Wang, Cheng-Der; Wang, Wei-Jer; Lin, Ya-Ting; Ruan, Zheng-Wei Wave propagation in an inhomogeneous transversely isotropic material obeying the generalized power law model. (English) Zbl 1293.74240 Arch. Appl. Mech. 82, No. 7, 919-936 (2012). Summary: The analytical solutions for body-wave velocity in a continuously inhomogeneous transversely isotropic material, in which Young’s moduli \((E,E')\), shear modulus \((G')\), and material density \((\rho)\) change according to the generalized power law model, \((a+bz)^c\), are set down. The remaining elastic constants of transversely isotropic media, \(\nu\), and \(\nu'\) are assumed to be constants throughout the depth. The planes of transversely isotropy are selected to be parallel to the horizontal surface. The generalized Hooke’s law, strain-displacement relationships, and equilibrium equations are integrated to constitute the governing equations. In these equations, utilizing the displacement components as fundamental variables, the solutions of three quasi-wave velocities \((V_{SV}\), \(V_P\), \(V_{SH})\) are generated for the present inhomogeneous transversely isotropic materials. The proposed solutions are compared with those of P. F. Daley and F. Hron [“Reflection and transmission coefficients for transversely isotropic media”, Bull. Seismol. Soc. Am. 67, No. 3, 661–675 (1977)], and F. K. Levin [“Seismic velocities in transversely isotropic media”, Geophysics 44, No. 5, 918–936 (1979; doi:10.1190/1.1440985)] when the inhomogeneity parameter \(c=0\). The agreement between the present results and previously published ones is excellent. In addition, the parametric study results reveal that the magnitudes of wave velocity are remarkably affected by (1) the inhomogeneity parameters \((a,b,c)\); (2) the type and degree of material anisotropy \((E/E'\), \(\nu/\nu'\), \(G/G')\); (3) the phase angle \((\theta)\); and (4) the depth of the medium \((z)\). Consequently, it is imperative to consider the effects of inhomogeneity when investigating wave propagation in transversely isotropic media. Cited in 5 Documents MSC: 74J10 Bulk waves in solid mechanics 74E10 Anisotropy in solid mechanics Keywords:inhomogeneous transversely isotropic material; generalized power law model; quasi-wave velocities; inhomogeneity parameters; material anisotropy; phase angle PDFBibTeX XMLCite \textit{C.-D. Wang} et al., Arch. Appl. Mech. 82, No. 7, 919--936 (2012; Zbl 1293.74240) Full Text: DOI References: [1] Sharma M.D.: Three-dimensional wave propagation in a general anisotropic poroelastic medium: phase velocity, group velocity and polarization. Geophys. J. Int. 156, 329–344 (2004) [2] Watanabe K., Payton R.G.: Green’s function and its non-wave nature for SH-wave in inhomogeneous elastic solid. Int. J. Eng. Sci. 42, 2087–2106 (2004) · Zbl 1211.74123 [3] Wang C.D., Lin Y.T., Jeng Y.S., Ruan Z.W.: Wave propagation in an inhomogeneous cross-anisotropic medium. Int. J. Numer. Anal. Method. Geomech. 34, 711–732 (2010) · Zbl 1273.74152 [4] Daley P.F., Hron F.: Reflection and transmission coefficients for transversely isotropic media. Bull. Seismol. Soc. Am. 67, 661–675 (1977) [5] Levin F.K.: Seismic velocities in transversely isotropic media. Geophysics 44, 918–936 (1979) [6] Eringen A.C., Suhubi E.S.: Elastodynamics: vol. II–Linear Theory. Academic Press, New York (1975) · Zbl 0344.73036 [7] Wang C.D.: Three-dimensional non-linearly varying rectangular loads on a transversely isotropic half-space. Int. J. Geomech. 4, 240–253 (2004) [8] Hu, T.B.: Assembly of an ultrasonic equipment and dynamic elastic properties of an anisotropic rock. Dissertation, National Chiao-Tung University (1995) [9] Crampin S.: A review of the effects of anisotropic layering on the propagation of seismic waves. Geophy. J. R. Astron. Soc. 49, 9–27 (1977) [10] Mathemaica®, R5.2: Wolfram Research, Inc. 100 Trade Center Drive, Champaign, IL 61820-7237, USA (2005) [11] Gerrard, C.M.: Background to mathematical modeling in geomechanics: the roles of fabric and stress history. In: Proceedings of the International Symposium on Numerical Methods, Karlsruhe, pp. 33–120 (1975) [12] Amadei B., Savage W.Z., Swolfs H.S.: Gravitational stresses in anisotropic rock masses. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24, 5–14 (1987) [13] Rowe R.K., Booker J.R.: The behavior of footings resting on a non-homogeneous soil mass with a crust, part I. Strip footings. Can. Geotech. J. 18, 250–264 (1981) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.