Mitigation of structural vibrations by hysteretic oscillators in internal resonance

The present paper deals with the dynamics of a two-degrees-of freedom system consisting of a nonlinear absorber attached to a primary linear structure under external excitations. The nonlinear attachment exhibits a hysteretic restoring force modeled with the classic Bouc–Wen law [hysteretic vibration absorber (HVA)]; furthermore, the mechanical characteristics of the nonlinear oscillator are tuned to regulate the ratio between the two natural frequencies and to lead the system near to internal resonance conditions. The steady-state periodic solutions are investigated, and particular attention is given to the study of modal interactions by means of frequency response curves for various excitation levels. A parametric investigation is performed to analytically detect the conditions for the occurrence of (n : 1) internal resonances for low and high external excitations. Finally, specific resonance conditions have been found under which the nonlinear attachment produces a notable reduction of the vibration amplitude of the primary system for a wide range of the excitation level. The aim of the paper is therefore twofold: the first purpose is to investigate the effect of the hysteretic damping on the passive mitigation of structural vibrations. The second purpose is to improve the system capacity of mitigating structural vibrations, by optimally choosing the characteristics of the HVA.