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Revisiting Bresse-Timoshenko theory for beams

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Date Issued:
2015
Abstract/Description:
In this study, a variational derivation of the simpler and more consistent version of Bresse-Timoshenko beams equations, taking into account both shear deformation and rotary inertia in vibrating beams, is presented. Whereas Timoshenko gets his beam equations in terms of the equilibrium, the governing equations and the boundary conditions are here derived using the Hamilton’s principle. First, a list of the different energy contributions is established, including the shear effect and the rotary inertia. Second, the Hamilton’s principle is applied demanding the stationary of an appropriate functional, leading to two different equations of motion. The resolution of these equations provides the governing differential equation. It turns out that an additional term appears. The derived equations are intended for dynamic stability applications. Specifically, the parametric vibrations will be studied when the axial force varies periodically. This problem has important aerospace applications.
Title: Revisiting Bresse-Timoshenko theory for beams.
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Name(s): Hache, Florian
Elishakoff, Isaac
Challamel, Noël
Graduate College
Type of Resource: text
Genre: Poster
Date Created: 2015
Date Issued: 2015
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 1 p.
Language(s): English
Abstract/Description: In this study, a variational derivation of the simpler and more consistent version of Bresse-Timoshenko beams equations, taking into account both shear deformation and rotary inertia in vibrating beams, is presented. Whereas Timoshenko gets his beam equations in terms of the equilibrium, the governing equations and the boundary conditions are here derived using the Hamilton’s principle. First, a list of the different energy contributions is established, including the shear effect and the rotary inertia. Second, the Hamilton’s principle is applied demanding the stationary of an appropriate functional, leading to two different equations of motion. The resolution of these equations provides the governing differential equation. It turns out that an additional term appears. The derived equations are intended for dynamic stability applications. Specifically, the parametric vibrations will be studied when the axial force varies periodically. This problem has important aerospace applications.
Identifier: FA00005880 (IID)
Collection: FAU Student Research Digital Collection
Note(s): The Sixth Annual Graduate Research Day was organized by Florida Atlantic University’s Graduate Student Association. Graduate students from FAU Colleges present abstracts of original research and posters in a competition for monetary prizes, awards, and recognition.
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00005880
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.