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- W4289388541 abstract "We consider the propagation of surface shear waves in a half-plane, whose shear modulus $mu(y)$ and density $rho(y)$ depend continuously on the depth coordinate $y$. The problem amounts to studying the parametric Sturm-Liouville equation on a half-line with frequency $omega$ and wave number $k$ as the parameters. The Neumann (traction-free) boundary condition and the requirement of decay at infinity are imposed. The condition of solvability of the boundary value problem determines the dispersion spectrum $omega(k)$ for the corresponding surface wave. We establish the criteria for non-existence of surface waves and for the existence of $N(k)$ surface wave solutions, with $N(k) to infty$ as $k to infty$. The most intriguing result is a possibility of the existence of infinite number of solutions, $N(k)=infty$, for any given $k$. These three options are conditioned by the properties of $mu(y)$ and $rho(y)$." @default.
- W4289388541 created "2022-08-02" @default.
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- W4289388541 date "2018-10-15" @default.
- W4289388541 modified "2023-09-27" @default.
- W4289388541 title "Surface shear waves in a half-plane with depth-variant structure" @default.
- W4289388541 doi "https://doi.org/10.48550/arxiv.1810.06294" @default.
- W4289388541 hasPublicationYear "2018" @default.
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