Wave propagation in an inhomogeneous cross‐anisotropic medium

Abstract

SUMMARYAnalytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E ) and shear modulus (G ) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, and remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain-displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, V P , V SV , and V SH , and the wave vectors, l P l SV , and l SH , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E , G /E , and / ); and (3) the phase angle, . Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium.

3D dynamic response of a multi-layered transversely isotropic half-space subjected to a moving point load along a horizontal straight line with constant speed

“…In contrast to the qSV-waves, SH-waves in a TI medium are still purely transversal. However, the phase velocity of the qSV-waves is different from that of the SH-waves since the S-waves split into the qSV-waves and SH-waves (Kerner et al, 1989;Wang et al, 2010).…”

“…waves (Kerner et al, 1989;Wang et al, 2010). Second, the exact stiffness matrices for the in-plane motion and out-of-plane motion are constructed, respectively.…”

Three-dimensional axisymmetric responses of exponentially graded transversely isotropic tri-materials under interfacial loading

“…For the analysis of wave propagation in an inhomogeneous cross-anisotropic solid, one may refer to [11]. Also, Eskandari-Ghadi and AmiriHezaveh [12] studied the wave propagation problem in an exponentially graded transversely isotropic halfspace by presenting two potential functions.…”

Propagation of Love wave in fiber‐reinforced medium lying over an initially stressed orthotropic half‐space

“…Wave propagation in an inhomogeneous cross‐anisotropic medium was discussed by Wang et al . . Singh studied the propagation of Love wave in a corrugated isotropic layer over a homogeneous isotropic half‐space bounded by irregular boundary surfaces.…”

“…Sharma and Garg [18] derived for three-dimensional wave propagation in a general anisotropic medium under initial stress. Wave propagation in an inhomogeneous cross-anisotropic medium was discussed by Wang et al [19]. Singh [20] studied the propagation of Love wave in a corrugated isotropic layer over a homogeneous isotropic half-space bounded by irregular boundary surfaces.…”