Analysis of Vibration and Wave Propagation in Cylindrical Grid-Like Structures

Abstract

The wave propagation in and the vibration of cylindrical grid structures are analyzed. The considered grids are composed of a sequence of identical elementary cells repeating along the axial and circumferential directions to form a two-dimensional (2D) periodic structure. Two-dimensional periodic structures are characterized by wave propagation patterns that are strongly frequency dependent and highly directional. Such unique characteristics can be utilized to design structures able to confine external perturbations to specified regions. The wave propagation characteristics of 2D periodic structures are determined through the analysis of the dynamic properties of the unit cell, which is described by its Finite Element mass and stiffness matrices. The cell is composed of curved beams to form a cylindrical grid. The combined application of the Finite Element formulation and the theory of 2D periodic structures yields the phase constant surfaces, which define, for the considered cell lay-out, the directions of wave propagation for assigned frequency values. The predictions from the phase constant surfaces analysis are verified by estimating the forced harmonic response of the complete grid. The results demonstrate the unique characteristics of this class of grid structures, and suggest how they may be designed to enhance attenuation capabilities of shell structures commonly used in aerospace or naval applications. Design configurations can be identified so that the transmission of vibrations towards specified locations and at certain frequencies is minimized. The study can be extended to include the optimization of the geometry and topology of the unit cell to achieve desired transmissibility levels in specified directions and for given excitation frequencies.