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THE VARIATIONAL THEORY OF COMPLEX RAYS FOR THREE-DIMENSIONAL HELMHOLTZ PROBLEMS

LMT Cachan, Ens Cachan/UPMC/CNRS/PRES UniverSud Paris, 61 avenue du Président Wilson — 94230 Cachan, France

EADS Foundation Chair Advanced Computational Structural Mechanics, LMT Cachan, Ens Cachan/UPMC/CNRS/PRES UniverSud Paris, 61 avenue du Président Wilson — 94230 Cachan, France

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HERVÉ RIOU

LMT Cachan, Ens Cachan/UPMC/CNRS/PRES UniverSud Paris, 61 avenue du Président Wilson — 94230 Cachan, France

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, and

MARC BONNET

POems (UMR 7231 CNRS-ENSTA-INRIA), 32 boulevard Victor, 75015 Paris, France

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https://doi.org/10.1142/S0218396X1250021XCited by:15 (Source: Crossref)

Abstract

This paper proposes an extension of the variational theory of complex rays (VTCR) to three-dimensional linear acoustics, The VTCR is a Trefftz-type approach designed for mid-frequency range problems and has been previously investigated for structural dynamics and 2D acoustics. The proposed 3D formulation is based on a discretization of the amplitude portrait using spherical harmonics expansions. This choice of discretization allows to substantially reduce the numerical integration work by taking advantage of well-known analytical properties of the spherical harmonics. It also permits (like with the previous 2D Fourier version) an effective a priori selection method for the discretization parameter in each sub-region, and allows to estimate the directivity of the pressure field by means of a natural definition of rescaled amplitude portraits. The accuracy and performance of the proposed formulation are demonstrated on a set of numerical examples that include results on an actual case study from the automotive industry.

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