An orthogonality relation-based technique for post-processing finite element predictions of wave scattering in solid waveguides

L. Moreau, M. Castaings, B. Hosten

Laboratoire de Mécanique Physique, University Bordeaux 1, UMR CNRS 5469, 351 cours de la Libération, 33405 Talence Cedex, France

M. V. Predoi

Department of Mechanics, University Politehnica Bucharest, Calea Plevnei 94, Bl. 10D2, Ap.12, Sect. 1, 010236-Bucharest, Romania

Received 21 December 2005; revised 24 May 2006; accepted 27 May 2006

Abstract

In this paper we propose an efficient way to post-process output data predicted by Finite Element (FE) or Boundary Element (BE) codes, when the scattering of Lamb modes by defects in plate-like structures is considered. The use of a general orthogonality relation is compared to classical post-processing made with spatial FFT. To get the amplitudes of incident or scattered modes, this orthogonality relation requires the numerical prediction of the through-thickness displacements, and stress-fields distributions, on each side of the scatterer. The distance between the location where these fields are predicted and the scatterer can be very small, thus allowing huge reductions in the size of the mesh. Through two examples, this orthogonality relation is used to calculate the reflection and transmission coefficients of a pure Lamb mode incident on a notch-like defect, in either an elastic or a viscoelastic plate. Thanks to efficient absorbing regions, the FE meshed domains are reduced to the vicinity of the defects, thus allowing several advantages of the method to be demonstrated in comparison to some weaknesses of the classical post-processing based on spatial FFT.

PACS number

s: 43.20.El, 43.20.Fn, 43.20.Gp DSB Pages: 611–620

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Journal of the Acoustical Society of America -- August 2006 -- Volume 120, Issue 2, pp. 611-620