The Mathematical Institute, University of Oxford, Eprints Archive

Frequency jumps in the planar vibrations of an elastic beam

Neukirch, S. and Frelat, J. and Goriely, A. and Maurini, C. (2011) Frequency jumps in the planar vibrations of an elastic beam. Journal of Sound and Vibration . (Submitted)

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Abstract

The small amplitude transverse vibrations of an elastic beam clamped at both extremities are studied. The beam is modeled as an extensible, shearable planar Kirchhoff elastic rod under large displacements and rotations, and the vibration frequencies are computed both analytically and numerically as a function of the loading. Of particular interest is the variation of mode frequencies as the load is increased through the buckling threshold. While for some modes there is no qualitative changes in the mode frequencies, other modes experience rapid variations after the buckling threshold. For slender beams, these variations become stiffer, eventually resulting in a discontinuous jump of frequency at buckling, in the limit of inextensible, unshearable beams.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1425
Deposited By:Peter Hudston
Deposited On:11 Nov 2011 07:50
Last Modified:09 Feb 2012 13:56

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