Propagation Characteristics of Rotation Waves in Transversely Isotropic Granular Media Considering Microstructure Effect

Abstract

The purpose of this study is to develop a micromechanical-based microstructure model for transversely isotropic granular media and then use it to investigate the propagation characteristics of particle rotation waves. In this paper, the particle translation and rotation are selected as basic independent variables and the particle displacement at contact due to particle rotation is ignored. The relative deformation tensors are introduced to describe the local deformational fluctuation because of their discrete nature and microstructure effect. Based on micro–macro deformation energy conservation, the constitutive relations are derived through transferring the summation into an integral and introducing the contact fabric tensor. The governing equations and corresponding boundary conditions can then be obtained based on Hamilton’s principle. Subsequently, the dispersion characteristics and bandgap features of particle rotation waves in transversely isotropic granular media are analyzed based on the present model. The research shows that: the present microstructure model can predict 12 particle rotation waves and reflect 8 dispersion relations; the effect of the change in fabric on the dispersion relation of particle rotation waves can be mainly attributed to the effect of equivalent stiffness on frequency; and the degree of anisotropy has significant effects on the width of frequency bandgap of longitudinal waves, while it has little effect on the width of frequency bandgap of transverse and in-plane shear waves.