On Using the Transfer Matrix Formulation for Transient Analysis of Nonlinear Rotor Bearing Systems

Abstract

For many years transfer matrices have been used to evaluate the steady‐state vibration response of linear rotor bearing systems. More recently, they have been used to evaluate the steady‐state periodic vibration response of nonlinear rotor bearing systems. For quasi‐periodic and chaotic response, a transient solution is mandated and transient solution software can also be gainfully used to evaluate the stability of the above‐mentioned periodic solutions. To date, transient solutions generally necessitate a different lumped parameter discretization of the rotor and involve solving simultaneously the differential equations for every degree of freedom. This article shows how transient analysis can be performed while maintaining the transfer matrix lumped parameter discretization. The technique is illustrated for a non symmetric unbalanced flexible rotor supported on hydrodynamic journal bearings or deep‐groove ball bearings.