Solitary waves in flexible, arbitrary elastic helix

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The traveling solitary wave was recently discovered to be a very stable object existing in an inextensible, flexible helical fiber. In the present work, a flexible helical fiber with an arbitrary stress-strain relation is considered, and a general, analytical, steady-state solution of the 3D nonlinear vector equation is found. This solution describes a new class of spatial motion of an elastic string, which is shown to be a waveguide for subsonic solitary waves. The results confirm that the known solution for an inextensible fiber is a low-velocity or low-energy asymptote of the solution presented here. Another type of asymptotic solution derived here corresponds to a high-energy wave. In this case, when the amplitude of the wave increases, the wave speed and energy tend to infinity, and the effective wavelength tends to zero.

Original languageEnglish
Pages (from-to)966-970
Number of pages5
JournalJournal of Engineering Mechanics - ASCE
Issue number9
StatePublished - Sep 1998


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