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Title: Active cloaking and waves in structured media
Author: O'Neill, J.
ISNI:       0000 0004 6059 8825
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2016
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This thesis presents a novel method for active cloaking problems involving finite defects embedded in thin elastic plates. We demonstrate the approach by considering several geometries and boundary conditions, which include circular geometries with clamped boundaries, circular shaped coated inclusions and a finite cluster of rigid pins. We use results from plate theory, including problems on scattering of flexural waves from canonical geometries and platonic crystals. Such systems are governed by the fourth-order biharmonic plate equation. The method employed involves surrounding an object with a configuration of active sources whose complex amplitudes are chosen such that the main contribution to the scattered wave is cancelled in the far field. The active sources are represented by the Green's function for the biharmonic operator, describing the response to a point force. This Green's function has the beneficial property of being non-singular at the origin and the approximate cloak leads to an analytical system of linear algebraic equations for calculating the amplitudes of the active sources, required for effective cloaking. We demonstrate that the method described is applicable to arbitrarily shaped scatterers; effective cloaking is presented for a scatterer with a smooth, clamped boundary. Cloaking is also demonstrated for a circular clamped inclusion subject to flexural waves generated by a remote point source. Studying this problem enables us to find a Green's function for the cloaking problem which can be used to cloak a discretely distributed time-harmonic load. The cloaking is shown to work well at lower frequency regimes, however, at higher frequency resonant regimes, rapid changes in scattering from the inclusion are observed in narrow frequency intervals. This makes the cloak vulnerable to detection using frequency swept probe beams; time lags can arise as the sources adapt to the alterations in frequency. We extend the approach to the case of a resonant inclusion, combining active and passive techniques to tame regions of rapid variation in scattering properties. We then apply the active cloaking method approach to the coated inclusion. Finally, we modify the method for cloaking finite clusters of pins, where the geometry of the cluster causes interactions between the evanescent terms of solutions to the biharmonic equation, leading to interesting scattering patterns. Our method of active cloaking in thin elastic plates is shown to work for scattering phenomena such as localisation, wave-trapping and neutrality. We analyse band diagrams and dispersion surfaces from the infinite structure to estimate frequencies at which these phenomena occur in the finite cluster, and demonstrate effective cloaking using a finite number of sources.
Supervisor: Selsil, O. ; Movchan, N. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral