Bifurcation dynamics and vibration suppression performance of viscoelastic energy sink under simple harmonic excitation

Abstract

The vibration suppression mechanism of nonlinear energy sink systems with viscoelastic damping under harmonic stimulation is investigated in this work, which is grounded in the bifurcation dynamics theory. First, the Zener model is utilized to build the system’s dynamic equations and the slow variable equations are derived using the slow variable averaging approach. The slow variable condition is then used to study the system’s bifurcation features. The energy spectrum of the controlled structure is employed as a quantitative indicator in conjunction with numerical simulations to demonstrate the inherent connection between the vibration suppression effect and various bifurcation types. The findings demonstrate that the system can produce chaotic motion in the parameter region of the saddle-node bifurcation-dominated three-periodic solution by focusing on the control response. This will greatly increase the target energy transfer effect and improve the vibration suppression performance. Additionally, the vibration suppression effect can be further improved by appropriately modifying the mechanical parameters of the viscoelastic energy sink. This work successfully builds a mapping relationship from bifurcation behavior to vibration suppression performance and methodically explains the nonlinear dynamics process of viscoelastic energy sinks, offering a theoretical foundation for practical applications.