Teymouri, Hamid; Khojasteh, Ali; Rahimian, Mohammad; Pak, Ronald Y. S. Wave motion in multi-layered transversely isotropic porous media by the method of potential functions. (English) Zbl 1446.74144 Math. Mech. Solids 25, No. 3, 547-572 (2020). Summary: Wave propagation in a multi-layered transversely isotropic porous medium has been considered in this paper, which consists of \(n\) parallel layers overlying on a half-space. Potential functions are used to solve elastodynamic differential equations of the poroelastic medium. Time-harmonic excitation is assumed and the procedure of solution is performed in the frequency domain. Generalized reflection and transmission matrices are generated for compressional and shear waves separately. By means of the Hankel transformation method, coupled differential equations are altered to ordinary ones and Riemann surfaces are used to establish the path of integrations. A closed-form solution is described to reach Green’s functions of displacements and stresses. Some special cases of excitations are discussed and verification of the solution is presented. The numerical results of a three-layered medium on a porous half-space are determined and discussed. Cited in 2 Documents MSC: 74J10 Bulk waves in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74S70 Complex-variable methods applied to problems in solid mechanics Keywords:multi-layered porous media; transversely isotropic; potential function; reflection/transmission matrix; wave motion PDFBibTeX XMLCite \textit{H. Teymouri} et al., Math. Mech. Solids 25, No. 3, 547--572 (2020; Zbl 1446.74144) Full Text: DOI References: [1] Biot, MA . General theory of three-dimensional consolidation. J Appl Phys 1941; 12: 155-164. · JFM 67.0837.01 [2] Biot, MA . The theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. 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