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Computation of periodic orbits for piecewise linear oscillator by Harmonic Balance Methods

Abstract:

In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems, are employed to investigate the dynamics of a non-smooth system, specifically a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits, including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.