集中黏性阻尼弦的本征问题  

Eigen problem of a taut string with concentrated viscous damping

作　　者：郑罡[1] 白钰[1] 张晓东 郭增伟[1] ZHENG Gang;BAI Yu;ZHANG Xiaodong;GUO Zengwei(State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学山区桥梁及隧道工程国家重点实验室,重庆400074

出　　处：《振动与冲击》2020年第12期177-181,212,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金面上项目(51978112;51478072;51878106)。

摘　　要：对张紧弦在任意有限项集中线性黏性阻尼下的运动方程进行无量纲化,提出求解阻尼混合弦本征问题的一般方法。通过分离变量,将该混合动力学系统的偏微分方程转化为常微分方程,用格林函数的加权和函数表示系统的本征函数,导出系统的本征方程组、本征向量和频率方程,给出了阻尼混合弦本征函数显式解析表达式的一般形式。The partial differential equation of the free vibration of a taut string with concentrated viscous damping was normalized and a general approach was proposed for solving the eigen problem of the hybrid unit string.The ordinary differential equation for the eigen problem was established by separating the time and space variables in the partial differential equation.The eigen vector equations and the frequency equation were derived with the eigen function expressed in weighed sum of the Green function series.The general analytical explicit expression of the eigen function was provided.

关 键 词：弦 集中黏性阻尼 混合系统 非经典阻尼 

分 类 号：O321[理学—一般力学与力学基础]