H∞ Optimization of a Novel Maxwell Dynamic Vibration Absorber with Lever, Inerter, and Grounded Stiffness

Abstract

In this paper, we propose a novel Maxwell dynamic vibration absorber (DVA) with lever, inerter, and grounded stiffness. Firstly, the governing equation of the coupled system is established. The analytical formula of the amplitude amplification factor of the primary system and the natural frequencies of the coupled system are derived. There are three fixed points in the amplitude–frequency response curve of the primary system, which are independent of damping. Then, based on H∞ optimization criterion, two possible optimal parameter designs of the proposed model are obtained. Considering the practical engineering application and ensuring the stability of the system, the optimal grounded stiffness ratio is selected, and six working ranges of inerter–mass ratio are calculated. Furthermore, the performance of the vibration reduction is compared for six cases. It is found that when the values of the mass ratio, lever amplification ratio, and inerter–mass ratio change in different intervals, and the optimal grounded stiffness ratio has different cases of negative, zero, and positive results. Especially when the stiffness coefficient of the viscoelastic Maxwell model and another grounded stiffness are positive at the same time, the vibration absorption effect is better theoretically. Finally, comparing with the traditional DVAs, the performance of the novel DVA is better under harmonic excitation and random excitation. The results could provide theoretical guidance for the design of inerter-based Maxwell-type DVA with a lever component.

Performance Analysis of a Vibration Absorber with the Inerter Element and Amplifying Mechanism

“…The connection positions of spring elements and damping elements are also varied. In recent years, new components such as negative stiffness spring [10], amplification mechanism [11], and inerter device [12] have been deeply investigated in structural vibration suppression due to their excellent vibration control performance, which play an important role and bring the possibility for further improvement of DVA performance. In order to pursue better vibration reduction performance and higher cost performance under different actual needs, the collocation and combination of the whole system and the corresponding parameter optimization method have always been the research content of various scholars.…”

H∞ Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm

“…As simple amplification mechanisms, levers were often used to amplify the displacement and force in the vibration control system and enhance the system's performance. Some scholars introduced levers into the inerter absorber to further optimize the structural design and vibration absorption performance of the absorber [27,28]. Liu et al [29] introduced linear and nonlinear inerters into locally resonant acoustic metamaterials and found that the structure based on the nonlinear inerter was insensitive to changes in the inerter's coefficient.…”