Sound characteristics of disordered granular disks: effects of contact damping

Abstract

We investigate numerically the sound properties of disordered dense granular packings in two dimensions. Employing linear equations of motion and excluding contact changes from our simulations, we demonstrate time evolution of sinusoidal standing waves of granular disks. We varied the strength of normal and tangential viscous forces between the disks in contact to explore the dependence of sound characteristics such as dispersion relations, attenuation coefficients, and sound speeds on the contact damping. For small wave numbers, the dispersion relations and sound speeds of acoustic modes are quite insensitive to the damping. However, a small dip in the phase speed of the transverse mode decreases as the viscous force in normal direction increases. In addition, the dispersion relation of the rotational mode differs qualitatively from the theoretical prediction for granular crystals. Therefore, disordered configurations with energy dissipation play a prominent role in sound properties of granular materials. Furthermore, we report how attenuation coefficients depend on the contact damping and quantify how they differ from the prediction of lattice theory. These improved relations, based on our numerical results, can in future be compared to advanced theories and experiments.

An explicit granular-mechanics approach to marine sediment acoustics

“…6 How packing structure affects dispersion and attenuation in disordered packings is an open question, the answer to which would have obvious implications for marine sediment acoustics as well as other systems. We note a recent paper, 58 which studied standing modes in disordered 2D packings. These authors demonstrated that, even at large P, the disordered packing structure affects the dispersion relation and attenuation (in time) of plane wave modes of plane wave modes.…”