Computation of Dispersion Curves in Elastic Waveguides of Arbitrary Cross- section embedded in Infinite Solid Media

Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. However, guiding structures are often buried in a large domain, considered as unbounded. Waveguides are then open and waves can be trapped or leaky. Analytical tools have been developed to model open solid waveguides but these tools are limited for simple geometries (plates, cylinders). With numerical methods, a difficulty is due to the unbounded geometry. Another issue is due to the presence of leaky modes, which grow exponentially along the transverse directions. The goal of this work is to implement a numerical approach to calculate modes in three dimensional elastic open waveguides, which combines the semi-analytical finite element method and the perfectly matched layers (PML) technique. Both Cartesian and cylindrical PML are implemented.

[1]  M. Lowe,et al.  Plate waves for the NDT of diffusion bonded titanium , 1992 .

[2]  Michael J. S. Lowe,et al.  Guided wave propagation in three-layer pavement structures , 2004 .

[3]  H. Wadley,et al.  Leaky axisymmetric modes in infinite clad rods , 2011 .

[4]  Ivan Bartoli,et al.  Modeling wave propagation in damped waveguides of arbitrary cross-section , 2006, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[5]  M Castaings,et al.  Torsional waves propagation along a waveguide of arbitrary cross section immersed in a perfect fluid. , 2008, The Journal of the Acoustical Society of America.

[6]  R. N. Thurston.  Elastic waves in rods and clad rods , 1978 .

[7]  B. Pavlakovic,et al.  Leaky guided ultrasonic waves in NDT. , 1998 .

[8]  Michel Castaings,et al.  Finite element model for waves guided along solid systems of arbitrary section coupled to infinite solid media. , 2008, The Journal of the Acoustical Society of America.

[9]  W. Marsden.  I and J , 2012 .

[10]  Benjamin Goursaud,et al.  Etude mathématique et numérique de guides d'ondes ouverts non uniformes, par approche modale. (Mathematical and numerical study of non uniform open waveguides, modal approach) , 2010 .

[11]  R. Collin.  Field theory of guided waves , 1960 .

[12]  A. Prieto,et al.  A multimodal method for non-uniform open waveguides , 2010 .

[13]  Joseph E. Pasciak,et al.  Analysis of a Cartesian PML approximation to acoustic scattering problems in R2 , 2010 .

[14]  Peter Cawley,et al.  Comparison of the modal properties of a stiff layer embedded in a solid medium with the minima of the plane‐wave reflection coefficient , 1995 .

[15]  Vahan Baronian,et al.  Couplage des méthodes modale et éléments finis pour la diffraction des ondes élastiques guidées : Application au Contrôle Non Destructif , 2009 .

[16]  A. Prieto,et al.  Finite element computation of leaky modes in stratified waveguides , 2009 .

[17]  C. Menyuk,et al.  Understanding leaky modes: slab waveguide revisited , 2009 .

[18]  Christophe Hazard,et al.  On the use of a SAFE-PML technique for modeling two-dimensional open elastic waveguides , 2012 .

[19]  J. Rose,et al.  Guided wave dispersion curves for a bar with an arbitrary cross-section, a rod and rail example. , 2003, Ultrasonics.

[20]  Fabien Treyssède,et al.  Elastic waves in helical waveguides , 2008 .

[21]  Joseph E. Pasciak,et al.  The computation of resonances in open systems using a perfectly matched layer , 2009, Math. Comput..

[22]  Anne-Christine Hladky-Hennion,et al.  Conical radiating waves from immersed wedges , 2000 .