【摘要】 提出了求解多自由度非比例阻尼系统自由振动的一种解析方法,得到了非比例阻尼系统的实解析表达式.把原来的二阶微分方程组化为等价的一阶微分方程组.利用一阶系统的特征根和系统矩阵,求出一阶系统的状态转移矩阵,可得到一阶系统的解,继而得到原非比例阻尼系统自由振动的解析解.更多还原

【Abstract】 An analytical solution to the free vibrations of multi-degree freedom systems with non-proportional damping is presented in this paper.By transforming 2-order non-proportional damping systems into 1-order ordinary differential equations and using the latent root and the system matrix of 1-order systems,we have solved the state transitional matrices and obtained the solutions to the new systems,thus gaining the solutions to the non-proportional damping system.更多还原