English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider the propagation of surface shear waves in a half-plane, whoseshear modulus $\mu(y)$ and density $\rho(y)$ depend continuously on the depthcoordinate $y$. The problem amounts to studying the parametric Sturm-Liouvilleequation on a half-line with frequency $\omega$ and wave number $k$ as theparameters. The Neumann (traction-free) boundary condition and the requirementof decay at infinity are imposed. The condition of solvability of the boundaryvalue problem determines the dispersion spectrum $\omega(k)$ for thecorresponding surface wave. We establish the criteria for non-existence ofsurface 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 apossibility 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 $\rho(y)$.

Surface shear waves in a half-plane with depth-variant structure