非经典阻尼系统的求解  

Solution of non-classical damped system

作　　者：徐涛[1] 程飞[1] 于澜[1] 陈文峰[1] 邱冰[1] 

机构地区：[1]吉林大学机械科学与工程学院,长春130022

出　　处：《吉林大学学报（工学版）》2006年第B03期49-52,共4页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家杰出青年科学基金资助项目(10125208)吉林大学"985工程"资助项目

摘　　要：针对非经典阻尼振动线性系统,为消除非经典阻尼项给求解带来的困难,通过引入矩阵函数变换消除了原系统的阻尼条件项,将非经典阻尼振动微分方程转化为拟时不变经典阻尼方程。利用具有完全特征向量系的矩阵在约化若当(Jordan)标准型过程中可正交相似对角矩阵的特性,将变换矩阵取为约化若当标准型过程中的分解矩阵,从而求出所求系统的特征问题的全部特征值和相应的特征向量。同时,根据矩阵正交相似的性质分析得知:不仅变换前后两个矩阵的特征值完全相同并与时间变量无关,而且时间变量对此系统的影响可以只由变换后系统的特征向量来描述,给出了非典型阻尼振动系统物理意义上的解释。In non-classical damped linear system a matrix function transformation was introduced to get rid of the damping term which is difficult to solve in the systems. The original differential equation with non-classical damped term is changed into to a quasi time-invariant equation with a classical damped one. A matrix which has a set of complete eigenvector system can be similar orthogonally to a diagonal one through reduce it to Jordan＇s normal form, and based on this property, the reducing matrix was taken as the transformation one. Thus all eigenvalues and eigenvectors of the system can be obtained. At the same time it is know by analysis about matrix characteristic of the similar orthogonally that not only the characteristic value after the transformation is equal to the ones before the transformation and they are independence to time variable of the system, but also the eigenvectors of the formed system can showed the effect of the time variable on original system. The transformation bears clear physical meaning to non-classical damped linear systems.

关 键 词：应用数学 非经典阻尼 矩阵函数变换 特征问题 拟时不变系统 

分 类 号：O321[理学—一般力学与力学基础]