Wiener-Hopf kernels versus lattice Green's functions in the analysis of wave propagation in semi-infinite discrete systems of elastic resonators

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• Alexander Movchan (University of Liverpool), Natasha Movchan (University of Liverpool)
• Friday 05 July 2024, 09:30-10:15
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

This is the joint talk with N.V. Movchan   The lecture addresses Wiener-Hopf formulations for mathematical models which describe wave propagation in discrete semi-infinite elastic systems, containing resonators. The dynamic response of resonators, attached to the main waveguide, appears in the governing equations as the inertial input, which may be positive or negative  depending on the phase shift of a resonator relative to the supporting structure.   When the structure is semi-infinite, the Wiener-Hopf approach provides an elegant model for a time-harmonic wave propagation, and the corresponding functional equation includes the kernel function, which is linked to the lattice Green’s function of a periodic lattice. This connection is exploited here to discuss different dynamic regimes for semi-infinite structured waveguides.   Examples and applications are discussed for flexural elastic waves in structured plates and beams, including modelling of waves induced by a moving load. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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