Implicit implementation of harmonic balance method for non-linear dynamic systems

Abstract

A simple numerical algorithm is developed for the implementation of the harmonic balance method to analyze periodic responses of a general dynamic system having geometrical nonlinearities of the quadratic and cubic types. The resulting nonlinear algebraic equations which are not explicitly determined are solved by nonlinear equation routines available in most mathematical libraries. Various nonlinear responses, such as the combinational resonances of a hinged-clamped beam, the nonlinear effect on degenerate vibration modes of a square plate and the nonlinear oscillation of thin rings, are presented to demonstrate the versatility of the algorithm.