Beneficial nonlinear dynamic regimes for vibration mitigation

Linear vibration absorbers represent a well-established benchmark for mitigation of resonances, widely used in engineering practice with excellent performance. In this realm, tuned mass damper (TMD) devices have been extensively studied. As known, in order to work properly, the TMD natural frequency must be tuned in the vicinity of the frequency of the resonance to be mitigated. This implies that a single vibration absorber can be used to damp only one resonance of the primary structure. To overcome the TMD narrow frequency band capabilities while relying on passive mitigation strategies based on a single device, many researchers studied the effect of additional nonlinearities in the absorber, aiming at letting the absorber resonate at more than one frequency. In this context, nonlinear energy sinks (NES), consisting of a small mass connected to the primary system by essential nonlinearities, have been proposed. As far as the pure cubic NES, it has been shown that this configuration is most effective at moderate-energy regimes. However, a well-defined threshold of input energy exists below that no significant energy absorption and dissipation by the NES can be achieved. This critical energy level represents a lower input energy bound below which the energy transfer is not significant and the NES is ineffective. Moreover, as the input energy increases, the dissipation capacity of the cubic spring NES decreases.

Aiming to overcome these limitations, the lightweight nonlinear attachment proposed is coupled to a linear damped oscillator (considered as the primary system) through a stiffness having negative linear and positive cubic terms. Such lightweight, bistable, nonlinear oscillator coupled to a primary linear subsystem exhibits several peculiar dynamical features that make it a viable candidate for acting as an effective nonlinear energy sink [1,2,3].

By adopting targeted analytical treatments for low and high-amplitude dynamics, a procedure to tune and optimize a bistable nonlinear energy sink (BNES) to obtain the so called tuned BNES (TBNES) was then proposed in [4]. The absorption performance assessment, conducted by including a comparison with the purely cubic (NES) and the purely linear (TMD) devices, has shown that the absorption capabilities of the TBNES are superior to those of the NES. Furthermore, by broadening the operational frequency range, the TBNES is able to overcome the TMD shortcomings.

[1] Manevitch L.I., Sigalov G., Romeo F., Bergman L., Vakakis A.I., Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Analytical Study, Journal of Applied Mechanics, doi: 10.1115/1.4025150, 2013.

[2] Romeo F., Sigalov G., Bergman L., Vakakis A.I., Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Numerical Study, Journal of Computational and Nonlinear Dynamics, doi: 10.1115/1.4027224, 2015.

[3] Romeo F., Manevitch L.I., Bergman L.A., Vakakis A., Transient and chaotic low-energy transfers in a system with bistable nonlinearity, Chaos, doi: 10.1063/1.4921193, 2015.

[4] Habib G., Romeo F., The tuned bistable nonlinear energy sink, Nonlinear Dynamics, doi:10.1007/s11071-017-3444-y, 2017.