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

V Denis,A Pelat,C Touzé,F Gautier

doi:10.1016/j.ijnonlinmec.2016.11.012

Abstract

Acoustic 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.

Highlights

Controlling vibration is a major concern in many industrial applications today
30 This paper presents an investigation of the nonlinear behavior of Acoustic Black Hole (ABH) beams and evaluates the interest of these nonlinear eects to improve the ABH damping eciency at low frequency
This study is devoted to the nonlinear eects in ABH beams, and the potential benet that can be obtained from using them as a vector for transferring energy from the low frequencies, where ABH is known to be usually inecient, to the high frequencies; this transfer is provided by the wave turbulence regime and its associated energy cascade

Summary

Introduction

Classical methods for passive vibration damping include the use of heavy viscoelastic layer [1] or tuned mass dampers [2]. These techniques are ecient and largely studied but their implementation is often limited by an important added mass or a 5 narrow frequency range. The Acoustic Black Hole (ABH) eect is a particular surface damping method adapted to mitigate vibrations on a wide frequency range without added mass. The name may not be completely adapted as referring to an astrophysical phenomenon it is kept in this paper in order to be consistent with the current developments around this 10 particular vibration absorber

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