Mechanical spectroscopy of vibrated granular matter

Granular matter submitted to external perturbations exhibits a variety of behaviour depending on the vibration intensity: when strongly vibrated, the granular system has a fluid aspect, whereas under low intensity perturbations, it is in a quasi-solid phase. We investigate the properties of shaken granular materials with an immersed torsion oscillator sensitive to the grains’ motion. The resulting angular deflections are analyzed to give information on the granular agitation. The system can also be used in the forced mode, allowing to obtain the mechanical susceptibility. In the case of strong vibrations, the combination of both the forced and free oscillations provides a way to introduce an “effective temperature” and an “effective viscosity” from the fluctuation–dissipation theorem, which is surprisingly valid, even for this complex non-equilibrium system. Thus, the motion of the oscillator is very similar to the Brownian motion of a pollen grain due to the molecular agitation of a surrounding liquid: here, the agitation is due to the grains of the “granular bath”. On the other hand, for weaker vibrations (with accelerations below that of gravity), the angular fluctuations of the oscillator become very small, and the “jamming route” to the frozen static state is reminiscent of a glass transition.