Measuring the Granular Density of Modes in 3D via Impact

The jamming transition is an important feature of granular materials, with prior work showing an excess of low frequency modes in the granular density of states (or modes). In this work, we present an experimental method for acoustically measuring the granular density of modes using a single impact event to excite vibrational modes in the granular material. We test three different granular materials, all of which are composed of spherical plastic beads. The first two systems are monodisperse collections of either 6 mm or 8 mm diameter beads. The third system is a bidisperse mixture of the previous two bead sizes. During data collection, the particles are confined to a 30x30x20 cm box; on top of this box, and resting on the granular material is a light, rigid sheet onto which weights can be placed. To excite the material, an impactor is dropped on top of the system. The response of the granular material to the impact pulse is recorded by piezoelectric sensors buried throughout the material, and the density of modes is computed from the spectrum of the velocity autocorrelation of these sensors. Our initial measurements of the density of modes differentiate between the three different systems and between different pressure states.