Possibility of useful mechanical energy from noise: the solitary wave train problem in the granular chain revisited
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A momentary velocity perturbation at an edge of a granular chain with the grains barely touching one another and held between fixed walls propagates as a solitary wave whereas a long lived perturbation, even if it is noisy, ends up as a solitary wave train. Here, we extend our earlier work but with a force instead of a velocity perturbation. Such a perturbation can propagate an extended compression front into the system. We find that a snapshot of the distribution of grain compressions in the solitary wave train shows parabolic as opposed to an approximate exponential decay with the leading edge at the front of the traveling pulse and the trailing edge following it. The system’s time evolution depends on three independent parameters-the material properties, duration of perturbation and the characteristic amplitude of the perturbation. Hence, the coefficients used to describe the parabolic decay of the grain compressions in the solitary wave train depend on these three parameters. When a random finite duration force perturbation is applied we find that the randomness is smoothed out by the system, which in turn suggests that long granular chains (or equivalent systems, such as circuits) can be potentially useful in converting random noisy signals to organized solitary wave trains and hence to potentially usable energy.
KeywordsGranular chains Nonlinear dynamics Solitary wave trains
We are grateful to the US Army Research Office for partial support of the work reported here. We would like to thank Robert W. Newcomb and Gary F. Dargush for their interest in the work. SC thanks Abhishek Venketeswaran and Kundan Goswami for useful discussions.
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Conflict of interest
The authors declare that they have no conflict of interest.
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