Winkler地基上有限长梁非线性自由振动  

NON-LINEAR FREE VIBRATION OF FINITE-LENGTH BEAMS ON THE WINKLER FOUNDATION

作　　者：马建军[1] 刘齐建[1] 王连华[1] 赵跃宇[1] 

机构地区：[1]湖南大学土木工程学院,长沙410082

出　　处：《工程力学》2012年第8期58-62,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(50808075;10972073;11032004);湖南省科技计划项目(2010FJ4145)

摘　　要：基于经典Winkler地基模型及Euler-Bernoulli梁理论,考虑梁的几何非线性效应,运用Newton第二定律建立了弹性地基上有限长梁的非线性运动方程。采用Galerkin方法对运动方程进行一阶模态截断,进而利用多尺度法求得了该系统自由振动的一阶近似解。揭示了两端简支梁的非线性自由振动特性,分析了弹性模量、长细比及地基刚度系数等参数对系统固有频率的影响。并通过该系统的位移时程曲线,分析了阻尼对弹性地基上梁运动特性的影响。The non-linear free vibration of a finite-length beam on the elastic foundation is investigated. Based on the Winkler foundation model and Euler-Bernoulli beam theory, the nonlinear motion equation of the finite-length beam on an elastic foundation with geometric nonlinearity is deduced based on the Newton＇s Second Law. The first-order mode truncation of the vibration function is obtained using the Galerkin method. The approximate solution of the free vibration of the finite-length beam is derived utilizing the multi-scale method to illustrate the behaviour of the non-linear free vibration. The effects of the slenderness ratio of beam, the modulus of elastic system and the stiffness of foundation on the natural frequency of the hinged-hinged beam on the Winkler foundation are analyzed. The influence of damping of the soil-beam system on the motion of the beam is also discussed.

关 键 词：WINKLER模型 Euler.Bernoulli梁 几何非线性 多尺度方法 时程曲线 

分 类 号：TU348[建筑科学—结构工程]