Elastic wave propagation in periodic structures

Abstract:
Many natural and engineered materials across different length scales present a geometry or a material composition with a periodic pattern. Originally, periodicity in both structural systems and engineered materials was introduced to achieve enhanced mechanical properties at a reduced weight. More recently periodicity has been utilized to design materials, structures or devices able to control the propagation of mechanical vibrations and waves. Periodic structures present, in fact, a unique dynamic response that can be exploited to impede the propagation of waves within desired frequency ranges and/or spatial directions. This course aims at introducing the fundamental aspects of elastic wave propagation in periodic structures. Basic concepts of lattice dynamics and wave propagation will be introduced by describing the response of 1D and 2D discrete systems. Dispersive features characteristic of periodic systems like bandgaps and wave beaming will be discussed. Additionally, appropriate computational techniques to extract the band structures properties of continuos periodic systems will be presented. In particular, the course will focus on Finite Element based techniques for band structure calculation, as the Wave Finite Element method and the Bloch operator Finite Element method.