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

Abstract

The Acoustic Black Hole (ABH) effect refers to a special vibration damping technique adapted to thin-walled structures such as beams or plates. It usually consists of a local decrease of the structure thickness profile, associated to a thin viscoelastic coating placed in the area of minimum thickness. It has been shown that such structural design acts as an efficient vibration damper in the high frequency range, but not at low frequencies. This paper investigates how different types of vibration absorbers, linear and nonlinear, added to the primary system can improve the low frequency performance of a beam ABH termination. In particular, the conjugated effects of the Acoustic Black Hole effect and a Tuned Mass Damper (TMD), a Nonlinear Energy Sink (NES), a bi-stable NES (BNES), and a vibro-impact ABH (VI-ABH) are investigated. Forced response to random excitation are computed in the time domain using a modal approach combined with an energy conserving numerical scheme. Frequency indicators are defined to characterize and compare the performance of all solutions. The simulation results clearly show that all the proposed methods are able to damp efficiently the flexural vibrations in a broadband manner. The optimal tuning of each proposed solution is then investigated through a thorough parametric study, showing how to optimize the efficiency of each solution. In particular, TMD and VI-ABH show a slight dependence on vibration amplitude, while the performance of NES and BNES have a peak of efficiency for moderate amplitudes.

Experimental evidence of energy transfer and vibration mitigation in a vibro-impact acoustic black hole

“…Note that either in the single and two-contact configurations, mode 4 is also attenuated, as the location of the involved impactors do not correspond to a node of mode 4. These observations agree very well with the numerical findings reported in [19,21] showing the good predictive capacity of the previously published model. In order to shed more light on the energy transfer and the related peak reduction brought by the VI-ABH, a noise excitation restricted to a low frequency range [5,400] Hz is now considered.…”

“…Other designs involving additional linear and/or nonlinear secondary absorber to control the lowfrequency modes have also been numerically studied in [21].…”

Dynamic analysis and optimization of a cantilevered beam with both the acoustic black hole and the nonlinear energy sink

“…Therefore, the optimization of m nes will be further studied in next section. It is clearly found that ''k nes = 1e9'' brings the best efficiency, and the same trend can be found in the linear ABH beam with a NES in (Li et al, 2021). However, it should be noted that the implementation of essential nonlinear stiffness in practical engineering is a hot topic, which is out of the scope of this paper.…”

“…With m nes = 0:005 and c nes = 0:5, Figure 7(b) shows the NES efficiency with k nes in the range of ½1e3, 1e12.Note that because the NES efficiency of the case k nes = 1e12 is very low, we do not plot it in this figure. It is clearly found that ''k nes = 1e9'' brings the best efficiency, and the same trend can be found in the linear ABH beam with a NES in(Li et al, 2021). However, it should be noted that the implementation of essential nonlinear stiffness in practical engineering is a hot topic, which is out of the scope of this paper.…”

Linear and nonlinear dynamics of a plate with acoustic black hole, geometric and contact nonlinearity for vibration mitigation

“…On the other hand, contact nonlinearity brings about immediate energy transfer, so that very effective improvements have been reported for beam ABH in [29]. The combination of added linear and nonlinear dampers to an ABH beam is studied in [30], showing also important improvements toward broadband vibration mitigation. In related fields, other studies considered similar ideas and reported results, see for example the quadratic hysteretic nonlinearity characteristic of micro-inhomogeneous materials investigated in [31] for diminishing the wave speed, or the tuned mass-loaded membranes as vibro-impact attachments on a baseline structure in [32].…”