This work focuses on elastic wave propagation in three-dimensional (3D) low-density lattices and explores their wave directionality and energy flow characteristics. In particular, we examine the dynamic response of Kelvin foam, a simple-and framed-cubic lattice, as well as the octet lattice, spanning this way a range of average nodal connectivities and both stretching-and bending-dominated behavior. Bloch wave analysis on unit periodic cells is employed and frequency diagrams are constructed. Our results show that in the low relative-density regime analyzed here, only the framed-cubic lattice displays a complete bandgap in its frequency diagram. New representations of iso-frequency contours and group-velocity plots are introduced to further analyze dispersive behavior, wave directionality, and the presence of partial bandgaps in each lattice. Significant wave beaming is observed for the simple-cubic and octet lattices in the low frequency regime, while Kelvin foam exhibits a nearly isotropic behavior in low frequencies for the first propagating mode. Results of Bloch wave analysis are verified by explicit numerical simulations on finite size domains under a harmonic perturbation.
Wave Directionality in Three-Dimensional Periodic Lattices
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 21, 2017; final manuscript received October 23, 2017; published online November 13, 2017. Assoc. Editor: Yihui Zhang.
Bayat, A., and Gaitanaros, S. (November 13, 2017). "Wave Directionality in Three-Dimensional Periodic Lattices." ASME. J. Appl. Mech. January 2018; 85(1): 011004. https://doi.org/10.1115/1.4038287
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