Analytical and computational methods for modeling mechanical filters against Bloch wave propagation

The free propagation of elastic waves through periodic microstructured materials can be studied by the analytical formulation of beam lattice models for the elementary cell, in combination with the Floquet-Bloch theory. Within this framework, the present paper deals with periodic tetrachiral materials characterized by a monoatomic cell. Alternative analytical formulations can be developed by continualization-homogenization techniques in micropolar equivalent continua, characterized by overall elastic and inertial tensors. Valid approaches for the solution of the wave propagation problems are offered by perturbation methods, numerical continuation techniques, and – finally – computational analyses, suited to account for some mechanical updates or improvements that can hardly be included in synthetic formulations. Based on these considerations, the dispersion curves achievable by different formulations are compared and discussed. The major interest is focused on the spectral effects determined by changes in the geometry, inertia, elasticity of the microstructural elements and, finally, by variations in the cellular symmetry. Some attention is paid to the parameter combinations, which might open band gaps in the low-frequency range, useful to filter undesired dynamic signals for vibration shielding purposes.