The quasi-static frequency response of a granular medium is measured by a
forced torsion oscillator method, with forcing frequency fp in the range
10−4 Hz to 5 Hz, while weak vibrations at high-frequency fs, in the
range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of
vibration, Γ, is below the fluidization limit. A loss factor peak is
observed in the oscillator response as a function of Γ or fp. In a
plot of lnfp against 1/Γ, the position of the peak follows an
Arrhenius-like behaviour over four orders of magnitude in fp. The data can
be described as a stochastic hopping process involving a probability factor
exp(−Γj/Γ) with Γj a fs-dependent characteristic
vibration intensity. A fs-independent description is given by
exp(−τj/τ), with τj an intrinsic characteristic time, and
τ=Γn/2πfs, n=0.5-0.6, an empirical control parameter with
unit of time. τ is seen as the effective average time during which the
perturbed grains can undergo structural rearrangement. The loss factor peak
appears as a crossover in the dynamic behaviour of the vibrated granular
system, which, at the time-scale 1/fp, is solid-like at low Γ, and
the oscillator is jammed into the granular material, and is fluid-like at high
Γ, where the oscillator can slide viscously.Comment: Final version to appear in PR