Band-gap structure in two- and three-dimensional cellular locally resonant materials

Wave propagation in periodic locally resonant materials (LRM) is characterized by the presence of band-gaps occurring at relatively low frequencies which can be exploited for vibration attenuation or impact absorption. In this work we consider the dispersion properties of three-components cellular LRM endowed with 2D (cylindrical) or 3D periodicity. Modal analyses on the unit cell, with Bloch-Floquet periodicity conditions, are performed by the finite element methods. For cylindrical LRM, the limits of plane analyses, which consider uncoupled in-plane and out-of-plane modes, are highlighted. Several different geometries for the 3D unit cells are also proposed and their influence on the band-gap width is studied.