A vibro-impact acoustic black hole for passive damping of flexural beam vibrations

Abstract

Nonlinear flexural vibrations of slender beams holding both an Acoustic Black Hole termination and a contact non-linearity are numerically studied. The Acoustic Black Hole (ABH) effect is a passive vibration mitigation technique, which has shown attractive properties above a given cut-on frequency. In this contribution, a vibro-impact acoustic black hole (VI-ABH) is introduced, the contact nonlinearity being used as a mean to transfer energy from low to high frequencies. A numerical model of a VI-ABH is derived from an Euler-Bernoulli beam. The contact law is handled with a penalization approach, the visco-elastic layer with a Ross-Kerwin-Ungard model and the problem is solved with a modal approach combined with an energy-conserving time integration scheme. Numerical results show that the VI-ABH brings about important modifications, and changes the nature of more traditional black holes, by redistributing all the vibrational energy. It can lead to a strong decrease of the resonance magnitude at low frequencies. Under steady state noise excitation, parametric studies are realised in the cases of a single contact, a grid of contacts and bilateral contacts layouts, in order to find some optimal designs. Transient dynamics is also studied through the analysis of displacement signal envelope and energy decay time. All the numerical results constantly show that the combination the ABH effect and an energy transfer provided by contact nonlinearity leads to very attractive mitigation template including low frequencies.

Combining nonlinear vibration absorbers and the Acoustic Black Hole for passive broadband flexural vibration mitigation

“…Modal approach and time integration A modal approach is used to describe the forced response of the ABH beam coupled to the vibration absorber. The numerical implementation is similar to the one described in [22] in the case of a VI-ABH configuration, and the interested reader is referred to this paper for more detailed explanations. For the sake of conciseness, the key points of the modelling are recalled here and the description is focused mainly on the coupling between the beam and the additional degree of freedom describing the absorber.…”

“…In order to offer an exhaustive comparative view on different techniques to enhance the low-frequency efficiency of the ABH, the results obtained by using added vibration absorbers, will be contrasted to the gains one can obtain with a vibro-impact ABH. This device, introduced in [22], consists of using the non-smooth nonlinearity generated at the contact point between the beam and a rigid barrier, in order to rapidly transfer energy to the high-frequency range. Following the general configuration depicted in Fig.…”

“…Following the general configuration depicted in Fig. 1(b), the modeling of the VI-ABH has already been established in [22]. The interested reader is thus referred to [22] for a detailed presentation.…”

“…Recent analytical advances for the exact solutions of ABHs in beam structures are shown in [14], and the numerical and experimental contributions that aims at optimizing the design of ABHs for vibration suppression have been discussed in [15][16][17][18][19] for various structures. In addition, applications of ABH to other areas, including elastic metastructures [20], energy harvesting [21], vibro-impact systems [22] and cochlear systems, have also been investigated.…”

“…The third idea is to rely on a Vibro-Impact ABH (VI-ABH), recently introduced in [22], in order to enhance the low-frequency efficiency. Adding contact points on which the structure will impact during its vibration, the VI-ABH encompasses a non-smooth nonlinear effect creating fast transfers of energy to the high-frequency range where it is most efficiently damped.…”