基于辛本征空间的线性阻尼振动系统动力学分析  

Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method

作　　者：李明武[1,2] 赵岩[1,2] 钟万勰[1,2] 

机构地区：[1]大连理工大学工程力学系 [2]工业装备结构分析国家重点实验室(大连理工大学),辽宁大连116024

出　　处：《应用数学和力学》2015年第1期1-15,共15页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(面上项目)(11472067);国家重点基础研究发展计划(973计划)(2014CB046803)~~

摘　　要：对于考虑阻尼项和陀螺项的一般线性动力学振动系统,建立了基于辛本征空间展开求解的一般方法.基于Rayleigh商本征值的模态展开方法被广泛应用于复杂结构动力系统振动分析,但对于很多机械系统,由于其不能有效考虑陀螺效应的影响,其适用性却受到很大限制.该文首先讨论了无阻尼系统Rayleigh商本征值问题与辛本征值问题的对应关系,表明前者实际可由后者的一种退化形式给出(也即忽略陀螺效应),而后者更具有一般性.在此基础上,进一步基于辛本征空间本征向量展开,推导了同时考虑阻尼和陀螺系统的一般线性动力学系统的有效求解方法.数值算例选取不考虑陀螺效应及考虑陀螺效应的两种线性阻尼振动系统对所提出的方法进行了验证,分析结果表明了该文所建立方法的正确性和有效性.A symplectic eigenspace expansion method was proposed for the dynamic analysis of linear systems with damping and gyroscopic effect. The modal expansion method based on the Rayleigh quotient had been widely used in the dynamics of complex structures. However, the applicability of the modal expansion method was restricted since the gyroscopic effect was not taken into account. Herein, the relation between the Rayleigh quotient eigenvalue problems and the symplectic eigenvalue problems was established fn-stly. For these two types of problems, it was found that the latter was more general and can be reduced to the former through neglection of the gyroscopic effect. Then, the symplectic eigenspace expansion method was derived to conduct the dynamic analysis of linear damped gyroscopic systems. Finally, effectiveness of the proposed method is shown with the numerical examples of damped systems with and without gyroscopic effect simulated respectively.

关 键 词：阻尼系统 陀螺项 RAYLEIGH商 辛本征值 

分 类 号：O322[理学—一般力学与力学基础]