弹性地基不可伸长梁的3次超谐共振响应分析

基于建立的弹性地基不可伸长梁的非线性动力学模型,针对横向简谐激励下弹性地基梁的3次超谐共振响应进行研究,分析了主要参数对其非线性动力学特性的影响.利用多尺度方法,求得弹性地基不可伸长梁的3次超谐共振幅频响应方程,进而得到梁的幅频响应曲线并分析了弹性地基模型、Winkler参数、外激励幅值及边界条件等对梁非线性动力响应的影响.结果表明:三参数模型中第二弹性层促进梁动力响应软弹簧特性的发展,且该模型强化梁动力响应的非线性特性;外激励幅值对梁3次超谐共振响应的动力学特性有一定影响,引起骨架曲线初始偏移量的改变.

Analysis of the Third Superharmonic Resonance of Inextensional Beams on Elastic Foundation

Based on the nonlinear dynamics model of an inextensional beam on elastic foundation,the 3 " superharmonic resonance of the beam subjected to the lateral harmonic excitation was investigated,and the effects of main parameters on the dynamic characteristic of the beam is analyzed.Applying the method of multiple scales,the frequency-response equation of the 3" superharmonic resonance of the beam was obtained.Moreover,the frequency-response curves of the beam were drawn,and the effects of the foundation models,Winkler parameter,excitation amplitude and boundary conditions on the dynamic response of the beam were studied.The numerical results showed that the second elastic layer included in the three-parameter foundation model promoted the increase of the softening characteristic of the dynamic response,and this foundation model enhanced the nonlinear characteristic of the beam.The excitation amplitude had a certain influence on the dynamic characteristic of the 3~(rd) superharmonic resonance of the beam,which causes the change of the initial drift of the backbone curve.