非对称系统的振动方程的响应求解

解耦对称系统的振动方程时,只需用右模态向量即可满足正交性条件,对非对称系统,讨论其振动系统响应的求解算法,则需引入左模态向量.本文首先将二阶非对称阻尼系统的振动方程转化为一阶状态方程形式,构造状态矩阵的左、右状态向量,然后利用左、右状态向量的正交规范化条件解耦非对称系统状态方程,在筒谐激励下化为一组可解的一阶线性微分方...

Algorithm for Solving Steady-state Response of Asymmetric System

While decoupling the symmetric system, the right modes of system are enough to satisfy the orthogonal conditions. But in the presence of the asymmetric system it needs left modes of system to discuss the dynamic response. In this study, firstly, the second - or- der differential equations are translated into first - order ones called state equations. The state matrix left and right state vector is con- structed. And then the left and right state vector deeoupling asymmetric orthogonal normalization condition of system state equation is used. Under simple harmonic excitation into the solvability of a set of first order linear differential equation, the integral factor method is adopted to establish the first order linear differential equation of the algorithm, to obtain the original asymmetric second - order steady - state response of the system. Because the algorithm is compact and flexible, it can be programmed easily in the large engineering struc- ture dynamic analysis