A Convolution Approach for the Transient Analysis of Locally Nonlinear Rotor Systems

Abstract

A computationally efficient convolution method, based on discretized impulse response and transition matrix integral formulations, is developed for the transient analysis of complex linear structures interacting through strong local nonlinearities. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a generic rotor-housing model representing a turbopump of a space shuttle main engine (SSME). In that model, the local nonlinearity is due to clearances between the rotor bearing outer races and the carrier attached to the housing. As compared to the fourth-order Runge-Kutta numerical integration methods, the convolution approach proved more efficient and robust for the same accuracy requirement. This is due to the closed-form formulation of the convolution approach which allows for the use of relatively larger time increments and for a reduction in the roundoff errors.