The quasi-static frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency $f_{ p}$ in the range $10^{ -4}$ Hz to 5 Hz, while weak vibrations at high-frequency $f_{ s}$, in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration, $\Gamma $, is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of $\Gamma $ or $f_{ p}$. In a plot of $\ln f_{ p}$ against $1/\Gamma $, the position of the peak follows an Arrhenius-like behaviour over four orders of magnitude in $f_{ p}$. The data can be described as a stochastic hopping process involving a probability factor $\exp(-\Gamma_{ j}/\Gamma)$ with $\Gamma_{ j}$ a $f_{ s}$-dependent characteristic vibration intensity. A $f_{ s}$-independent description is given by $\exp(-\tau_{ j}/\tau)$, with $\tau_{ j}$ an intrinsic characteristic time, and $\tau =\Gamma ^{ n}/2\pi f_{ s}$, n=0.5-0.6, an empirical control parameter with unit of time. $\tau$ 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/f_{ p}$, is solid-like at low $\Gamma$, and the oscillator is jammed into the granular material, and is fluid-like at high $\Gamma$, where the oscillator can slide viscously.
Categories: cond-mat