Soroush Sepehri - PhD. student, School of Mechanical Engineering, University of Tehran, Tehran, Iran
Mahmoud Mosavi Mashhadi - Professor, School of Mechanical Engineering, University of Tehran, Tehran, Iran
Mir Masoud Seyyed Fakhrabadi - Assistant professor, School of Mechanical Engineering, University of Tehran, Tehran, Iran

Unlike the extensive studies on the in-plane motions of macroscale lattices, their out-of-plane motions have received drastically less attention in the mechanical engineering community. However, the practical limitations of the detection of very high-frequency in-plane vibrations in small-structures have restricted their investigations considerably leading the researchers toward their out-of-plane analysis. The necessity of measuring the out-of-plane displacements of the periodic lattices, especially in small-scale structures, demands a thorough perception of their out-of-plane behavior. As a result, in this paper, the out-of-plane wave propagation of periodic lattices with hexagonal, square, triangular, and kagome topologies is investigated using the finite element method and Bloch’s theorem. For the analysis of the out-of-plane wave propagation, the unit cells are discretized into grid elements, with three degrees of freedom (out-of-plane displacement, torsion, and out-of-plane bending) at each node. Additionally, the impact of shear deformation on the dispersion curves of the out-of-plane wave propagation is studied. Also, the directionality of the out-of-plane waves at low frequencies is investigated by analyzing the iso-frequency contours of each structure. The results reveal that the out-of-plane dispersion curves with much more isotropic behavior have different patterns compared to their in-plane counterparts. Besides, the wave-attenuation capabilities of the structures with various topologies are investigated and compared with the in-plane mode.Keywords: Wave propagation, Out-of

Wave propagation, Out-of-plane motion, Lattice materials, Finite element method, Bloch’s theorem.