Propagation of elastic waves in an anisotropic functionally graded hollow cylinder in vacuum

Aristegui, 2001, Guided waves in fluid-filled pipes surrounded by different fluids, Ultrasonics, 39, 367, 10.1016/S0041-624X(01)00064-6 Ashman, 1984, A continuous wave measurement of the elastic properties of cortical bone, Journal of Biomechanics, 17, 349, 10.1016/0021-9290(84)90029-0 Auld, 1973 C. Baron, Le dTveloppement en sTrie de Peano du matricant pour l’Ttude de la propagation d’ondes en milieux continvment variables – Peano expansion of the matricant to study elastic wave propagation in continuously heterogeneous media. Ph.D. thesis, UniversitT Bordeaux 1, France, 2005. Baron, 2010, Propagation of elastic waves in a fluid-loaded anisotropic functionally graded waveguide: application to ultrasound characterization, Journal of Acoustical Society of America, 127, 1307, 10.1121/1.3292949 Baron, 2007, Impact of localized inhomogeneity on the surface-wave velocity and bulk-wave reflection in solids, Ultrasonics, 46, 1, 10.1016/j.ultras.2006.09.001 Baron, 2007, Effect of porosity on effective diagonal stiffness coefficients (cii) and anisotropy of cortical at 1MHz: a finite-difference time domain study, Journal of Acoustical Society of America, 122, 1810, 10.1121/1.2759165 Bensamoun, 2004, Transmission scanning acoustic imaging of human cortical bone and relation with the microstructure, Clinical Biomechanics, 19, 639, 10.1016/j.clinbiomech.2004.02.009 Bousson, 2001, Distribution of intracortical porosity in human midfemoral cortex by age and gender, Journal of Bone and Mineral Research, 16, 1308, 10.1359/jbmr.2001.16.7.1308 Dong, 2004, The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity, Journal of Biomechanics, 37, 1281, 10.1016/j.jbiomech.2003.12.011 L. Elmaimouni, J.E. Lefebvre, T. Gryba, V. Zhang, Polynomial method applied to acoustic waves in inhomogeneous cylinders, in: IEEE Ultrasonics Symposium, 2003. Elmaimouni, 2008, Acoustical guided waves in inhomogeneous cylindrical materials, Ferroelectrics, 372, 115, 10.1080/00150190802382074 Elmaimouni, 2005, Guided waves in radially graded cylinders: a polynomial approach, NDT & E International, 38, 344, 10.1016/j.ndteint.2004.10.004 Gazis, 1959, Three-dimensional investigation of the propagation of waves in hollow circular cylinders. I. Analytical foundation, Journal of Acoustical Society of America, 31, 568, 10.1121/1.1907753 Griffith, 2008, Bone mass and architecture determination: state of the art, Best Practice & Research Clinical Endocrinology & Metabolism, 22, 737, 10.1016/j.beem.2008.07.003 Haiat, 2009, Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: application to axial transmission, Journal of Acoustical Society of America, 125, 4043, 10.1121/1.3117445 Han, 2002, Characteristics of waves in a functionally graded cylinder, International Journal for Numerical Methods in Engineering, 53, 653, 10.1002/nme.305 Haskell, 1953, The dispersion of surface waves on multilayered media, Bulletin of the Seismological Society of America, 43, 377, 10.1785/BSSA0430010017 Hedia, 2004, Design optimization of functionally graded dental implant, Bio-Medical Materials and Engineering, 14, 133 Honarvar, 2007, Wave propagation in transversely isotropic cylinders, International Journal of Solids and Structures, 44, 5236, 10.1016/j.ijsolstr.2006.12.029 Hosten, 2003, Surface impedance matrices to model the propagation in multilayered media, Ultrasonics, 41, 501, 10.1016/S0041-624X(03)00167-7 Kenneth, 1982, A propagator matrix method for periodically stratified media, Journal of Acoustical Society of America, 73, 137 Lamb, 1917, On waves in an elastic plate, Proceedings of the Royal Society of London A, 93, 114, 10.1098/rspa.1917.0008 S.B. Lang, Ultrasonic method for measuring elastic coefficients of bone and results on fresh and dried bovine bones, in: IEEE Transactions on Biomedical Engineering, vol. 17, 1970. Lefebvre, 