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Controlling Flexural Waves in Semi-Infinite Platonic Crystals with Resonator-Type Scatterers

Haslinger, SG, Movchan, NV, Movchan, AB, Jones, IS and Craster, RV (2017) Controlling Flexural Waves in Semi-Infinite Platonic Crystals with Resonator-Type Scatterers. Quarterly Journal of Mechanics and Applied Mathematics, 70 (3). pp. 215-247. ISSN 0033-5614

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Abstract

We address the scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener–Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems that exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.

Item Type: Article
Uncontrolled Keywords: 0102 Applied Mathematics, 0913 Mechanical Engineering, 0905 Civil Engineering
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Maritime and Mechanical Engineering
Publisher: Oxford University Press
Related URLs:
Date Deposited: 07 Nov 2017 13:23
Last Modified: 14 Jun 2019 11:00
DOI or Identification number: 10.1093/qjmam/hbx005
URI: http://researchonline.ljmu.ac.uk/id/eprint/7486

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