“Caging” and resonant trapping for flexural waves in constrained elastic plates

The paper presents a model of a vibrating constrained Kirchhoff plate, which includes a region “caged” by one or two rings of rigid pins. It is tempting to assume that the “caged” region will see no vibrations and hence it is protected from an incident wave. It is demonstrated in this paper that this assumption is not correct. In particular, we identify resonant regimes for which localised trapped vibration modes, whose amplitudes exceed the amplitude of the incident wave, may occur inside the “caged” region.