亚谐共振响应进行研究。利用弹性地基梁的非线性运动方程和多尺度方法,求得梁1/2次亚谐共振响应的二次近似解。进而,运用幅频响应曲线对梁的亚谐共振响应进行研究,并分析了边界条件、地基模型、Winkler参数等对梁非线性共振响应的影响。结果表明:三参数地基模型中弹性层的引入对其支承梁的亚谐共振响应影响显著;临界激励幅值决定了弹性地基梁1/2次亚谐共振响应非平凡解的存在性;梁端约束条件在一定程上改变了Winkler参数对梁非线性动力响应的作用效应。更多还原

【Abstract】 In this paper,the 1 /2 sub-harmonic resonance of the beam subjected to a harmonic lateral excitation is investigated. Based on the nonlinear dynamics model of an inextensional beam on elastic foundation,the frequencyresponse equation and the second-order approximate solution of the 1 /2 sub-harmonic resonance are obtained,employed the nonlinear motion equation of the beam and the method of multiple scales. Then,by means of the frequency-response curves,the effects of boundary conditions,foundation models and Winkler parameter on the 1 /2sub-harmonic resonances of the beam are analyzed. The results show that the effect of the spring layer included in Kerr model on the sub-harmonic resonance of the beam is significant. Obviously,the existence of the nontrivial solutions of the 1 /2 sub-harmonic resonance depended on the critical excitation amplitude. Moreover,the boundary condition changed the influence of Winkler parameter on the nonlinear response of the beam,in a sense.更多还原