拉索-阻尼器系统的改进实模态分析方法  

An Improved Method to Real Modal Analysis of Cable-Damper Systems

作　　者：陈志[1] 彭文林 禹见达[1] 韩艳[2] 田静莹 Chen Zhi;Peng Wenlin;Yu Jianda;Han Yan;Tian Jingying(School of Civil Engineering,Hunan University of Science and Technology,Xiangtan411201,China;School of Civil Engineering,Changsha University of Science and Technology,Changsha410114,China)

机构地区：[1]湖南科技大学土木工程学院,湘潭411201 [2]长沙理工大学土木工程学院,长沙410114

出　　处：《动力学与控制学报》2023年第4期7-14,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(52278307);湖南省自然科学基金资助项目(2022JJ30261)。

摘　　要：阻尼减振是拉索振动控制的主要措施,目前拉索-阻尼器系统的主要分析方法为复模态法.虽然采用复模态法可以精确分析拉索-阻尼器系统的阻尼比和频率等主要特征参数,但采用复模态法求出的拉索复振型由于不包含减振所需要的参数而被研究较少,而系统的振型对研究阻尼器的减振效果又具有非常重要的意义.文中首先采用复模态法求解了拉索-阻尼器系统,基于复振型的物理意义,引入相位函数,提出了一种改进的实数分离变量法,分析了阻尼力在拉索中的传递特征;建立了拉索-阻尼器系统的改进实模态分析方法,采用该方法求解得到的非线性运动方程通解与复模态法一致.基于该新方法计算得到的实模态振型,分析了阻尼器对拉索实际振型以及相位的影响.Damper are the main measure for cable vibration control,and complex modal analysis is the main approach of cable-damper system analysis.The complex frequencies derived from complex modal analysis allow an accurate analysis of system’s damping ratio and frequency,which is of major interest of bridge researchers.There is few studies for investigating the complex mode shape of cable since it does not contain the key parameters for vibration suppression.This paper focuses on the analysis of cable’s phase contained in the complex modal shape.Firstly,the complex modal analysis is used to analysis the cable-damper system,and the physical meaning of complex mode shape is explained.Subsequently,based on its physical meanings,the real separating variable method is improved by adding phase function,thus it is possible to explain how the damping force is translated in the cable.In this process,a set of nonlinear equations are obtained and their general solutions are solved,and the results obtained are consistent with those by the complex modal analysis.Finally,the effect of the damper on the cable’s real modal shape and phase is analyzed based on the results obtained.

关 键 词：拉索-阻尼器系统 复模态 分离变量法 相位差 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]