Application of the incremental harmonic balance method to cubic non-linearity systems

Abstract

In this paper, the formulation of the incremental harmonic balance (IHB) method is derived for a general system of differential equations with cubic non-linearity, which governs a wide range of engineering problems such as large-amplitude vibration of beams or plates. An incremental arc-length method combined with a cubic extrapolation technique is adopted to trace the response curve automatically. The stability of its periodic solutions can also be evaluated from the IHB formulation by multi-variable Floquet theory. Hsu's method is adopted for computing the transition matrix at the end of one period. Two numerical examples are presented which demonstrate the effectiveness of the IHB method and Hsu's method in treating the non-linear vibration of a strongly non-linear multiple degree of freedom system. © 1990.