Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Université Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
fax : +33 1 44 27 52 59
e-mail: sebastien.neukirch (-atat-) upmc.fr

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

S. Neukirch, A. Goriely, and O. Thomas

Journal of Sound and Vibration, vol. 333 #3 (2014) 962-970

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 com- puted 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.

Key words : planar elatica, rod dynamics, asymptotics

DOI: 10.1016/j.jsv.2013.10.009

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