Year: 2001
Type: article
Abstract: The quasistatic frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency ${f}_{p}$ in the range ${10}^{\ensuremath{-}4} \mathrm{Hz}$ 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 $\ensuremath{\Gamma}$ is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of $\ensuremath{\Gamma}$ or ${f}_{p}.$ In a plot of $\mathrm{ln}{f}_{p}$ against $1/\ensuremath{\Gamma},$ the position of the peak follows an Arrhenius-like behavior over four orders of magnitude in ${f}_{p}.$ The data can be described as a stochastic hopping process involving a probability factor $\mathrm{exp}(\ensuremath{-}{\ensuremath{\Gamma}}_{j}/\ensuremath{\Gamma})$ with ${\ensuremath{\Gamma}}_{j}$ a ${f}_{s}$-dependent characteristic vibration intensity. An ${f}_{s}$-independent description is given by $\mathrm{exp}(\ensuremath{-}{\ensuremath{\tau}}_{j}/\ensuremath{\tau}),$ with ${\ensuremath{\tau}}_{j}$ an intrinsic characteristic time, and $\ensuremath{\tau}={\ensuremath{\Gamma}}^{n}/2\ensuremath{\pi}{f}_{s},$ $n=0.5--0.6,$ an empirical control parameter with unit of time. $\ensuremath{\tau}$ 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 behavior of the vibrated granular system, which, at the time scale ${1/f}_{p},$ is solidlike at low $\ensuremath{\Gamma},$ and the oscillator is jammed into the granular material, and is fluidlike at high $\ensuremath{\Gamma},$ where the oscillator can slide viscously.
Authors: G. D’Anna, G. Gremaud
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1781131995