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On the Accuracy of Timoshenko's Beam Theory
Journal of the Engineering Mechanics Division, 1968The deflection and rotation which appear in Timoshenko's beam theory may be defined either (a) in terms of the deflection and rotation of the centroidal element of a cross-section or (b) in terms of average values over the cross-section. By consideration of an example for which a theoretically exact solution is available it is shown that the Timoshenko
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Thick/Slender Plane Beams. Timoshenko Theory
2013This chapter studies Timoshenko plane beam elements. Timoshenko beam theory accounts for the effect of transverse shear deformation. Timoshenko beam elements are therefore applicable for “thick” beams \(\left(\lambda = \frac{L}{h} 100)\) where this influence is irrelevant [Ti].
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A theory for transverse vibrations of the timoshenko beam
Journal of Applied Mathematics and Mechanics, 1993The author studies the Timoshenko equation which describes transverse vibrations of an elastic beam taking into account rotational inertia and transverse shear deformation. For each spatial shape of the vibrations, this equation gives two frequency values, i.e. it predicts two series of frequencies, hence two modes of vibration.
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On the Use of Deflection Components in Timoshenko Beam Theory
Journal of Applied Mechanics, 1997The growing use of variational principles encouraged researchers to obtain the governing equations and boundary conditions directly in terms of the bending deflection and shear deflection instead of making the substitutions for the total deflection and the rotation.
Lee, K. H., Wang, C. M.
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On the shear coefficient in Timoshenko's beam theory
Journal of Sound and Vibration, 1983Abstract Some existing formulations for the shear coefficient in Timoshenko's beam theory are discussed, especially through evaluation of the accuracy to which natural frequencies of simply supported, prismatic, thin walled beams can be obtained. The main conclusion drawn is that if a consistent expression for the shear coefficient, such as those ...
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Variational principle of partial-interaction composite beams using Timoshenko's beam theory
International Journal of Mechanical Sciences, 2012Abstract Based on the kinematic assumptions of Timoshenko's beam theory, this paper formulates the principle of virtual work and reciprocal theorem of work for the partial-interaction composite beams. Then the principle of minimum potential energy and minimum complementary energy are derived and proved. The variational principles for the frequency of
Rongqiao Xu, Guannan Wang
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Distributed Control of Laminated Beams: Timoshenko Theory vs. Euler-Bernoulli Theory
Journal of Intelligent Material Systems and Structures, 1997In this paper, the governing equations and boundary conditions of laminated beamlike components of smart structures are reviewed. Sensor and actuator layers are included in the beam so as to facilitate vibration suppression. Two mathematical models, namely the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model, are ...
Osama J. Aldraihem +2 more
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Buckling of Multiwalled Carbon Nanotubes Using Timoshenko Beam Theory
Journal of Engineering Mechanics, 2006A Timoshenko beam model is presented in this paper for the buckling of axially loaded multiwalled carbon nanotubes surrounded by an elastic medium. Unlike the Euler beam model, the Timoshenko beam model allows for the effect of transverse shear deformation which becomes significant for carbon nanotubes with small length-to-diameter ratios. These stocky
Zhang, Y.Y., Wang, C.M., Tan, V.B.C.
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Modeling and Stability Analysis of a Flexible Rotor Based on the Timoshenko Beam Theory
Acta Mechanica Solida Sinica, 2020Yongwang Zhang, Xiaodong Yang, Wei Zhang
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