Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

Abstract

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

Vibration band gap characteristics of two-dimensional functionally graded grids using the spectral element method

“…Based on Euler beam theory, FEM, and Bloch theorem of periodic structures, Jafari et al (2020) investigated the band gap characteristics of FG auxiliary resonators incorporated in the 2-D periodic structure composed of homogeneous materials, which is significant for the manufacture of FGMs filters. However, when A et al (Sepehri et al) calculated the 2-D grids composed of thick beams of homogeneous material, the shear deformation moves the band gap to low frequency compared to Euler beam theory. Therefore, the influence of shear deformation should be considered when calculating thick beams or medium and the high frequency band gap.…”