Abstract

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.