Abstract
This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.
Highlights
The study of interface waves has always attracted the interest of the scientific community because of the importance and complexity of the waves that propagate in such interfaces
For the three interface models studied in this work, the resulting state of tractions, displacements, and pressures at any point of the models can be expressed as the sum of an incident field and a diffracted one
We expand the use of the indirect boundary element method to study the propagation of elastic waves in vacuum-solid, solid-solid, and fluid-solid interfaces
Summary
The study of interface waves has always attracted the interest of the scientific community because of the importance and complexity of the waves that propagate in such interfaces. Most of the energy in this type of wave is presented in the interface and decays exponentially into the solid medium and fluid one. Numerical modeling to simulate the propagation of acoustic and elastic waves generated by a borehole source embedded in a layered medium was formulated in terms of the boundary element technique, where Green’s functions were calculated by the discrete wavenumber method. A numerical method known as the indirect boundary element method IBEM is used to study, in frequency and time domain, the behavior of three canonical models of interface giving rise to the emergence of Rayleigh’s, Stoneley’s, and Scholte’s waves. To validate the equations used here, we included in The appendix, a comparison between the IBEM and discrete wave number DWN , for the case of a fluid-solid interface, where an initial pressure is applied in the fluid using a Hankel’s function of second kind and zero order
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