The coupling of elastic, surface-wave modes by a slow, interfacial inclusion

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2005-12, Vol.461 (2064), p.3765-3783
• Main Authors: Harris, John G, Block, Gareth
• Format: Article
• Language: English
• Subjects: Acoustic modes; Approximation; Boundary conditions; Coupled mode theory; Coupled Modes; Coupling coefficients; Eigenvalues; Elastic Surface Waves; Elastic waves; Interfacial Inclusion; Musical intervals; Surface waves; Waveguides
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2005.1541

A layer of homogeneous, isotropic, elastic material overlays a substrate of similar material. The shear wavespeed within the layer is less than that of the substrate causing waves to be trapped within the layer. At the interface a long inclusion, that grows gradually until it reaches a constant thickness, is introduced. The inclusion is composed of a material whose shear wavespeed is less than that in the layer; it is described as slow. It is imagined that the lowest surface-wave mode of the structure is incident to the growing inclusion. Numerical calculations show that the growth of the slow inclusion brings the wavenumber of this lowest mode into an interval where it is close to that of the second mode, thus exciting it. This process is repeated when the wavenumber of the second mode is brought close to that of the third. Within these intervals, energy is exchanged among the coupling modes. Outside of these localized intervals, the modes propagate independently of one another and their amplitudes vary such that the flux of energy in each mode is conserved; they are said to propagate adiabatically. Reflections are also excited, but are shown to be very small in magnitude.