The use of an orthogonality relation for reducing the size of finite element models for 3D guided waves scattering problems

• Published in: Ultrasonics 2008-09, Vol.48 (5), p.357-366
• Main Authors: Moreau, L., Castaings, M.
• Format: Article
• Language: English
• Subjects: Acoustics; Algorithms; Computer Simulation; Computing Methodologies; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Finite Element Analysis; Fundamental areas of phenomenology (including applications); Guided waves; Imaging, Three-Dimensional - methods; Materials science; Materials testing; Materials Testing - methods; Models, Theoretical; Orthogonality; Physics; Scattering; Scattering, Radiation; Structural acoustics and vibration; Ultrasonography - methods
• ISSN: 0041-624X; 1874-9968
• DOI: 10.1016/j.ultras.2008.01.005

The scattering of guided waves by complex shaped defects in three-dimensional (3D) waveguides is considered. For such problems, analytical solutions do not exist, and modal decomposition techniques based on the establishment of the displacement and stress fields in the vicinity of the scatterer are quite heavy and complicated to perform. On the other hand, finite elements (FE)-based methods constitute a powerful way to obtain solutions, but they are known to be very memory consuming. This paper proposes a post-processing technique, based on a 3D orthogonality relation, to decompose a complex acoustic field produced by a scatterer and predicted by a 3D FE model, into plane waves, the amplitudes of which are quantified in the far field. This technique allows important reductions in the size of the FE models to be made. Two applications are presented to demonstrate the potential of this method. The first one concerns the scattering of the S 0 Lamb wave incident on a flat bottom circular hole. In this example, the amplitude of each mode is calculated via the orthogonality relation-based method, and compared to that obtained by simply monitoring the displacements at appropriate through-thickness positions. In the second application, the incident S 0 Lamb mode is converted into five modes scattered by a defect of complex geometry.