Bandgap mechanism analysis of elastically restrained periodic cylindrical shells with arbitrary periodic thickness

Abstract

A unified model is established to investigate the wave propagation characteristics of cylindrical shells with arbitrary periodic variable thickness distribution and general boundary conditions. The finite periodic shell including any number of unit cells is considered in a unified pattern using energy principle and Rayleigh-Ritz procedure. System governing equation is formulated based on Love's shell theory, and an improved Fourier series expansion is employed to construct longitudinal, circumferential and radial vibration displacements, in which the unity auxiliary terms are used to overcome differential discontinuity of vibration displacements at elastic boundaries. Arbitrary periodic thickness variation information is condensed into Fourier expansion coefficients. Validity of the proposed model is verified through the comparison with results calculated from WFEM and FEM. High precision and excellent convergence can be observed with only several truncated terms of Fourier series. Results show that the bandgap characteristics is greatly dominated by the variation of shell thickness distributions, which is closely associated with the resonant frequency. Moreover, the translational spring stiffness has a more obvious influence on the bandgap characteristics comparing with the rotational spring stiffness. The mechanism of bandgap characteristics is explained, and the influences of the number of unit cells and boundary reflection on the bandgaps are also investigated.