Small-scale effects on wave propagation in planar micro-lattices

Abstract Experiments revealed considerable differences in the mechanical properties of micro/nanomaterials and their macroscale counterparts. In recent years, many researchers have made attempts to develop proper theories addressing these differences and investigate their associated effects on various mechanical behaviors of individual micro-components such as beams, tubes, plates, and shells. On the other hand, recent developments in micro/nanofabrication have led to noticeable size-reduction of lattice structures down to micro/sub-microscale. However, unlike the extensive research on the size-dependency of single mechanical micro-elements, this issue has not been addressed yet adequately in their assemblies and networked structures. Hence, in this paper, the size-dependent wave propagation of planar micro-lattices with hexagonal, square, triangular, and Kagome architectures is studied. The modified couple stress theory is used and the governing equations for the motion of a nonclassical micro-lattice are obtained via the finite element method. To study the wave propagation of the infinite periodic structures, Bloch's theorem is used and the dispersion curves of the size-dependent microstructures are attained. It is found that the size of the structure has a significant effect on the phononic band diagrams of the small-scale lattice structures and decreasing the size of the structure can lead to substantial changes in the dispersion curves. More specifically, decreasing the thickness of constituent microbeams shifts the dispersion bands to higher values. As a result, by introducing the length-dependent material constant in their dynamic modeling, the wave-filtering capabilities of the structures are subject to considerable changes. Additionally, the size-dependent directionality of the wave propagation is also studied and the results obtained by the modified couple stress theory are compared with the ones achieved by classic formulations.