Trapping flexural waves in thin elastic plates by complex engineered surfaces

Abstract

This document proposes the design of geometrical structures of resonators on top of a thin elastic plate in order to trap waves that propagate through the plate in a reduced area. Multiple scattering theory has been used as a mathematical tool to examine these structures. First of all, a mechanical analogue of the well-known twisted bilayer structures has been studied. These systems are made of two periodic lattices superimposed with a relative rotation between them. Then, quasiperiodic arrangements of resonators in one dimension have been explored. These configurations offer the possibility of confining waves with certain robustness against disorder (typically due to fabrication processes). Finally, a solution for designing bound states in the continuum (BICs) in circular arrays of scatterers has been found, both for flexural waves and for acoustic waves.