Computation of dispersion relations for axially symmetric guided waves in cylindrical structures by means of a spectral decomposition method

Su, 2006, Guided Lamb waves for identification of damage in composite structures: a review, J. Sound Vib., 295, 753, 10.1016/j.jsv.2006.01.020 Baltazar, 2010, Study of wave propagation in a multiwire cable to determine structural damage, NDT&E Int., 43, 726, 10.1016/j.ndteint.2010.08.007 Banerjee, 2009, A wave propagation and vibration-based approach for damage identification in structural components, J. Sound Vib., 322, 167, 10.1016/j.jsv.2008.11.010 Gangadharan, 2009, On the sensitivity of elastic waves due to structural damages: time-frequency based indexing method, J. Sound Vib., 320, 915, 10.1016/j.jsv.2008.09.008 Lowe, 1998, Defect detection in pipes using guided waves, Ultrasonics, 36, 147, 10.1016/S0041-624X(97)00038-3 Lowe, 2006 Pochhammer, 1876, Ueber die Fortpflanzungsgeschwindigkeiten kleiner Schwingungen in einem unbegrenzten isotropen Kreiscylinder, J. Reine. Angew. Math., 81, 324 Chree, 1890, On the longitudinal vibrations of aeolotropic bars with one axis of material symmetry, Quart. J. Pure Appl. Math., 96, 340 Lamb, 1917, On waves in an elastic plate, Proc. Roy. Soc. Lond. Ser. A, Containing Pap. Math. Phys. Charact., 93, 114, 10.1098/rspa.1917.0008 Gazis, 1958, Exact analysis of the plane-strain vibrations of thick walled hollow cylinders, J. Acoust. Soc. Am., 30, 786, 10.1121/1.1909761 Gazis, 1959, Three-dimensional investigation of the propagation of waves in hollow circular cylinders. I. Analytical foundation, J. Acoust. Soc. Am., 31, 568, 10.1121/1.1907753 Gazis, 1959, Three-dimensional investigation of the propagation of waves in hollow circular cylinders. II. Numerical results, J. Acoust. Soc. Am., 31, 573, 10.1121/1.1907754 Zemanek, 1972, An experimental and theoretical investigation of elastic wave propagation in a cylinder, J. Acoust. Soc. Am., 51, 265, 10.1121/1.1912838 Pavlakovic, 1997, Disperse: a general purpose program for creating dispersion curves, 185 Seco, 2011, Modelling the generation and propagation of ultrasonic signals in cylindrical waveguides, 1 Lowe, 1995, Matrix techniques for modeling ultrasonic waves in multilayered media, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 42, 525, 10.1109/58.393096 Gavric, 1994, Finite element computation of dispersion properties of thin-walled waveguides, J. Sound Vib., 173, 113, 10.1006/jsvi.1994.1221 Mace, 2005, Finite element prediction of wave motion in structural waveguides, J. Acoust. Soc. Am., 117, 2835, 10.1121/1.1887126 Sorohan, 2011, Extraction of dispersion curves for waves propagating in free complex waveguides by standard finite element codes, Ultrasonics, 51, 503, 10.1016/j.ultras.2010.12.003 Hayashi, 2003, Guided wave dispersion curves for a bar with an arbitrary cross-section a rod and rail example, Ultrasonics, 41, 175, 10.1016/S0041-624X(03)00097-0 Mazzotti, 2012, Guided wave dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method, Int. J. Solids Struct., 49, 2359, 10.1016/j.ijsolstr.2012.04.041 Marzani, 2008, A semi-analytical finite element formulation for modeling stress wave propagation in axisymmetric damped waveguides, J. Sound Vib., 318, 488, 10.1016/j.jsv.2008.04.028 Bartoli, 2006, Modeling wave propagation in damped wave guides of arbitrary cross-section, J. Sound Vib., 295, 685, 10.1016/j.jsv.2006.01.021 Mazzotti, 2013, A coupled SAFE-2.5D BEM approach for the dispersion analysis of damped leaky guided waves in embedded waveguides of cross-section, Ultrasonics, 53, 1227, 10.1016/j.ultras.2013.03.003 Gravenkamp, 2012, A numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method, J. Sound Vib., 331, 2543, 10.1016/j.jsv.2012.01.029 Gravenkamp, 2013, The computation of dispersion relations for three-dimensional elastic waveguides using the scaled boundary finite element method, J. Sound Vib., 332, 3756, 10.1016/j.jsv.2013.02.007 Gravenkamp, 2014, The computation of dispersion relations for axisymmetric waveguides using the scaled boundary finite element method, Ultrasonics, 54, 1373, 10.1016/j.ultras.2014.02.004 Gravenkamp, 2014, On the computation‘of dispersion curves for axisymmetric elastic waveguides using the scaled boundary finite element method, Comput. Struct., 131, 46, 10.1016/j.compstruc.2013.10.014 Pagneux, 2001, Determination of Lamb mode eigenvalues, J. Acoust. Soc. Am., 110, 1307, 10.1121/1.1391248 Adamou, 2004, Spectral methods for modelling guided waves in elastic media, J. Acoust. Soc. Am., 116, 1524, 10.1121/1.1777871 Chapman, 2010, The finite-product method in the theory of waves and stability, Proc. Roy. Soc. Lond. Ser. A, Containing Pap. Math. Phys. Charact., 466, 471, 10.1098/rspa.2009.0255 Pagneux, 1996, A study of wave propagation in varying cross-section waveguides by a modal decomposition. Part I. Theory and validation, J. Acoust. Soc. Am., 100, 2034, 10.1121/1.417913 Félix, 2001, Sound propagation in rigid bends: a multimodal approach, J. Acoust. Soc. Am., 110, 1329, 10.1121/1.1391249 W.P. Bi, D. Lafarge, Sound propagation in ducts lined with porous materials by a multi-modal marching method, in: 27th AIAA Aeroacoustics Conference, Cambridge, Massachusetts, USA, 2006. Bi, 2006, Modelling of sound propagation in a non-uniform lined duct using a multi-modal propagation method, J. Sound Vib., 289, 1091, 10.1016/j.jsv.2005.03.021 W.P. Bi, On the calculations of modes in circumferential nonuniform lined intakes, in: 28th AIAA Aeroacoustics Conference, Rome, Italy, 2007. Bi, 2008, Calculations of modes in circumferentially nonuniform lined ducts, J. Acoust. Soc. Am., 123, 2603, 10.1121/1.2897105 Maurel, 2014, Improved multimodal admittance method in varying cross section waveguides, Proc. Roy. Soc. A, 470, 10.1098/rspa.2013.0448 W. Rosenheinrich, Tables of Some Indefinite Integrals of Bessel Functions, <http://www.fh-jena.de/rsh/Forschung/Stoer/besint.pdf> version: 14.04.2014 (291 pages) (last accessed: 19.08.14). G. Teschl, Ordinary Differential Equations and Dynamical Systems, <http://www.mat.univie.ac.at/gerald/ftp/book-ode/ode.pdf> 2012 (364 pages) (last accessed: 22.08.14).