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

Sébastien Neukirch, Alain Goriely, Olivier Thomas

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load. © 2013 Elsevier Ltd.
Original languageEnglish (US)
Pages (from-to)962-970
Number of pages9
JournalJournal of Sound and Vibration
Volume333
Issue number3
DOIs
StatePublished - Feb 2014
Externally publishedYes

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