Scattering of flexural waves by a pit of quadratic profile inserted in an infinite thin plate

Self Cite

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.

Section: Modal Parameters and Mobilities Of A Typical Abh Beamsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

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

Touzé

Pelat

et al. 2019

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“…Further investigations from Denis et al [10] show that the small thickness of the extremity induces a local plate behaviour in a beam with an ABH extremity, and that a two-dimensional behaviour has to be taken into account to model the tapered zone; local transverse eigenmodes can be found in the beam structure. Note that two-dimensional ABH have also been described in the literature: circular ABH used as plate vibration damper has been firstly proposed by Gautier et al [11] and studied both experimentally [11,12,13] and theoretically [14,15,16].…”

Section: The Development Of Passive Vibration Control Techniques Withmentioning

confidence: 99%

Scattering effects induced by imperfections on an acoustic black hole placed at a structural waveguide termination

Denis¹,

Pelat²,

Gautier³

2016

International audienceThe so-called " acoustic black hole " effect (ABH) is a passive vibration control technique based on the flexural waves properties in thin structure of varying thickness. A usual implementation consists in using a plate with tapered extremity with a power-law profile, covered with a thin damping layer. The inhomogeneity of the structure leads to a decrease of flexural wave speed and an increase of their amplitude, therefore resulting in an efficient energy dissipation if damping layer is placed where the thickness is minimal. The manufacture of an efficient extremity is difficult because of the small thickness, and often generates imperfections and tearing. Moreover , previous works suggest multiple that flexural modes are propagating across the width of the ABH tip. A model of an ABH multimodal waveguide taking into account an imperfect termination is developed. It shows that an elementary imperfection can affect the reflection coefficient of the extremity and reduce it. Scattering and propagation properties of the extremity are also studied. An incident mode excites several modes that are localised in the tapered region and local resonances explain the drops in the reflection coefficient. Experimental evidence of the influence of the imperfection on the reflection coefficient is provided. A key result of the paper is that manufacturing imperfections are not detrimental to the ABH effect

“…Further investigations from Denis et al [9] show that a two-dimensional behaviour has to be taken into account to model the tapered zone: the small thickness of the extremity induces a local plate behaviour in a beam with an ABH extremity, and local transverse eigenmodes can be found in the beam structure. Note that two-dimensional ABH has also been described in the literature: circular ABH used as plate vibration damper has been firstly proposed by Gautier et al [10] and studied both experimentally [10][11][12] and theoretically [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Measurement and modelling of the reflection coefficient of an Acoustic Black Hole termination

Denis

Gautier

Pelat

et al. 2015

102

a b s t r a c tThe flexural waves propagating in a beam can be efficiently absorbed if one extremity is tapered with a power law profile and covered by a thin layer of additional damping material. Such a termination induces the so-called "Acoustic Black Hole effect" (ABH): if the thickness decreases locally, flexural waves slow down and the amplitude of the displacement field increases, leading to efficient energy dissipation if an absorbing layer is placed where the thickness is minimum. This paper presents a specific study of the reflection coefficient of ABH beam terminations. A Kundt-like measurement method of the reflection coefficient of a beam termination is proposed. The method is validated using theoretical results in the case of a beam free end. Results for several ABH extremities show a clear decrease of the modulus of the reflection coefficient R. The phase of R due to the decreasing thickness profile is also investigated and is interpreted by defining a correction length for the tapered termination. These experimental results are compared with several models: geometrical acoustics based model, beam waveguide model and plate model.