Abstract
The natural frequencies and mode shapes of Timoshenko beams of constant cross section, continuously variable cross section, and cross sections with step changes in properties for numerous combinations of boundary conditions and boundary and in-span attachments are obtained. The in-span and boundary attachments include springs, concentrated masses, and single degree-of-freedom systems. The responses of these systems to externally applied forces to its interior and the natural frequencies of elastically connected beams, which have been used to model double-wall carbon nanotubes, are determined. For all numeral results, comparisons are made to the numerical results obtained from the Euler-Bernoulli theory and regions of applicability are inferred. In this chapter, an improved beam theory called the Timoshenko beam theory is introduced. This theory includes the effects of transverse shear and rotary inertia of the beam’s cross section.
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© 2012 Springer Science+Business Media B.V.
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Magrab, E.B. (2012). Timoshenko Beams. In: Vibrations of Elastic Systems. Solid Mechanics and Its Applications, vol 184. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2672-7_5
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DOI: https://doi.org/10.1007/978-94-007-2672-7_5
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