Using Transfer Matrices for Parametric System Forced Response

Abstract

For many years, engineers and scientists have sought to deal with the many phenomena exhibiting parametric characteristics. While many approximate techniques are available for the analysis of such systems, the harmonic balance technique can be used to accurately model the response of systems where the coefficient variation is large. Also, in analyzing complex physical systems, analysts have sought to develop efficient computational techniques that are sufficiently general for the analysis of arbitrary systems. In this paper, it is shown that combining the harmonic balance technique with transfer matrices produces an efficient computational technique for the analysis of parametric systems where the coefficient variations can be large. The technique is demonstrated by considering a single-degree-of-freedom system with time varying stiffness. The harmonic balance technique is used to frequency-branch the transfer matrices, thus allowing multifrequency response calculations to be done simultaneously. The results are compared with direct numerical integrations of the equations. Lastly, this technique is applied to a simple gear coupled rotor system to demonstrate the application of this technique to large order systems of more engineering relevance.