Keywords: finite element method, boundary element method, vibroacoustics, piezoelectric patches, shunt damping technique, noise and vibration attenuation.

During the last two decades there has been an increasing level of interest in the control of noise radiation and sound transmission from vibrating structures using active piezoelectric techniques in the low frequency range. In this context, resonant shunt damping techniques have been recently used for interior structural-acoustic problems [1,2]. This paper concerns the extension of this technique to external vibroacoustic problems using an integrated finite element-boundary element method (FEM-BEM) for the numerical resolution of the fully coupled electro-mechanical-acoustic system.

First, a finite element formulation of an elastic structure with surface-mounted piezoelectric patches and subjected to pressure load from the presence of an external fluid is derived from a variational principle involving structural displacement, electrical voltage of piezoelectric elements and acoustic pressure at the fluid-structure interface. This formulation, with only one couple of electric variables per patch, is well adapted to practical applications since realistic electrical boundary conditions, such that equipotentiality on the electrodes and prescribed global electric charges, naturally appear. The global charge or voltage variables are intrinsically adapted to include any external electrical circuit into the electromechanical problem and to simulate the effect of resistive or resonant shunt techniques.

In the second part of this paper, the direct boundary element method is used for modelling the scattering or radiation of sound by the structure submerged in the acoustic domain. The BEM is derived from the Helmholtz integral equation involving the surface pressure and normal acoustic velocity at the boundary of the acoustic domain. A compatible mesh at the fluid-structure interface is considered. The coupled FE-BE model is obtained by using a compatible mesh at the interface. The present coupling procedure is quite general and suitable for modelling any three-dimensional geometry for bounded and especially unbounded structural-acoustic radiation problems.

Finally, the efficiency of the proposed coupling methodology is demonstrated on two examples. First, the vibration reduction of an elastic plate backed by a closed acoustic cavity is analysed. For this example, the complete FE method developed by the authors in [1] is compared with the present FEM-BEM approach. The second example is the simulation of the attenuation of the sound field emitted from a submerged plate in an acoustic domain by means of a piezoelectric shunt system.

1

W. Larbi, J.-F. Deü, R. Ohayon, "Finite element formulation of smart piezoelectric composite plates coupled with acoustic fluid", Composite Structures, 94 (2), 501-509, 2012. doi:10.1016/j.compstruct.2011.08.010

2

W. Larbi, J.-F. Deü, M. Ciminello, R. Ohayon, "Structural-Acoustic Vibration Reduction Using Switched Shunt Piezoelectric Patches: A Finite Element Analysis", Journal of Vibration and Acoustics, 132(5), 051006, 2010. doi:10.1115/1.4001508

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