TRANSIENT RESPONSE ANALYSIS OF LARGE-SCALE ROTOR-BEARING SYSTEM WITH STRONG NON-LINEAR ELEMENTS BY A TRANSFER MATRIX-NEWMARK FORMULATION ITEGRATION METHOD

This paper extends the transfer matrix technique (TMT) to the transient response analysis of a large complex non-linear rotor-bearing system by a transfer matrix-Newmark formulation itegration method. Firstly, the transfer matrix is obtained via the Newmark formulation. Secondly, the deflections and velocities at the stations, containing non-linear element, are determined by iteration. Finally, the deflections, velocities and accelerations of all stations are computed by TMT and the Newmark formulation consistent with the boundary conditions. In order to eliminate the numerical instability of TMT, the transfer vector {fT ⋮ ëT}T is used, instead of the traditional one {fT ⋮ ëT}T. Owing to the advantages of TMT and the Newmark formulation, this method can be applied to calculate the transient response of a large-scale rotor-bearing system with strong non-linear elements, and to analyze its stability. Two illustration examples are given, and the results agree well with those by Runge–Kutta method, and by modal synthetic method.