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 language||English (US)|
|Number of pages||9|
|Journal||Journal of Sound and Vibration|
|State||Published - Feb 2014|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.