Forced Nonlinear Oscillations of an Autoparametric System—Part 1: Periodic Responses

Abstract

Forced oscillations of a two degree-of-freedom autoparametric system are studied with moderately high excitations. The approximate results obtained by the method of harmonic balance are found to be satisfactory by comparing with those obtained by numerical integration. In the primary parametric instability zone, separate regions of stable and unstable harmonic solutions are obtained. In the regions of unstable harmonic solutions, depending on the forcing amplitude and frequency, the solutions may be amplitude modulated or completely nonperiodic. In the latter case the numerical integrations do not converge.