Study on dispersion and wave velocity in 2D elliptic granular crystals by a micromechanics-based micromorphic model

Abstract

This study considers two-dimensional elliptic granular crystals respectively with different aspect ratios. Using a micromechanics-based micromorphic model, macroscopic micromorphic constitutive modulus tensors of elliptic granular crystals are obtained. Two modes of Taylor expansion of relative displacements are used to establish contact relation between particles. This study obtains micromorphic transverse-rotational and longitudinal waves. Obvious dispersions of micromorphic waves are given in 2D elliptic granular crystals. With increase of aspect ratio, width of frequency band gap increases when wave propagates along [Formula: see text] direction but decreases when wave propagates along [Formula: see text] direction. Two modes of Taylor expansion of relative displacements only have influence on dispersions and frequency band gap of transverse-rotational waves. Velocities of longitudinal and transverse-rotational waves first decrease to zero, keep zero for a range of frequency and then increase to a larger wave velocity with increase of frequency for different aspect ratios. The situation with a larger aspect ratio leads to larger transverse-rotational and longitudinal velocities, and ratio between transverse-rotational and longitudinal velocities decreases from 0.7 to 0.59, when wave propagates along [Formula: see text] direction. However, it leads to smaller transverse-rotational and longitudinal velocities, and ratio between two velocities decreases from 0.88 to 0.56, when wave propagates along [Formula: see text] direction.