求解弱非比例阻尼系统实模态解的阻尼矩阵摄动法  

DAMPING MATRIX PERTURBATION METHOD FOR SOLVING THE NON-PROPORTIONALLY DAMPED SYSTEMS

作　　者：周君求[1] 彭跃社[1] 

机构地区：[1]邵阳学院电气工程系,邵阳422000

出　　处：《动力学与控制学报》2008年第4期322-326,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金(10672053);湖南省自然科学基金(05JJ30003)资助项目~~

摘　　要：提出了一种求解弱非比例阻尼振动系统实模态解的摄动方法和将非比拟阻尼矩阵分解为比例阻尼矩阵和余项阻尼矩阵的方法.对于弱非比例阻尼振动系统,通过同时对阻尼矩阵和响应矢量进行小参数摄动,将原非比例阻尼系统分解为一系列的比例阻尼振动系统,在此基础上用正则模态变换将各阶比例阻尼的摄动方程解耦,从而求得原非比例阻尼振动系统的近似解析解.计算实例表明,此方法的结果与数值计算结果十分吻合.A new method for resolving non-proportionally damping matrix into proportional damping matrix and remainder dampng matrix and a new method for solving non-proportionally damped systems were proposed respectively.After introducing the perturbation method in to the non-proportional damping matrix and response vector,the non-proportionally damped system was reduced to a series of proportionally damped systems,which can be decoupled by using modal transformation. Based on this,an approximatelly analytical solut...

关 键 词：非比例阻尼 阻尼矩阵摄动法 实模态理论 解耦 

分 类 号：O321[理学—一般力学与力学基础]