连续空间离散时间—Riccati传递矩阵积分法

CSDT-RICCATI TRANSFER MATRIX INTEGRATION METHOD FOR TRANSIENT ANALYSIS OF NONLINEAR ROTOR-BEARING SYSTEMS

本文提出了分析非线性转子 -支承系统瞬态响应的一种传递矩阵积分法 ,它借助Newmark差分公式 ,建立传递关系 ,使用的传递向量是 { f e} T ,而不是以往的 { f e} T ;它用Riccati法计算的是各站位的加速度 ,而不是以往的位移 ,提高了方法的数值稳定法。本法具有Riccati法的优点 ,尤其适合于计算含有非线性元件的复杂转子系统的瞬态响应。

Based on the work of Chu and Pilkey,a new direct integration method for the transient analysis of nonlinear rotor-bearing systems is proposed,called Continuous-Space Discrete-Time(CSDT)-Riccati transfer matrix integration method. In this method,the transfer vector ｛f…｝ Trather than the previous ｛f…e｝ T is used with the aid of the Newmark generalized acceleration formulation;the accelerations of all stations,not the deflections,are computed by the Riccati transfer matrix method,in result the method′s numerical instabilities are improved.The method sustains the advantages of the Riccati transfer matrix method,i.e.,it is staightforward,easy to be understood,very convenient to use,quite stable,and capable to reduce the computation time and memory space significantly.So,it is especially fit to calculate the transient response of large complex rotor-bearing systems containing nonlinear elements.The method is illustrated and tested for the transient response of an unbalanced flexible rotor incorporating squeeze-film damper without centralizing spring.The obtained results agree well with those of the lumped mass method.For comparison an numerical example of the transient response of the above system has been also computed,using the transfer vector｛f…e｝ T.The obtained results show that such an integration is unstable.The reason of the unstability is also analyzed in this paper.