The periodically extended stiffness nonlinear energy sink

Abstract

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.

A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types

“…In Type I, II and III, the high performance is only achieved at or near the input energy used for optimization of the NES parameters which limits their application. Therefore, stiffness-based NESs performance has been enhanced by employing hardening and softening in the nonlinear coupling element [68], employing unsymmetrical nonlinear coupling force [69,70], or by including negative linear or nonlinear stiffness content in the coupling nonlinear force [71][72][73][74][75][76][77]. This has resulted in substantial enhancement in the performance of the NES even at high intensity impulsive loadings [73].…”

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

“…its natural frequency tends to a constant value. Considering possible practical realizations of a softening NES, in [25,36,38] a device was presented that can tailor-make stiffness characteristics. It would not be able to achieve sgn(x a ) 3 |x a | because of its infinity derivative; therefore, to facilitate computation and future experimental works, the softening and saturation arctan function will be used later on to showcase inverted resonance cascade, as its frequency-energy relation is very similar to the sgn(x a ) 3 |x a | function.…”

“…where A h (T ), B j (T ) ∈ C, * stands for complex conjugate and z j is the contribution of mode j to z. Deriving 2A h (T )e iω h T = q h − i qh /ω h and 2B j (T )e jωj T = z j − i żj /ω j yields, after some steps [36]:…”

“…To verify this assumption, the stability of B h in τ 0 is determined by linearizing the last set of equations of ( 18) around the fixed points on the SIM obtained from (20), and determining the eigenvalues of the Jacobian matrix. This procedure is common to determine the stability of SIMs [29,36]. We obtain from the linearization…”

A negative stiffness inertial nonlinear energy sink

“…Consequently, NES has recently attracted the continuous attention of many researchers [11]. Dekemele et al proposed a periodically extended stiffness NES; their results demonstrated that the periodically extended stiffness could overcome the disadvantage of the small effective energy range of the traditional NES [12]. The instantaneous model makes the system coupled with the vibro-impact (VI) NES fall into nonphysical chaotic states.…”