2002, Development of a new ultrasonic technique for bone and biomaterials in vitro characterization, Journal of Biomedical Material Research, Part B, 63, 441, 10.1002/jbm.10261 Lin, 2009, Design optimization of functionally graded dental implant for bone remodeling, Composites: Part B, 40, 668, 10.1016/j.compositesb.2009.04.015 LTvesque, 1992, A robust transfer matrix simulation for ultrasonic response of multilayered absorbing media, Journal of Acoustical Society of America, 92, 452, 10.1121/1.404256 Meitzler, 1961, Mode coupling occurring in the propagation of elastic pulses in wires, Journal of the Acoustical Society of America, 33, 435, 10.1121/1.1908685 Mirsky, 1964, Axisymmetric vibrations of orthotropic cylinders, Journal of the Acoustical Society of America, 36, 2106, 10.1121/1.1919329 Mirsky, 1965, Wave propagation in transversely isotropic circular cylinders, part I: theory, Journal of the Acoustical Society of America, 37, 1016, 10.1121/1.1909508 Moilanen, 2008, Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius, Journal of the Acoustical Society of America, 124, 2364, 10.1121/1.2973228 Nelson, 1971, Vibrations and waves in laminated orthotropic circular cylinders, Journal of Sound and Vibration, 18, 429, 10.1016/0022-460X(71)90714-0 Nicholson, 2002, Guided ultrasonic waves in long bones: modelling, experiment and in vivo application, Physiological Measurement, 23, 755, 10.1088/0967-3334/23/4/313 Nishino, 2001, Modal analysis of hollow cylindrical guided waves and applications, Japanese Journal of Applied Physics, 30, 364, 10.1143/JJAP.40.364 Pithioux, 2002, An alternative ultrasonic method for measuring the elastic properties of cortical bone, Journal of Biomechanics, 35, 961, 10.1016/S0021-9290(02)00027-1 Plona, 1992, Axisymmetric wave propagation in fluid-loaded cylindrical shells. II: theory versus experiment, Journal of Acoustical Society of America, 92, 1144, 10.1121/1.404041 Protopappas, 2006, Guided ultrasound wave propagation in intact and healing long bone, Ultrasound in Medicine and Biology, 32, 693, 10.1016/j.ultrasmedbio.2006.02.001 Protopappas, 2007, Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones, Journal of the Acoustical Society of America, 121, 3907, 10.1121/1.2354067 Rayleigh, 1885, On wave propagating along the plane surface of an elastic solid, Proceedings of the London Mathematical Society, 7, 4, 10.1112/plms/s1-17.1.4 Rose, 1999 Saned, 2008, Spatial distribution of anisotropic acoustic impedance assessed by time-resolved 50-MHz scanning acoustic microscopy and its relation to porosity in human cortical bone, Bone, 43, 187, 10.1016/j.bone.2008.02.015 Shuvalov, 2003, A sextic formalism for three-dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials, Proceedings of the Royal Society of London A, 459, 1611, 10.1098/rspa.2002.1075 Soldatos, 1994, Wave propagation in anisotropic laminated hollow cylinders of infinite extent, Journal of the Acoustical Society of America, 96, 3744, 10.1121/1.410564 Stroh, 1962, Steady state problems in anisotropic elasticity, Journal of Mathematics and Physics, 41, 77, 10.1002/sapm196241177 Thomson, 1950, Transmission of elastic waves through a stratified solid medium, Journal of Applied Physics, 21, 89, 10.1063/1.1699629 Viktorov, 1970 Wang, 2001, Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media, Ultrasonics, 39, 413, 10.1016/S0041-624X(01)00082-8 Watari, 2004, Biocompatibility of materials and development to functionally graded implant for bio-medical application, Composites Science and Technology, 64, 893, 10.1016/j.compscitech.2003.09.005 Youssef, 2007, Picard iteration algorithm combined with Gauss–Seidel technique for initial value problems, Applied Mathematics and Computation, 190, 345, 10.1016/j.amc.2007.01.058 Zemanek, 1972, An experimental and theoretical investigation of elastic wave propagation in a cylinder, Journal of the Acoustical Society of America, 51, 265, 10.1121/1.1912838