Improvement of the acoustic black hole effect by using energy transfer due to geometric nonlinearity

Abstract

International audienceAcoustic Black Hole effect (ABH) is a passive vibration damping technique without added mass based on flexural waves properties in thin structures with variable thickness. A common implementation is a plate edge where the thickness is locally reduced with a power law profile and covered with a viscoelastic layer. The plate displacement in the small thickness region is large and easily exceeds the plate thickness. This is the origin of geometric nonlinearity which can generate couplings between linear eigenmodes of the structure and induce energy transfer between low and high frequency regimes. This phenomenon may be used to increase the efficiency of the ABH treatment in the low frequency regime where it is usually inefficient. An experimental investigation evidenced that usual ABH implementation gives rise to measurable geometric nonlinearity and typical nonlinear phenomena. In particular, strongly nonlinear regime and wave turbulence are reported. The nonlinear ABH beam is then modeled as a von Kármán plate with variable thickness. The model is solved numerically by using a modal method combined with an energy-conserving time integration scheme. The effects of both the thickness profile and the damping layer are then investigated in order to improve the damping properties of an ABH beam. It is found that a compromise between the two effects can lead to an important gain of efficiency in the low frequency range

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

“…1. The effect of this viscoelastic layer can be taken into consideration by using the Ross-Ungar-Kerwin model [1,23], which proposes an expression of the complex bending stiffness D * (x), where () * refers to the complex representation of the term. For an added viscoelastic layer located in the interval [x abh , L], the complex bending stiffness D * (x) writes…”

“…The idea of using a nonlinear mechanism to transfer energy from low frequencies -where the black hole is ineffective -to high frequencies -where the black hole is very efficient, has emerged recently. Geometric nonlinearity as a mean to realize this transfer has been successfully studied in a previous work [23]. However, the time scale of this mechanism is large as compared to typical periods of the targeted low frequency waves, so that the expected gains remain limited and cannot be obtained immediately.…”

Acoustic Black Holes in Structural Design for Vibration and Noise Control

“…Further work investigates that NWV < 0.4 is a good rule for designing ABHs [60]. In the study of Denis et al which investigated ABH as a vector for energy transfer from the low frequencies to high frequencies in the framework of nonlinear vibration, a parametric study on a number of beams shown in Figure 43 was developed [61]. Longer additional termination, which means longer LABH, can improve the efficiency of energy transfer.…”

“…Krylov indicate that the damping material with higher material loss factor makes the damping effect of the ABH have better performance [29]. Denis et al indicate that a good compromise has been found by using a long additional termination with a moderate length of the damping layer in the framework of nonlinear vibration, which can develop into a turbulent regime [61]. An optimization study was developed by Lee et al [69] and indicates that the damping performance can be enhanced by treating the tip with an appropriate size of damping layer.…”

“…Beams with various lengths of ABHs and various lengths of damping. Reprinted with permission from[61]. Copyright Elsevier, 2017.…”