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, a quasi-3D beam theory for buckling and free vibration analysis of functionally graded (FG) sandwich beams with various boundary conditions using a Ritz-type analytical solution is presented.
85 citations
TL;DR: In this article, a general beam theory has been proposed which is applicable to all regular prismatic systems and is used to find the appropriate beam-like flexibilities for trusses.
84 citations
TL;DR: In this paper, the beam models are obtained by assuming higher-order (up to fourth) expansions for the unknown displacement variables over the cross-section, which allows bending/torsion modes to be coupled and capture any other vibration modes that require in-plane and warping deformation of the beam sections to be detected.
Abstract: This work extends advanced beam models to carry out a more accurate free-vibration analysis of conventional (straight, or with sweep/dihedral angles) and joined wings. The beam models are obtained by assuming higher-order (up to fourth) expansions for the unknown displacement variables over the cross-section. Higher-order terms permit bending/torsion modes to be coupled and capture any other vibration modes that require in-plane and warping deformation of the beam sections to be detected. Classical beam analyses, based on the Euler- Bernoulli and on Timoshenko beam theories, are obtained as particular cases. Numerical solutions are obtained by using the finite element (FE) method, which permits various boundary conditions and different wing/section geometries to be handled with ease. A comparison with other shell/solid FE solutions is given to examine the beam model. The capability of the beam model to detect bending, torsion, mixed and other vibration modes is shown by considering conventional and joined wings with different beam axis geometries as well as with various sections (compact, plate-type, thin-walled airfoil-type). The accuracy and the limitations of classical beam theories have been highlighted for a number of problems. It has been concluded that the proposed beam model could lead to quasi-three-dimensional dynamic responses of classical and nonclassical beam geometries. It provides better results than classical beam approaches, and it is much more computationally efficient than shell/solid modeling approaches. DOI: 10.1061/(ASCE)AS.1943-5525.0000130. © 2012 American Society of Civil Engineers. CE Database subject headings: Beams; Finite element method; Vibration; Thin-wall structures; Aerospace engineering. Author keywords: Beams; Finite element method; Higher-order theories; Vibration; Thin-walled structures; Aerospace engineering.
84 citations
TL;DR: In this paper, a nonlocal Timoshenko beam model is developed to study the nonlinear vibrations of embedded multiwalled carbon nanotubes (MWCNTs) in thermal environments.
Abstract: A nonlocal Timoshenko beam model is developed to study the nonlinear vibrations of embedded multiwalled carbon nanotubes (MWCNTs) in thermal environments. The Timoshenko beam model, unlike its Bernoulli–Euler beam counterpart, takes the effects of transverse shear deformation and rotary inertia into consideration. These effects become more significant for short-length nanotubes that are normally encountered in applications such as nanoprobes. The nested nanotubes are coupled via the van der Waals (vdW) force that considers interactions between adjacent and non-adjacent nested nanotubes. The set of coupled nonlinear equations are then analytically solved using the harmonic balance approach. The effects of small-scale parameter, nanotube geometries, temperature change and the elastic medium are investigated.
84 citations
TL;DR: In this article, the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition, was studied, and it was shown that for certain polynomial variations of the material mass density, elastic modulus and shear modulus along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients.
Abstract: In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.
84 citations