Dynamic Nonlinear Forcing of Elastic Rings
Abstract
Equations of motion are derived that govern the largedeformational dynamics of thinwalled elastic rings due to arbitrary forcing. The derivation follows an `exact' nonlinear shell theory. Traditional smallorder assumptions, usually associated with linear shell theory, are not made, nor is the ring material assumed to be circumferentially `inextensible'. Of particular note is the retention of rotary inertia, the rational inclusion of shear deformation and the identification of the undeformed shell. Conservation of mass and the first PiolaKirchhoff identity are used to express the continuum mechanics in terms of the known undeformed geometry. At any time, the shell is the massweighted average of the continuum particle positions. Particle positions relative to the shell satisfy a dynamic consistency condition. Because the shell is the centreofmass axis, the equations of motion are dynamically uncoupled. This uncoupling of accelerations renders the equations amenable to explicit numerical integration in time using the method of lines.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1996
 DOI:
 10.1098/rspa.1996.0102
 Bibcode:
 1996RSPSA.452.1927D