Phononic crystal investigation using a fluid-structure circular cylindrical shell spectral element

Abstract

Cylindrical shells are frequently applied as structural elements in engineering, and have been used for many applications due to their favorable stiffness to weight ratio. More recently they have been used as new periodic composite materials known as phononic crystals, which are a periodic arrangement of unit cells built as a combination of layers with high impedance variation. Periodicity generates Bragg wave scattering that produces stop bands or band gaps where waves do not propagate. This attribute allows us to search by new and efficient solutions to control noise and vibration in structures. The aim of this paper is to propose a spectral element based on the analytical model of a closed circular cylindrical shell with internal fluid. The formulation is verified and its performance and efficiency in calculating periodic structures and elastic phononic crystals are evaluated. In this sense, the band gaps generated by the Bragg scattering effect and the attenuation bands of forced responses are calculated for phononic crystals modeled with the proposed cylindrical shell spectral element. The Spectral Element model involves exactly (or approximately) solving the governing equations of motion in the frequency domain and uses the solutions to derive the dynamic stiffness matrix formulated in a way analogous to the conventional Finite Element method. Free and forced responses for homogeneous cylindrical shells are investigated and the results are verified. Simulated examples using conventional structures and phononic crystals modeled with the proposed cylindrical shell spectral element (with and without internal fluid) are presented and the results are shown as dispersion diagrams and displacement responses.