Trapping flexural waves in thin elastic plates by complex engineered surfaces

Abstract

The main objective of this PhD thesis has been to design geometrical structures of resonators on top of a thin elastic plate for trapping waves that propagate through the medium in a reduced space. High density of modes in a wide frequency range is desired, as it can be appealing for developing mechanical wave control devices. Structures discussed throughout this work have been analysed using multiple scattering theory. This mathematical tool has proved to be really adequate when treating with point-like interactions between resonators and the continuum medium, as is the case in our systems. In the first place, a mechanical analogue for the twisted bilayer structure has been studied. This system is based on two periodic lattices superimposed with a relative rotation angle between them. It has recently attracted the attention of the scientific community due to its exotic properties as conductor/isolator. In this work, we will study a mechanism for describing the behavior of the eigenmodes of the structure based on the dimerized interaction between resonators. Quasi-periodic one-dimensional distribution of scatterers offers the possibility of confining waves that propagate through the medium, and presents robustness against disorder based on its topological protection. This work has proven the possibility of confining mechanical waves in a two-dimensional space using one-dimensional quasi-periodic structures, simplifying the necessary system for confining waves and showing similar results to the same kind of structures applied in other domains. Lastly, solutions for having bound states in the continuum (BICs) within a circular arrangement of scatterers have been studied and developed. These solutions to the wave equation allow to have infinite lifetime modes that do not propagate through the rest of the system, and therefore present perfect confinement. In this work, solutions have been found both for flexural waves in thin elastic plates, and for two-dimensional acoustic waveguides.