简谐荷载作用下弹性地基上不可伸长梁的2次超谐共振响应研究  

Study on second super-harmonic resonance of an inextensional beam on elastic foundation under harmonic lateral load

作　　者：马建军[1] 刘丰军[1] 谢镭[1] 高笑娟[1] 

机构地区：[1]河南科技大学土木工程学院,洛阳471023

出　　处：《应用力学学报》2016年第1期80-85,182,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11502072;51474095);河南省教育厅科学技术研究重点项目(14A410003);河南科技大学科研创新能力培育基金(2014ZCX005)

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,利用梁的量纲归一化运动方程和多尺度方法求得梁2次超谐共振的幅频响应方程和位移的二次近似解。进而,运用梁的幅频响应曲线对其超谐共振响应特性进行研究,同时分析了弹性地基模型、Winkler参数、外激励幅值、边界条件等对该共振响应的影响效应。结果表明:弹性地基模型中剪切参数的引入增大了梁2次超谐共振响应的幅值和多值区域;弹性地基Winkler参数的增加会抑制系统的共振响应,但同时会增加系统动力响应的软弹簧特性;在外激励幅值较小的情况下,系统共振响应未展现出明显的非线性特征;边界约束对弹性地基剪切参数作用于梁2次超谐共振响应的效应有显著影响,可在一定程度上改变系统响应幅值及多值区域。Based on the refined nonlinear dynamics model of an inextensional beam on elastic foundation, employing the nondimensional motion equation of the beam and the method of multiple scales, the frequency-response equation and the second-order approximate solution of the second super-harmonic resonance of the beam are obtained. Then, the nonlinear response of super-harmonic resonance of the beam is examined by means of the frequency-response curves. Meanwhile, the effects of foundation models, Winkler parameter, excitation amplitude and boundary conditions on the second super-harmonic resonance of the beam are explored. The numerical results show that, when the shear parameter is introduced in the elastic foundation model, the value of amplitude and multi-value region of the second super-harmonic resonance of the beam will increase. The boundary conditions related to the shear parameter influence significantly the second super-harmonic resonance of the beam, to a certain extent, which change the amplitude and multi-value area of the system. With the increase of Winkler parameter, the resonance response of the beam may be suppressed, and significantly increase the softening behavior of the dynamic response of the beam at the same time. Moreover, it should also be noted that the nonlinear phenomena may not be observed in the second super-harmonic resonance of the beam, under the low excitation amplitude.

关 键 词：弹性地基 不可伸长梁 非线性振动 多尺度方法 2次超谐共振 

分 类 号：TU348[建筑科学—结构工程] O322[理学—一般力学与力学基础]