The transfer matrix–component mode synthesis has been developed for the analysis of critical speed, response to imbalance and rotordynamic optimal design of multi–spool rotor system. This method adopted the advantages of the transfer matrix method for the train structure and the component mode synthesis for reducing degrees of freedom. In this method, the whole system is divided into several subsystems at the boundary coordinates. The constrained vibration modes and the static deflection curves of the constrained rotor subsystems are analysed by the improved transfer matrix method. The whole system is connected together by the component mode synthesis in accordance with the coordinate transformation. Numerical examples show that this method is superior to the traditional transfer matrix method and the component mode synthesis by FEM. This method has been successfully used for the rotordynamic analysis and optimal design of the compressors and the gas turbine aeroengines.

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