Abstract
The paper includes novel results for the scattering and localization of a time-harmonic flexural wave by a semi-infinite herringbone waveguide of rigid pins embedded within an elastic Kirchhoff plate. The analytical model takes into account the orientation and spacing of the constituent parts of the herringbone system, and incorporates dipole approximations for the case of closely spaced pins. Illustrative examples are provided, together with the predictive theoretical analysis of the localized waveforms.
Highlights
Herringbone systems are a source of great interest in the scientific community across a broad spectrum of fields encompassing branches of physics, chemistry and biology
We have presented a new type of flexural waveguide designed in the form of a herringbone system
We have demonstrated that the herringbone system can significantly enhance the localization effects, in terms of amplitudes and focusing, compared with a simpler two-grating waveguide
Summary
Herringbone systems are a source of great interest in the scientific community across a broad spectrum of fields encompassing branches of physics, chemistry and biology. Belov & Simovski [30] used knowledge of the eigenmodes for infinite crystals to give insight on the problems of scattering of plane waves by analogously composed semi-infinite crystals Another recent study [31] considered the wave dynamics at the interface of a homogeneous half-space and a half-space of plasmonic nanospheres, using a discrete Wiener–Hopf technique incorporating the assumption that each nanosphere may be described by the single dipole approximation. The first part of the paper analyses the case of a shifted pair of semi-infinite gratings in detail, with an emphasis on using the dipole approximation This idea is taken further by considering the replacement of each of the dipole pairs by an array of points with two prescribed boundary conditions, zero displacement and zero directional derivative.
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