Connecting vibrational modes and structural rigidity in granular materials: insights from photoelastic experiments

Granular materials undergo a transition from a fluid-like to a solid-like state as packing fraction increases, with rigidity emerging from force-chain networks. Near the jamming transition, theories of disordered systems predict that structurally weak ("floppy") regions dominate the low-frequency acoustic modes. Our central hypothesis is that a spatial correspondence exists between the rigid vs. floppy mesoscale structures and their vibrational dynamics. To test this, we have developed an air-table experiment with photoelastic disks, where stress-induced birefringence under polarized light allows direct visualization of the force-chain network, and a scanning laser doppler vibrometer (SLDV) records particle-scale vibrations driven by the air flow. From photoelastic force imaging, we apply the PhotoElastic Grain Solver (PEGS) to reconstruct interparticle forces and contact geometries, and analyze these using the Pebble Game algorithm to identify rigid and floppy regions within the packing. We report comparisons between the results of this rigidity percolation analysis and the vibrational modes recorded by the SLDV.