hide
Free keywords:
-
Abstract:
Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These
experiments produce resonance curves that represent the response amplitude as a function of the driving frequency.
We propose a model to reproduce the resonance curveswith observed features that include (a) the log-time recovery
of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the
driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward
and downward, and (d) the presence of a “cliff” segment to the left of the resonant peak under the condition of
strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds
back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics
in resonance experiments.We further show that the asymmetry of the resonance curve is caused by the softening,
which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the
resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving
frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping
curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference.With
strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the
presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.
