Dynamic analysis of multi-stepped, distributed parameter rotor-bearing systems

Exact solutions for a distributed parameter system are of great use for the physical understanding of the system or the sensitivity analysis and design of the system. However, exact or closed-form solutions for multi-stepped rotor-bearing systems with distributed parameters have been rarely investigated. The present paper proposes a modelling and analysis method to obtain exact solutions for multi-stepped rotor-bearing systems with distributed parameters. To this end, a modelling procedure to obtain an exact dynamic matrix for a Timoshenko shaft element is presented by using a spatial state equation and the Laplace transformation. The assembling procedure for constructing the global matrix can be accomplished in the same manner as the finite element method. The proposed method can readily provide exact eigensolutions, frequency responses and unbalance responses for multi-stepped rotor-bearing systems with distributed parameters. Three numerical examples are also presented for validating or illustrating the proposed method. The numerical study shows that the proposed method is very useful for the analysis of rotor-bearing systems. (C) 1999 Academic Press.