Based on the granular micromechanical approach and energy conservation principle

an anisotropic micromorphic constitutive relationship has been obtained for granular materials. It is noted that the particle displacement induced by particle rotation has been ignored. Furthermore

the expressions of anisotropic constitutive tensors are derived through a recursive formula of the unit contact direction integral. On this basis

according to Hamilton’s principle

the motion balance equation and boundary conditions of the anisotropic granular material are derived

and the dispersion relationship of the plane wave can be obtained for the anisotropic granular material. Finally

a detailed parameter analysis is carried out on the dispersion relationship and the frequency band gap. The research shows that: (1) The proposed model predicts that there are three types of waves in the granular materials

which consists of three kinds of longitudinal waves

six kinds of transverse waves and three kinds of in-plane transverse shear waves. For the transverse isotropic condition

the larger the value of the anisotropic parameter a20 is

the higher the frequency of the longitudinal wave and the transverse wave are

and the lower the frequency of the in-plane transverse shear wave is. For the orthogonal anisotropy conditions

with the increase of the anisotropic parameter a22

the frequency of transverse waves corresponding to the kinematics related to the 2-direction increases

whereas the frequency of transverse waves corresponding to the kinematics related to the 3-direction decreases. However

the coefficient a22 has minor effects on the longitudinal wave. (2) The degree of fabric anisotropy has minor effects on the bandwidth of the transverse wave

but it has a greater effect on the bandwidth of the longitudinal wave: the increase of a20 reduces the bandwidth between acousto-optical waves

whereas the bandwidth between optical waves increases. When a20 is greater than 0.84

the band gap between acousto-optical waves disappears. In contrast

the increase of a22 increases the bandwidth between acoustic and optical waves

whereas the bandwidth between optical waves decreases. When simplified to consider the isotropic condition

the dispersion curves of the three types of waves predicted by the proposed model show a good agreement with other benchmark theories.