Analysis of vibration and wave propagation in cylindrical grid-like structures

The wave propagation in and the vibration of cylindrical grid structures are analyzed. The grids are composed of a sequence of identical elementary cells repeating along the axial and the circumferential direction to form a two-dimensional periodic structure. Two-dimensional periodic structures are characterized by wave propagation patterns that are strongly frequency dependent and highly directional. Their wave propagation characteristics are determined through the analysis of the dynamic properties of the unit cell. Each cell here is modelled as an assembly of curved beam elements, formulated according to a mixed interpolation method. The combined application of this Finite Element formulation and the theory of two-dimensional periodic structures is used to generate the phase constant surfaces, which define, for the considered cell lay-out, the directions of wave propagation at assigned frequencies. In particular, the directions and frequencies corresponding to wave attenuation are evaluated for cells of different size and geometry, in order to identify topologies with attractive wave attenuation and vibration confinement characteristics. The predictions from the analysis of the phase constant surfaces are verified by estimating the forced harmonic response of complete cylindrical grids, obtained through the assembly of the unit cells. The considered analysis provides invaluable guidelines for the investigation of the dynamic properties and for the design of grid stiffened cylindrical shells with unique vibration confinement characteristics.