Basic Constraints for Design Optimization of Cubic and Bistable Nonlinear Energy Sink

Abstract

This work mainly concentrates on the optimization of cubic and bistable NES to find the maximum efficiency point under harmonic excitation. The conservative system is considered to reveal the inner property of the damping system. With the application of the multiple scales method and the complex variables method, the threshold of excitation and different response regimes are distinguished under the assumption of 1:1 resonance. The maximum efficiency point of cubic and bistable NES occurs when SMR disappears. The factors that affect the optimal efficiency limit are explored. The result indicates that the maximum absorption efficiency level is mainly determined by the damping parameters. Compared with the cubic case, the bistable case involves more complex regimes in terms of chaos oscillation. The influence of damping parameters on the chaos threshold is discussed to adopt different energy levels. With the help of analytical predictions, the proper nonlinear stiffness is determined for certain harmonic excitation. This work offers some fundamental insights into the optimal design of cubic and bistable NES.

Qualitative analysis of the response regimes and triggering mechanism of bistable NES

“…The optimal point occurs in the transition from the SMR stage to a stable response. Adjusting a variable pitch spring can provide the desired nonlinear stiffness with the optimal design [25]. The robustness of optimal design is verified in [16], which also concludes that the damping condition mainly determines the ceiling of maximum efficiency in the optimal cubic NES.…”

“…Various types of NES, such as piecewise NES [10], rotary NES [11], and vibro-impact NES (VI NES) [12,25], have been investigated to better explore the potential of NES. The absorption performance of different configurations among cubic NES and bistable NES shows the priority of the latter NES to reduce the band width of the initial energies input [14,15].…”

Estimation of Energy Pumping Time in Bistable Nonlinear Energy Sink and Experimental Validation

“…The occurrence of chaos always results from the global homoclinic bifurcation, and the Melnikov analysis provides an approximate criterion to predict the chaos regime. Based on that, the parameter boundary of chaos in bistable NES [28,31] and the relative performance of various kinds of NES is verified [32].…”

“…The VI NES contains a ball that can move freely inside the clearance and dissipates its excessive energy through consecutive impacts [19]. The bistable NES introduces the two equilibria, one on either side, and the negative stiffness offers a higher absorbing efficiency limitation than the same cubic NES case [28]. In the presentation of negative stiffness, the response regimes under various energy levels are more complex than in the cubic NES case, especially the chaos behaviours.…”

Targeted energy transfer in a vibro-impact cubic NES: Description of regimes and optimal design

“…The simulation parameters are fixed for ϵ = 0.01, λ 1 = 1.67, λ 2 = 0.167 and K = 1742. Those parameters are the same as reference [34]. The initial conditions for following simulations are same v(0) = v(0) = w(0) = ẇ(0) = 0.…”