Investigation of a bistable dual-stage vibration isolator under harmonic excitation

Abstract

This study explores the steady-state performance of a dual-stage vibration isolator, which is configured by a bistable oscillator and a linear oscillator. The potential force of the bistable stage comprises negative linear and positive cubic nonlinear stiffnesses such that the two restoring force contributions may counterbalance to minimize dynamic force transmission. By applying a first-order harmonic balance, it is predicted that the bistable dual-stage isolator may significantly outperform an equivalent pure linear dual-stage isolator. This conclusion is verified through a series of numerical investigations. Following a parametric study, design guidelines are detailed to achieve performance improvements. Then, the 'valley' response, which is the special phenomenon of the bistable dual-stage isolator due to the counterbalance of the negative linear and positive nonlinear potential forces, is revealed and quantitatively explained. Numerical studies demonstrate the role of initial conditions, and it is shown that the likelihood of beneficial single periodic valley and intra-well responses for isolation purposes can be increased by greater bistable stage damping. Finally, a bistable dual-stage isolator prototype is developed and tested, and the numerical and experimental results verify the theoretical predictions.

Dynamic stabilization of a bistable suspension system attached to a flexible host structure for operational safety enhancement

“…Recently, a similar performance improvement of 2dof force transmissibility isolation was corroborated by the authors' work [15]. In that study, a bistable dual-stage isolator composed of two mass elements was designed to attenuate transmissibility passed from an excitation force imposed on the first (bistable) stage mass to a rigid foundation.…”

“…In that study, a bistable dual-stage isolator composed of two mass elements was designed to attenuate transmissibility passed from an excitation force imposed on the first (bistable) stage mass to a rigid foundation. In contrast to the previous work [15], the aim of the present study is base excitation suspension enhancement, which represents the reversed isolation path compared to the prior force transmissibility study and only one mass element is in the suspension assembly. Due to the inherent strong nonlinearity, a change of excitation transmission path would lead to significantly distinct dynamic behaviors and the present focus of performance improvement for frequencies adjacent to the roll-off bandwidth represent unresolved challenges as compared to the authors' previous work [15].…”

“…In contrast to the previous work [15], the aim of the present study is base excitation suspension enhancement, which represents the reversed isolation path compared to the prior force transmissibility study and only one mass element is in the suspension assembly. Due to the inherent strong nonlinearity, a change of excitation transmission path would lead to significantly distinct dynamic behaviors and the present focus of performance improvement for frequencies adjacent to the roll-off bandwidth represent unresolved challenges as compared to the authors' previous work [15]. Therefore, in summary, this research seeks to investigate the unexplored potential for a bistable suspension when attached to a flexible host structure, to enhance operational safety by harnessing the dynamic stabilization phenomenon.…”

Vibration power flow and force transmission behaviour of a nonlinear isolator mounted on a nonlinear base

“…For the current system, note that when nonlinearity only exists in the isolator with η λ = = 0 (or in the base with ρ ϵ = = 0), a 2 (or b 2 ) can be expressed as a function of b 2 (or a 2 ) and system parameters using Eq. (6). A substitution of this function into Eq.…”

“…(6) and (7) In the method of averaging, it is assumed that these time change rates can be approximated by their average values over a cycle of excitation: (7) in the main content can be obtained.…”