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Free vibration of a rod undergoing finite strain
Amirkabir University, Iran.
Aalto University, Finland.ORCID iD: 0000-0001-8515-9907
2012 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 382, no 1Article in journal (Refereed) Published
Abstract [en]

The finite strain longitudinal free vibration of a rod is studied. Utilizing second Piola-Kirchhoff stress and Green strain tensors, the equation of motion is written in terms of displacement in reference configuration. Three different types of homogenous boundary conditions may be considered for the rod, leading to three nonlinear eigenvalue problems. The series solutions with three terms satisfying the boundary conditions are utilized and the relationships between amplitudes of vibration are obtained by means of the Galerkin method. The backbone curves are drawn and the internal resonance between different modes of vibration is analyzed.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2012. Vol. 382, no 1
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kau:diva-65048DOI: 10.1088/1742-6596/382/1/012011ISI: 000309290500011OAI: oai:DiVA.org:kau-65048DiVA: diva2:1154081
Available from: 2017-11-01 Created: 2017-11-01 Last updated: 2017-11-01Bibliographically approved

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Publisher's full texthttp://stacks.iop.org/1742-6596/382/i=1/a=012011

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