Eur. Phys. J. Spec. Top. (2022) 231: 2359-2370
https://doi.org/10.1140/epjs/s11734-022-00425-9

Regular Article

New force transmissibility and optimization for a nonlinear dynamic vibration absorber

¹ State Key Laboratory of Mechanical Behavior and System Safety of Trafficss Engineering Structures, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
² Department of Engineering Mechanics, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
³ Key Laboratory of Smart Materials and Structures Mechanics, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
⁴ Shijiazhuang Institute of Railway Technology, 050041, Shijiazhuang, China

^c yxwtrl@tju.edu.cn

Received: 4 July 2021
Accepted: 18 December 2021
Published online: 24 January 2022

Abstract

Combining the nonlinear characteristic of the smooth and discontinuous (SD) oscillator and the magnetorheological fluid (MRF), a nonlinear dynamic vibration absorber (DVA) with variable frequency and variable damping is constructed. To evaluate its performance, new force transmissibility based on the accessibility and wide applicability of the acceleration is proposed. Specifically, the root mean square is employed to define the force transmissibility as the ratio of the inertial force of the main system and the external force. Furthermore, with the proposed transmissibility as the evaluation index, a two-step optimization method is designed to optimize the parameters of the nonlinear DVA in a wide frequency range, which overcomes the limitation of the traditional single optimization method in broadband vibration reduction. The time-domain dynamic analysis of the main structure is carried out to show the effectiveness and superiority of the two-step optimization method using the time history diagram, phase diagram, Poincaré map, and frequency spectrum. It is worthwhile noting that the two-step optimization method makes it possible to obtain great broadband damping with fewer parameter adjustments, which leads to extend the life of the nonlinear system.