State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

Lowe, 1995, Matrix techniques for modeling ultrasonic waves in multilayered media, IEEE Trans. ultrasonics, Ferroelectr. Freq. control, 42, 525, 10.1109/58.393096 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 Bartoli, 2006, Modeling wave propagation in damped waveguides of arbitrary cross-section, J. Sound. Vib., 295, 685, 10.1016/j.jsv.2006.01.021 Mindlin, 1989, Waves and vibrations in isotropic, elastic plates, Struct. Mech., 199 Pao, 1974 Solie, 1973, Elastic waves in free anisotropic plates, J. Acoust. Soc. Am., 54, 50, 10.1121/1.1913575 Nayfeh, 1989, Free wave propagation in plates of general anisotropic media, J. Appl. Mech-t Asme, 56, 881, 10.1115/1.3176186 Liu, 1990, Lamb wave propagation in anisotropic laminates, J. Appl. Mech., 57, 923, 10.1115/1.2897662 Potel, 1993, Propagation in an anisotropic periodically multilayered medium, J. Acoust. Soc. Am., 93, 2669, 10.1121/1.405842 Verma, 2008, On the wave propagation in layered plates of general anisotropic media, Int. J. Adv. Eng. Sci. Appl. Math., 4, 444 Pavlakovic, 1997 Gavrić, 1994, Finite element computation of dispersion properties of thin-walled waveguides, J. Sound. Vib., 173, 113, 10.1006/jsvi.1994.1221 Gavric, 1995, Computation of propagative waves in free rail using a finite-element technique, J. Sound. Vib., 185, 531, 10.1006/jsvi.1995.0398 Mace, 2008, Modelling wave propagation in two-dimensional structures using finite element analysis, J. Sound. Vib., 318, 884, 10.1016/j.jsv.2008.04.039 He, 2014, Propagation characteristics of ultrasonic guided wave in rails based on vibration modal analysis, Zhendong Yu Chongji/J. Vib. Shock, 33, 9 Wu, 2013, Analysis of dispersion characteristic eigenfrequency method for waveguides and application in plate strip, Jisuan Lixue Xuebao/Chin. J. Comput. Mech., 30, 514 Willberg, 2015, Simulation methods for guided wave-based structural health monitoring: a review, Appl. Mech. Rev., 67, 10.1115/1.4029539 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 Treyssède, 2010, Investigation of elastic modes propagating in multi-wire helical waveguides, J. Sound. Vib., 329, 1702, 10.1016/j.jsv.2009.11.021 Karpfinger, 2008, Modeling of wave dispersion along cylindrical structures using the spectral method, J. Acoust. Soc. Am., 124, 859, 10.1121/1.2940577 Zharnikov, 2013, Application of the spectral method for computation of the spectrum of anisotropic waveguides, J. Acoust. Soc. Am., 133, 3456, 10.1121/1.4806144 Quintanilla, 2015, Modeling guided elastic waves in generally anisotropic media using a spectral collocation method, J. Acoust. Soc. Am., 137, 1180, 10.1121/1.4913777 Lefebvre, 1999, Legendre polynomial approach for modeling free-ultrasonic waves in multilayered plates, J. Appl. Phys., 85, 3419, 10.1063/1.369699 Lancellotti, 1998, Guided waves in layered cubic media: convergence study of a polynomial expansion approach, J. Acoust. Soc. Am., 104, 2638, 10.1121/1.423847 Lefebvre, 2001, Acoustic wave propagation in continuous functionally graded plates: an extension of the Legendre polynomial approach, Ieee T Ultrason. Ferr., 48, 1332, 10.1109/58.949742 Yu, 2008, Determination of material properties of functionally graded plate using the dispersion of guided waves and an artificial neural network, J. Test. Eval., 36, 103 Yu, 2013, Toroidal wave in multilayered spherical curved plates, J. Sound. Vib., 332, 2816, 10.1016/j.jsv.2012.12.032 He, 2013, The propagation of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates, J. Sound. Vib., 332, 7243, 10.1016/j.jsv.2013.08.035 Bou Matar, 2013, Legendre and Laguerre polynomial approach for modeling of wave propagation in layered magneto-electro-elastic media, J. Acoust. Soc. Am., 133, 1415, 10.1121/1.4776198 Sanderson, 2015, A closed form solution method for rapid calculation of guided wave dispersion curves for pipes, Wave Motion, 53, 40, 10.1016/j.wavemoti.2014.11.003 Cao, 2011, Calculation of propagation properties of Lamb waves in a functionally graded material (FGM) plate by power series technique, Ndt E Int., 44, 84, 10.1016/j.ndteint.2010.09.010 Towfighi, 2002, Elastic wave propagation in circumferential direction in anisotropic cylindrical curved plates, J. Appl. Mech., 69, 283, 10.1115/1.1464872 Vasudeva, 2008, Dispersion of circumferential waves in cylindrically anisotropic layered pipes in plane strain, J. Acoust. Soc. Am., 123, 4147, 10.1121/1.2902180