Inverted resonance capture cascade: modal interactions of a nonlinear energy sink with softening stiffness

Abstract Nonlinear energy sinks (NESs) are broadband passive vibration absorbers that are nonlinearly connected to a host system. If an NES is attached to a multi-degree-of-freedom mechanical host system under transient loading, the vibrations in the host system will transfer to and dissipate in the NES. During this transfer, the NES sequentially resonates with the modal frequencies of the host system, dissipating one mode at a time. This phenomenon is called resonance capture cascade (RCC). So far, RCC has only been investigated for NESs with a hardening nonlinear stiffness. Because of this stiffness, the transfer of modal vibrations happens from high to low frequency. In this study, an NES with a softening stiffness is proposed. Investigating the slow invariant manifolds reveals that an inverted resonance capture cascade occurs, where the transfer of vibrations to the NES is from low to high frequency. The analysis is carried out by exploiting high-dimensional slow invariant manifolds. The proposed NES is compared to the conventional NES with hardening stiffness.