一种分析非线性转子－支承系统非协调响应的近似方法

An approximate method for analyzing nonsynchronous responses of nonlinear rotor bearing system

运用文献［１］提出的线性化法，将系统做非协调响应下的非线性元件转换为等效线性元件和等效外谐和力两部分，随后用子模态综合法并借助二阶非完整约束系统的Ｒｏｕｔｈ型方程，建立了全部连接条件下非线性转子－支承系统的运动微分方程；大此基础上，将求解微分方程转化为求解代数方程，从而通过简单地迭代过程便可求得系统的非协调响应，与Ｒｕｎｇｅ－Ｋｕｔａ法的结果比较表明：本文的方法简捷、近似程度高。

Using a linear technique of Ref., nonlinear elements are substituted for the sum of the equivalent linear elements and the equivalent external harmonic forces in a state of the nonsynchronous responses.Then,with the aid of Rouths equation with nonholonomic constrains, the differential equations of motion of the equivalent system are derived by component mode synthesis technique,considering all boundary conditions .Further, the set of the differential equations is changed into a set of algebraic equations.The solutions of the algebraic equations can be obtained by simply iterative procedure.Numerical results show that the approximate solution is very near the real solution,and computing efficiency can be improved greatly.