Vibrational density of states and boson peak in two-dimensional frictional granular assemblies

Abstract

In this paper, the two-dimensional granular assemblies composed of 2048 mono-dispersed frictional disks are simulated by the discrete element method. A set of eigenvalues and corresponding eigenvectors is obtained by diagonalizing the Hessian matrix for each stable configuration. The effects of the friction coefficient of disk on mechanical and geometrical properties of these systems under isotropic confining are studied. Results show that at a fixed pressure, with increasing from 0.001 to 1.0, the crossover frequency *, which separates the Debye scale region from the platform of vibrational density of states, and the boson peak BP gradually shift towards lower frequency, and the intensity of the boson peak D(BP) / BP increases. These results are mainly attributed to the fact that the system becomes more and more disordered with the increase of (i.e., the decrease of the average coordination number), resulting in more excess modes at *. For a better understanding of the different vibration modes of the two-dimensional frictional granular systems, we plot the polarization vector diagrams for different frequencies ( 1 = 0.15, 2 = 1.5 and 3 = 6.0) for configurations with = 0.001 and = 1.0, respectively. Mode analysis results show that the mode at low ( 1.0) has a mixed translational-rotational but translational-dominated character; the mode at intermediate frequency (1.0 4.0) is localized and has a mixed translational-rotational but translational-dominated character; and the mode at high frequency ( 4.0) have a strongly rotational in character. It is worth noting that the low-frequency modes become more localized and the rotational participation fraction also increases as increases, implying that the rotational modes play more important role in the system with higher friction coefficient.