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 paper, Bernoulli-Euler beam bending theory is used to infer the Young's Modulus, and the validity of such an approach using a simple elastic sheet model and show that at the nanotube scale the assumptions of continuum mechanics must be carefully respected to obtain reasonable results.
311 citations
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TL;DR: In this article, the nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory and Timoshenko beam theory was investigated, and a detailed parametric study was conducted to study the influences of the non-local parameter, temperature change and external electric voltage on the size-dependent non-linear vibration characteristics of the PNE.
307 citations
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TL;DR: In this article, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams, and the neutral surface position for such beams in which the material properties vary in the thickness direction is determined.
Abstract: In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (ez ≠ 0) is also included in the present theory Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors The neutral surface position for such beams in which the material properties vary in the thickness direction is determined Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses
307 citations
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TL;DR: In this paper, the free and forced vibration characteristics of functionally graded (FG) porous beams with non-uniform porosity distribution whose elastic moduli and mass density are nonlinearly graded along the thickness direction were investigated.
305 citations
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TL;DR: In this paper, nonlocal elasticity and Timoshenko beam theory are implemented to investigate the stability response of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium.
Abstract: Nonlocal elasticity theory is a popular growing technique for the mechanical analyses of MEMS and NEMS structures. The nonlocal parameter accounts for the small-size effects when dealing with nano-size structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to investigate the stability response of SWCNT embedded in an elastic medium. For the first time, both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the (SWCNT) with the surrounding elastic medium. A differential quadrature approach is utilized and numerical solutions for the critical buckling loads are obtained. Influences of nonlocal effects, Winkler modulus parameter, Pasternak shear modulus parameter and aspect ratio of the SWCNT on the critical buckling loads are analyzed and discussed. The present study illustrates that the critical buckling loads of SWCNT are strongly dependent on the nonlocal small-scale coefficients and on the stiffness of the surrounding medium.
302 citations