Modes for the coupled Timoshenko model with a restrained end

The modes of the second-order Timoshenko system for the displacement and rotation of a fixed beam with a restrained end at the left are formulated in terms of a fundamental spatial response. This is done without decoupling the system into fourth-order scalar equations. The restrained end leads to ti...

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Bibliographic Details
Published in:Journal of sound and vibration 2006-10, Vol.296 (4), p.1053-1058
Main Authors: Claeyssen, J.R., Costa, S.N.J.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
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Summary:The modes of the second-order Timoshenko system for the displacement and rotation of a fixed beam with a restrained end at the left are formulated in terms of a fundamental spatial response. This is done without decoupling the system into fourth-order scalar equations. The restrained end leads to time–space boundary conditions which introduce the frequency as a parameter into the system of equations for determining the modes. These equations involve first-order derivatives and, consequently, the modes are determined by solving a non-conservative differential system. This modal differential equation is discussed in terms of a fundamental matrix response. It is determined by applying a closed formula that was obtained by the first author and involves the characteristic polynomial of the modal differential equation.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2006.02.025