几何非线性效应对受迫振动索理论解的影响评估  

Evaluation of the Influence of Geometrical Nonlinearity on Theoretical Solutions of Forced Vibration Cables

作　　者：梁浩博 刘小会[1,2] 杨曙光 闵光云 伍川 LIANG Haobo;LIU Xiaohui;YANG Shuguang;MIN Guangyun;WU Chuan(School of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China;State Key Laboratory of Bridges and Tunnels in Mountainous Areas,Chongqing Jiaotong University,Chongqing 400074,China;Henan Electric Power Research Institute,Zhengzhou 450052,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074 [2]重庆交通大学省部共建山区桥梁及隧道工程国家重点实验室,重庆400074 [3]国网河南省电力公司电力科学研究院,郑州450052

出　　处：《噪声与振动控制》2021年第5期1-8,44,共9页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(51308570,51808085,51507106);重庆市研究生科研创新资助项目(CYS19240);重庆市科委基础科学与前沿技术研究资助项目(cstc2017jcyjAX0246);重庆市教委科学技术研究资助项目(KJ201600712182)。

摘　　要：为研究单跨水平拉索背景下几何非线性的强弱对Galerkin离散法适用性产生的影响,首先引入两种不同的无量纲参数,将拉索面内非线性运动方程无量纲化,运用Galerkin离散法将偏微分运动方程转化为常微分方程,利用多尺度法进行摄动求解,得到幅频响应函数,并绘制幅频响应曲线;接着应用MATLAB得出系统时间历程曲线,最后应用ABAQUS软件进行有限元模拟,将有限元解与本文方法计算得到的数值解进行对比。在通过数值模拟得到系统时间历程曲线的同时,将两种无量纲方法也进行对比。结果表明:Galerkin离散法对于几何非线性较弱的系统适用性较高。无量纲化会导致系统非线性项系数变大。两种无量纲方法随着Irvine系数的增大,所得数值解更接近。研究成果可为索的非线性振动数值求解提供依据且有助于理论的完善。The influence of the intensity of geometric nonlinearity on the applicability of Galerkin discrete method in the case of single horizontal suspension cable is studied.Two kinds of different dimensionless parameters are introduced to non-dimensionalize the nonlinear equations of motion in the cable plane,which is then transformed into an ordinary differential equation using Galerkin method.Using the multi-scale method to get its perturbation solution,the corresponding frequency response functions are derived and the amplitude-frequency response curve is plotted.Then,MATLAB code is used to obtain the time history curve of the system.Finally,ABAQUS software is used to carry out finite element simulation,and the results are compared with the numerical solutions of this method.While the time history curve of the system is obtained by numerical simulation,the two dimensionless methods are also compared mutually.The results show that the Galerkin discrete method is more suitable for the systems with weak geometric non-linearity.Dimensionless will lead to the increase of the nonlinear term coefficient of the system.The numerical solutions obtained by the two dimensionless methods are more similar with the increase of Irvine coefficient.The research results may provide a basis for the numerical solution of nonlinear vibration of cables and are helpful for the perfection of the theory.

关 键 词：振动与波 拉索 模态分析 有限元 离散法 无量纲化 

分 类 号：TM753[电气工程—电力系统及自动化]