TY - JOUR
T1 - Vibrations of post-buckled rods: The singular inextensible limit
AU - Neukirch, Sébastien
AU - Frelat, Joël
AU - Goriely, Alain
AU - Maurini, Corrado
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: It is a pleasure to thank Olivier Thomas for discussions on Eq. (25). This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/1
Y1 - 2012/1
N2 - The small-amplitude in-plane vibrations of an elastic rod clamped at both extremities are studied. The rod 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 are no qualitative changes in the mode frequencies, other frequencies experience rapid variations after the buckling threshold, the thinner the rod, the more abrupt the variations. Eventually, a mismatch for half of the frequencies at buckling arises between the zero thickness limit of the extensible model and the inextensible model. © 2011 Elsevier Ltd. All rights reserved.
AB - The small-amplitude in-plane vibrations of an elastic rod clamped at both extremities are studied. The rod 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 are no qualitative changes in the mode frequencies, other frequencies experience rapid variations after the buckling threshold, the thinner the rod, the more abrupt the variations. Eventually, a mismatch for half of the frequencies at buckling arises between the zero thickness limit of the extensible model and the inextensible model. © 2011 Elsevier Ltd. All rights reserved.
UR - http://hdl.handle.net/10754/600169
UR - https://linkinghub.elsevier.com/retrieve/pii/S0022460X11007644
UR - http://www.scopus.com/inward/record.url?scp=80055072934&partnerID=8YFLogxK
U2 - 10.1016/j.jsv.2011.09.021
DO - 10.1016/j.jsv.2011.09.021
M3 - Article
SN - 0022-460X
VL - 331
SP - 704
EP - 720
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 3
ER -