Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber

TL;DR

This paper analyzes the dynamics of a linear oscillator coupled with a small, strongly nonlinear hysteretic absorber, revealing energy transfer mechanisms, stability conditions, and resonance phenomena through analytical and numerical methods.

Contribution

It introduces a detailed study of a two-degree-of-freedom system with a Bouc-Wen hysteretic nonlinear absorber, highlighting localization and energy transfer effects.

Findings

Localization causes passive energy transfer from linear to nonlinear oscillator.

Dissipative nonlinearity influences energy transfer efficiency.

Resonant responses exhibit vibration localization and jump phenomena.

Abstract

The present investigation deals with the dynamics of a two-degrees-of-freedom system which consists of a main linear oscillator and a strongly nonlinear absorber with small mass. The nonlinear oscillator has a softening hysteretic characteristic represented by a Bouc-Wen model. The periodic solutions of this system are studied and their calcu- lation is performed through an averaging procedure. The study of nonlinear modes and their stability shows, under specific conditions, the existence of localization which is responsible for a passive irreversible energy transfer from the linear oscillator to the nonlinear one. The dissipative effect of the nonlinearity appears to play an important role in the energy transfer phenomenon and some design criteria can be drawn regarding this parameter among others to optimize this energy transfer. The free transient response is investigated and it is shown that the energy transfer appears when the energy input is sufficient in accordance with the predictions from the nonlinear modes. Finally, the steady-state forced response of the system is investigated. When the input of energy is sufficient, the resonant response (close to nonlinear modes) experiences localization of the vibrations in the nonlinear absorber and jump phenomena.