NDLI: The Nonlinear Dynamics of Filaments

Content Provider	Springer Nature Link
Author	Goriely, Alain Tabor, Michael
Copyright Year	2000
Abstract	The Kirchhoff equations provide a well-established framework tostudy the statics and dynamics of thin elastic filaments. The study ofstatic solutions to these equations has a long history and provides thebasis for many investigations, both past and present, of theconfigurations taken by filaments subject to various external forces andboundary conditions. Here we review recently developed techniquesinvolving linear and nonlinear analyses that enable one to study, insome detail, the actual dynamics of filament instabilities and thelocalized structures that can ensue. By introducing a novel arc-lengthpreserving perturbation scheme a linear stability analysis can beperformed which, in turn, leads to dispersion relations that provide theselection mechanism for the shape of an unstable filament. Thesedispersion relations provide the starting point for nonlinear analysisand the derivation of new amplitude equations which describe thefilament dynamics above the instability threshold. Here we will mainlybe concerned with the analysis of rods of circular cross-sections andsurvey the behavior of rings, rods, helices and show how these resultslead to a complete dynamical description of filament buckling.
Starting Page	101
Ending Page	133
Page Count	33
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	21
Issue Number	1
e-ISSN	1573269X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2000-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mechanics Vibration, Dynamical Systems, Control Mechanical Engineering Automotive and Aerospace Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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