水平地震激发的等截面立柱的非线性动力响应  

NONLINEAR DYNAMIC RESSPONSE OF COLUMNS SUBJECTED TO HORIZONTAL SEISMIC EXCITATION

作　　者：范家参[1] 范磊 

机构地区：[1]云南工业大学建筑工程系,昆明650051 [2]深圳海神置业有限公司工程部,深圳518000

出　　处：《工程力学》1999年第1期128-133,共6页Engineering Mechanics

基　　金：云南省教委1997年科研基金

摘　　要：本文采用非线性Ｒｎｙｌｅｉｇｈ阻尼来描述立柱在地震响应初期有激发而加速运动，至最大速度后开始衰减至停止运动，取适合所有边界条件的振型函数代入由非线性偏微分方程构成的控制方程，当立柱两端铰支时，其振型函数的系数为时间自变量的函数构成的富氏级数，应用富氏级数的正交性，此控制方程化为一无穷非线性常微分方程组，用逐次渐近法求解即每次只取一个未知函数，得到一个非齐次ＶａｎｄｅｒＰｏｌ方程，从而给出其头两次的渐近解，并给出其数值结果和讨论了解的分岔的意义。In this study, the nonlinear Rayleigh damping is adopted which can depict the excitingduring the initial stage of seismic response, and the decaying after the motion velocity reaches itsmaximum value in the neat stage. Since the governing equation is a nonlinear PDE, the vibrationpattern function is assumed to fulfill all the boundary conditions as a Fourier series withcoefficients to be functions of time variable only. By applying the orthogonality of Fourier series,this nonlinear PDE is deduced to be an infinite system of nonlinear ODEs. By successiveapproximation method, only one unknown function is taken in each computational process whichis a nonhomogeneous van der Pol equation, and its first tWo asymptotic solutions are obtained.Finally, numerical results are given to show the bifurcation of the solutions.

关 键 词：水平地震激发 等截面 柱 非线性动力响应 

分 类 号：TU311.3[建筑科学—结构工程]