Manipulation of Energy Transfer between Internally Resonant Globally Coupled Two Vibro-Impact Oscillators by Wave Algorithm

Abstract

In this paper, we have proposed wave algorithm for manipulating energy transfer between globally coupled two harmonic oscillators with internal resonance by intermittent perfect elastic impacts at balanced point. When the temporal interval of the impacts, Δt, is the same of the periodic time, 2π, the coupled oscillators exchange their energies slowly and periodically. Its periodicity depends on the ratio between the mass of the oscillators. By skipping an impact, we can reverse the direction of energy flow. And by skipping an impact in every 2nπ period, the system shows 4nπ-periodic recurrence phenomena. By controlling the intermittent of the impacts, we can keep maximizing or minimizing the amplitude of one certain oscillator. We can analytically explain these phenomena from the combinations of unitary operators under wave algorithm. Moreover, under the periodic 2π impacts, the system shows periodic recurrence phenomena, only when the rational ratio between the mass of two coupled oscillators, γ =1, 1/3 or 3; otherwise, it shows strictly ergodic behavior in velocity space.