An 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 analyse periodic responses of a general dynamic system having geometrical non‐linearities of the quadratic and cubic types. The resulting non‐linear algebraic equations which are not explicitly determined are solved by non‐linear equation routines available in most mathematical libraries. Various non‐linear responses, such as the combinational resonances of a hinged‐clamped beam, the non‐linear effect on degenerate vibration modes of a square plate and the non‐linear oscillation of thin rings, are presented to demonstrate the versatility of the algorithm.

Citation

Cheung, Y.K. and Iu, V.P. (1988), "An implicit implementation of harmonic balance method for non‐linear dynamic systems", Engineering Computations, Vol. 5 No. 2, pp. 134-140. https://doi.org/10.1108/eb023731