Bandgap characteristics of cylindrical shells with periodic configuration of arbitrary thickness variation and elastic supports

Wave propagation characteristics of cylindrical shell structures with periodic elastic supports and thickness variation is modeled and analyzed via wave finite element method (WFEM). General supporting conditions of periodicity are realized through the introduction of artificial translational and rotational restraining springs in a unit cell, and various supporting conditions can be simulated by setting the stiffness coefficients accordingly. Arbitrary thickness variation of periodicity is considered in the finite element model matrix construction of a unit cell. Making use of periodicity condition and Floquet-Bloch theory in the post-process of mass and stiffness matrices leads to the system eigenvalue problem, from which the dispersion relationship can be derived. The unit cell dynamic matrix assembled in various types of finite element model for engineering applications can be post-processed directly and efficiently by WFEM. Several examples are presented to investigate the bandgap characteristics of such cylindrical shell structures using WFEM. The correctness and reliability of current model is verified through the comparison with the results available in the literature or calculated from FEM. Continuous variation of supporting condition from the free to clamped cases can cause a complete bandgap evolution of periodic cylindrical shells. For the cases of step-wise thickness and functional thickness variation in general power form, bandgap characteristics of such periodic shell structures is ultimately dominated by the corresponding variation of mass and stiffness distribution. Mechanism of bandgap characteristics is explained by the cellular natural frequencies, and the denser the natural frequencies, the more the bandgaps.