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

Handle URI:
http://hdl.handle.net/10754/599641
Title:
Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions
Authors:
Neukirch, Sébastien; Goriely, Alain; Thomas, Olivier
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.
Citation:
Neukirch S, Goriely A, Thomas O (2014) Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions. Journal of Sound and Vibration 333: 962–970. Available: http://dx.doi.org/10.1016/j.jsv.2013.10.009.
Publisher:
Elsevier BV
Journal:
Journal of Sound and Vibration
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Feb-2014
DOI:
10.1016/j.jsv.2013.10.009
Type:
Article
ISSN:
0022-460X
Sponsors:
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. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledged.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorNeukirch, Sébastienen
dc.contributor.authorGoriely, Alainen
dc.contributor.authorThomas, Olivieren
dc.date.accessioned2016-02-28T06:06:29Zen
dc.date.available2016-02-28T06:06:29Zen
dc.date.issued2014-02en
dc.identifier.citationNeukirch S, Goriely A, Thomas O (2014) Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions. Journal of Sound and Vibration 333: 962–970. Available: http://dx.doi.org/10.1016/j.jsv.2013.10.009.en
dc.identifier.issn0022-460Xen
dc.identifier.doi10.1016/j.jsv.2013.10.009en
dc.identifier.urihttp://hdl.handle.net/10754/599641en
dc.description.abstractIn-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.en
dc.description.sponsorshipThis 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. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledged.en
dc.publisherElsevier BVen
dc.titleSingular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditionsen
dc.typeArticleen
dc.identifier.journalJournal of Sound and Vibrationen
dc.contributor.institutionCNRS Centre National de la Recherche Scientifique, Paris, Franceen
dc.contributor.institutionUniversite Pierre et Marie Curie, Paris, Franceen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionENSAM - Paris, Paris, Franceen
kaust.grant.numberKUK-C1-013-04en
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