The Mathematical Institute, University of Oxford, Eprints Archive

Singular inextensible limit in the vibrations of post-buckled rods: analytical derivation and role of boundary conditions

Neukirch, S. and Goriely, A. and Olivier, T. (2013) Singular inextensible limit in the vibrations of post-buckled rods: analytical derivation and role of boundary conditions. Journal of Sound and Vibration . (Submitted)

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Abstract

In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1728
Deposited By: Peter Hudston
Deposited On:30 Jul 2013 13:10
Last Modified:29 May 2015 19:25

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