Abstract: This paper developes the transfer matrix-direct integration method. In this research the support reactions, squeeze film forces and unbalance forces are separated into different vectors. Therefore, it is easy to analyze the response from unbalance of any disk or some disks by the governing equations derived for a definite characteristic disk. It can be used to analyze the vibration matching fo the rotor and stator, to modify the structure and make sensitivity analysis.This method is also applicable to the analysis of the rotor-support system with unsymmetric stiffness.To solve the transient response of the system, expressions of the transient squeeze film force and expressions of the transfer matrix of a disk in transient response are derived. An numerical example of a double-spool-support system is given in this paper.

Key words: transient response, rotor dynamics, transfer matrix-direct integration method, rotating machinery