Abstract
This paper presents a simple treatment of elastic wave scattering at periodically structured surfaces and interfaces of solids, and the existence and nature of surface acoustic waves (SAW) and interfacial (IW) waves at such structures. Our treatment is embodied in phenomenological models in which the periodicity resides in the boundary conditions. These yield zone folding and band gaps at the boundary of, and within the Brillouin zone. Above the transverse bulk wave threshold, there occur leaky or pseudo-SAW and pseudo-IW, which are attenuated via radiation into the bulk wave continuum. These have a pronounced effect on the transmission and reflection of bulk waves. We provide examples of pseudo-SAW and pseudo-IW for which the coupling to the bulk wave continuum vanishes at isloated points in the dispersion relation. These supersonic guided waves correspond to embedded discrete eigenvalues within a radiation continuum. We stress the generality of the phenomena that are exhibited at widely different scales of length and frequency, and their relevance to situations as diverse as the guiding of seismic waves in mine stopes, the metrology of periodic metal interconnect structures in the semiconductor industry, and elastic wave scattering by an array of coplanar cracks in a solid.
Highlights
This paper presents a simple treatment of elastic wave scattering at periodically structured surfaces and interfaces of solids, and the existence and nature of surface acoustic waves (SAW) and interfacial (IW) waves at such structures
We stress the generality of the phenomena that are exhibited at widely different scales of length and frequency, and their relevance to situations as diverse as the guiding of seismic waves in mine stopes, the metrology of periodic metal interconnect structures in the semiconductor industry, and elastic wave scattering by an array of coplanar cracks in a solid
The guiding and scattering of elastic waves at periodically-structured surfaces and interfaces of solids are of interest in such diverse fields as seismology, fracture mechanics, NDE and phononics, and equivalent effects may be observed at widely different length and frequency scales
Summary
The guiding and scattering of elastic waves at periodically-structured surfaces and interfaces of solids are of interest in such diverse fields as seismology, fracture mechanics, NDE and phononics, and equivalent effects may be observed at widely different length and frequency scales. This section is concerned with the scattering of bulk longitudinal (L) and SV polarized transverse (T) elastic waves at an interface between two identical isotropic elastic half spaces, periodically joined in strips of width b located in the xy-plane parallel to the y-direction and detached in between, and the existence of guided waves at the interface, see Figure 3 It is treated as mixed boundary condition plane strain problem of spatial period D, with incident and scattered fields confined to xz-plane and independent of y. The symmetric combination of kx = kz = ω β/ 2 SV waves has the normal displacement on the two sides of the interface opposite in direction, and so must have the Bloch harmonics to satisfy the boundary conditions This explains the absence of a symmetric supersonic interfacial wave. SIW(S), and the existence of PIW(S) for only a limited parameter range
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