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Research Papers

Fully Coupled Finite-Element Modeling of Active Sandwich Panels With Poroelastic Core

[+] Author and Article Information
Tomasz G. Zieliński

Department of Intelligent Technologies,  Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5B, 02-106 Warszawa, Polandtzielins@ippt.gov.pl

Marie-Annick Galland

 Laboratoire de Mécanique des Fluides et d’Acoustique, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France

Mohamed N. Ichchou

 Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France

J. Vib. Acoust 134(2), 021007 (Jan 18, 2012) (10 pages) doi:10.1115/1.4005026 History: Received February 24, 2011; Revised August 05, 2011; Published January 18, 2012; Online January 18, 2012

Active sandwich panels are an example of smart noise attenuators and a realization of hybrid active-passive approach for the problem of broadband noise reduction. The panels are composed of thin elastic faceplates linked by the core of a lightweight absorbent material of high porosity. Moreover, they are active, so piezoelectric actuators in the form of thin patches are fixed to their faceplates. Therefore, the passive absorbent properties of porous core, effective at high and medium frequencies, can be combined with the active vibroacoustic reduction necessary in a low frequency range. Important convergence issues for fully coupled finite-element modeling of such panels are investigated on a model of a disk-shaped panel under a uniform acoustic load by plane harmonic waves, with respect to the important parameter of the total reduction of acoustic transmission. Various physical phenomena are considered, namely, the wave propagation in a porous medium, the vibrations of elastic plate and the piezoelectric behavior of actuators, the acoustics-structure interaction and the wave propagation in a fluid. The modeling of porous core requires the usage of the advanced biphasic model of poroelasticity, because the vibrations of the skeleton of porous core cannot be neglected; they are in fact induced by the vibrations of the faceplates. Finally, optimal voltage amplitudes for the electric signals used in active reduction, with respect to the relative size of the piezoelectric actuator, are computed in some lower-to-medium frequency range.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

3D finite-element mesh for a disk of sandwich panel with PZT-patch, coupled to a fragment of air waveguide

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Figure 3

Finite-element meshes for the two-dimensional axially symmetric domain of a disk of sandwich panel, with or without PZT-patch, coupled to an air waveguide

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Figure 4

Frequency-dependent wavelengths and wave velocities in the PU foam used for the core of panel

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Figure 5

Transmission results for the passive sandwich panel — the sound pressure level (SPL) at point D: (a) 2D coarse mesh with linear approximation in the poroelastic domain, (b) 2D dense mesh with linear approximation, (c) 2D coarse mesh with quadratic approximation, (d) analytical solution

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Figure 6

Transmission results for the passive sandwich panel – the amplitude of acoustic pressure and transmission reduction at point D: (a) 3D model with passive piezo-patch, (b) 2D coarse mesh with passive piezo-patch, (c) 2D coarse mesh with no piezo-patch, (d) analytical solution

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Figure 7

Passive and active behavior of panel at 400 Hz, with isolines of the amplitude of total displacement (in micrometers)

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Figure 8

The h- and p-convergence solutions for the active reduction at 400 Hz: (a) 2D coarse mesh with linear approximation in poroelastic domain (364 DOF), (b) 2D dense mesh with linear approximation in poroelastic domain (2738 DOF), (c) 2D very dense mesh with linear approximation in poroelastic domain (10040 DOF), (d) 2D coarse mesh with quadratic approximation in poroelastic domain (551 DOF), (e) 2D very dense mesh with quadratic approximation everywhere (39305 DOF)

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Figure 9

Validation of 3D modeling with 2D axial-symmetry solution for the active reduction at 400 Hz: (a) 3D model with quadratic approximation (12136 DOF), (b) 2D coarse mesh with quadratic approximation (551 DOF), (c) 2D very dense mesh with quadratic approximation (39305 DOF)

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Figure 10

Optimal voltage amplitudes for the active reduction of vibroacoustic transmission at different frequencies

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Figure 11

Optimal voltage amplitudes for the active reduction signals

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Figure 12

(Negligible) phase angles for the optimal active reduction signals

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Figure 1

A lateral view of an axially symmetric disk-shaped sandwich panel with a poroelastic core and a PZT-patch fixed to one of its faceplates, coupled to a fragment of air waveguide (the region ABCD represents a modeled domain)

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