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横向荷载作用下Winkler地基上有限长梁3次超谐共振分析
引用本文:马建军,王连华,刘齐建.横向荷载作用下Winkler地基上有限长梁3次超谐共振分析[J].应用力学学报,2012,29(2):177-181,240.
作者姓名:马建军  王连华  刘齐建
作者单位:湖南大学土木工程学院,长沙,410082
基金项目:国家自然科学基金(50808075;10972073;11032004);湖南省科技计划(2010FJ4145)
摘    要: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。

关 键 词:Winkler模型  Euler-Bernoulli梁  非线性振动  3次超谐共振  参数分析

Third super-harmonic resonance of finite-length beams on the winkler foundation under lateral load
Ma Jianjun Wang Lianhua Liu Qijian.Third super-harmonic resonance of finite-length beams on the winkler foundation under lateral load[J].Chinese Journal of Applied Mechanics,2012,29(2):177-181,240.
Authors:Ma Jianjun Wang Lianhua Liu Qijian
Institution:Ma Jianjun Wang Lianhua Liu Qijian(College of Civil Engineering,Hunan University,410082,Changsha,China)
Abstract:The third super-harmonic resonance of finite-length beams on the Winkler foundation is investigated in this paper.Based on the Winkler foundation model and the Euler-Bernoulli beam theory,the nonlinear motion equation of the finite-length beam on an elastic foundation is obtained.The approximate solution of the finite-length beam for the case of the third super-harmonic resonance is obtained by using the Galerkin method and the multi-scale method.To illustrate the characteristic of the third super-harmonic resonance,the effects of the slenderness ratio,modulus of elasticity,stiffness coefficient of foundation,damp coefficient and beam density on the frequency-response curves of the finite-length beam on the Winkler foundation are studied.The effect of the third super-harmonic resonance on the actual dynamic response of this system is analyzed by contrasting with the non-resonant situation.The numerical results show that the system’s third super-harmonic resonance including delay and jumping phenomena;the increase of damping or stiffness coefficient of foundation may suppress the third super-harmonic resonance;the third super-harmonic resonance may enlarge the displacement and acceleration of the stationary response.
Keywords:Winkler model  Euler-Bernoulli beam  nonlinear vibration  third super-harmonic resonance  parameter analysis  
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