The periodically extended stiffness nonlinear energy sink

Conventional nonlinear energy sinks (NES) are considered to be a more robust alternative to linear vibration absorbers such as the tuned-mass-damper (TMD). While the conventional NES has a larger efficient frequency bandwidth than the TMD, it is only really efficient for a small energy range. This implies a deterioration of the NES's mitigation properties if the primary system's amplitude varies. To overcome this issue, other researchers resort to increasing the complexity of the NES by adding degrees-of-freedom. Here, another line of thought is presented, by proposing an unconventional stiffness characteristic. To increase the energy bandwidth the NES in this paper features a non-smooth, periodically extended stiffness characteristic. This NES is attached to an uncertain primary system and its performance is compared with that of the conventional NES and of the TMD by deriving the slow invariant manifolds (SIMs) in transient 1:1 resonance. The SIMs are curves that relate the vibration amplitudes of the primary system and the NES, and serve as an easy and computationally efficient tool to analyze performance. The research in this paper will prove that the newly proposed NES can be both robust regarding energy and frequency uncertainty, by considering the novel periodically extended stiffness characteristic.