集中阻尼弦初值问题的解析复模态叠加法  

An analytical complex mode superposition method for the initial value problem of a string with a concentrated viscous damper

作　　者：张晓东 唐春霞 郑罡[1] 俞成雯 Zhang Xiaodong;Tang Chunxia;Zheng Gang;Yu Chengwen(State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学桥隧长期性能与安全省部共建国家重点实验室,重庆400074

出　　处：《土木工程学报》2024年第1期76-82,共7页China Civil Engineering Journal

基　　金：国家自然科学基金(51978112,51808085)。

摘　　要：实际工程中常用黏滞阻尼器对斜拉索进行减振,然而基于阻尼拉索系统模态叠加法求解系统动力时程问题的研究还很少。研究设置集中黏性阻尼器的拉索在任意给定初始条件下的自由振动问题,提出采用解析复模态叠加法进行求解的思路。给出系统复模态正交性条件,并提出利用正交性条件确定复模态叠加系数的思路。通过三个数值算例,验证了方法的正确性和高效性。该文计算结果表明,对于集中阻尼弦初值问题,一般只需利用系统的前数阶模态进行叠加即可得到理想的结果。Viscous dampers have been commonly used in practice to reduce the vibration of stay cables.Few researches,however,have been done on the time-history analysis of the cable-damper system based on the mode superpostion method for the system.The free vibration problem for a string with a concentrated viscous damper under arbitrary initial conditions was studied and for solving this problem an analytical complex mode superpostion method was proposed.The orthogonality condition for the complex mode of the system was presented and with this condition a method of determining the complex mode superpostion coefficients was proposed.Based on three examples,the correctness and effectiveness of the proposed method were verified.The calculation results show that only the lowest several order complex modes are usually required for the mode superpostion to get idealized results.

关 键 词：解析复模态叠加法 正交性 集中阻尼 初值问题 

分 类 号：O321[理学—一般力学与力学基础]