Topic
Timoshenko beam theory
About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.
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TL;DR: In this article, the authors derived the governing equations for linear vibration of a rotating Timoshenko beam by the d&Alembert principle and the virtual work principle and used the consistent linearization of the fully geometrically non-linear beam theory to solve the natural frequency of the rotating beam.
139 citations
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TL;DR: In this paper, a generalized Bernoulli-Euler and Timoshenko sandwich beam models are derived by means of a computational homogenization technique and two additional length scale parameters involved in the models are validated by matching the lattice response in benchmark problems for static bending and free vibrations calibrating the strain energy and inertia gradient parameters, respectively.
139 citations
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TL;DR: In this paper, a unified size-dependent high-order beam model which contains various higher-order shear deformation beam models as well as Euler-Bernoulli and Timoshenko beam models is developed to study the simultaneous effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory.
138 citations
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SIDI1
TL;DR: In this article, an elastic, rectangular, and simply supported, sigmoid functionally graded material (S-FGM) beam of thick thickness subjected to uniformly distributed transverse loading has been investigated.
138 citations
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TL;DR: In this paper, the authors pre-sents the deflection and stress resultants of single-span Timoshenko beams, with general loading and boundary conditions, in terms of the corresponding Euler-Bernoulli beam solutions.
Abstract: The Timoshenko beam theory is an extension of the Euler-Bernoulli beam theory to allow for the effect of transverse shear deformation. This more refined beam theory relaxes the normality assumption of plane sections that remain plane and normal to the deformed centerline. The relaxation takes the form of allowing an additional rotation to the bending slope, and thus admits a nonzero shear strain. This paper pre-sents the deflection and stress resultants of single-span Timoshenko beams, with general loading and boundary conditions, in terms of the corresponding Euler-Bernoulli beam solutions. These exact relationships allow engineering designers to readily obtain the bending solutions of Timoshenko beams from the familiar Euler-Bernoulli solutions without having to perform the more complicated flexural–shear-deformation analysis.
137 citations