Investigation of an Unforced Duffing Equation having Fractional Power Damping

Details Investigation of an Unforced Duffing Equation having Fractional Power Damping Investigation of an Unforced Duffing Equation having Fractional Power Damping

Mar 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aps..aprt14001m&link_type=abstract

American Physical Society, APS April Meeting 2012, March 31-Apr 3, 2012, abstract #T14.001

Physics

Scientific paper

The Duffing ODE provides a standard model for nonlinear oscillations for a broad range of phenomena in the natural and engineering sciences. The effects of dissipation are generally included by adding a ``friction" force term, f(v), proportional to an integer power of the velocity. Thus, oscillations take place, but with a decreasing amplitude, and which only decrease to zero in an infinite time interval. We examine the case where f(v)=-av^p, a>0 and 0 < p < 1, and demonstrate that the amplitude of the oscillations become zero in a finite time [1]. This result may have relevance for the vibrations of carbon nanotubes and sheets of graphene sheets [2]. [4pt] [1] R. E. Mickens, Truly Nonlinear Oscillators (World Scientific, London, 2010). [0pt] [2] A. Eichler et al., Nature Nanotechnology, Vol. 6 (June 2011), 339--342.

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