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Journal ArticleDOI

Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials

01 Jul 2012-Applied Mathematical Modelling (Elsevier)-Vol. 36, Iss: 7, pp 3094-3111
TL;DR: In this paper, the free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams were studied through solving the governing differential equations of motion. But, the convergence rate of the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, and a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence of the method.
About: This article is published in Applied Mathematical Modelling.The article was published on 2012-07-01 and is currently open access. It has received 189 citations till now. The article focuses on the topics: Differential equation.
Citations
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Journal ArticleDOI
TL;DR: In this article, the vibration response of non-homogenous and non-uniform microbeams is investigated in conjunction with Bernoulli-Euler beam and modified couple stress theory, where boundary conditions of the microbeam are considered as fixed at one end and free at the other end.

321 citations

Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions is performed based on the classical and first order shear deformation beam theories.
Abstract: Present investigation is concerned with the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions. The analysis is based on the classical and first order shear deformation beam theories. Material properties of the beam vary continuously in the thickness direction according to the power-law exponent form. Trial functions denoting the displacement components of the cross-sections of the beam are expressed in simple algebraic polynomial forms. The governing equations are obtained by means of Rayleigh–Ritz method. The objective is to study the effects of constituent volume fractions, slenderness ratios and the beam theories on the natural frequencies. To validate the present analysis, comparison studies are also carried out with the available results from the existing literature.

258 citations

Journal ArticleDOI
TL;DR: In this paper, the free vibrations and buckling analysis of nanocomposite Timoshenko beams reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation are investigated.

244 citations

Journal ArticleDOI
TL;DR: In this article, free and forced vibration of a bi-directional functionally graded (BDFG) Timoshenko beam under the action of a moving load was investigated by means of Lagrange equations based on TBT and Euler-Bernoulli beam theory.

196 citations

Journal ArticleDOI
TL;DR: In this paper, the forced vibration behavior of carbon-nanotube reinforced composite (CNTRC) beams, uniform distribution (UD) and three types of functionally graded (FG) distribution patterns of SWCNT reinforcements are considered.

177 citations

References
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Journal ArticleDOI
TL;DR: The differential quadrature method (DQM) as discussed by the authors is a numerical solution technique for initial and/or boundary problems, which was developed by the late Richard Bellman and his associates in the early 70s.
Abstract: The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

1,217 citations

Journal ArticleDOI
TL;DR: In this article, a beam element based on first-order shear deformation theory is developed to study the thermoelastic behavior of functionally graded beam structures, and the stiffness matrix has super-convergent property and the element is free of shear locking.

521 citations

Journal ArticleDOI
TL;DR: In this paper, the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law are presented. But the model is more effective for replacing the non-uniform geometrical beam with axially and transversely uniform geometrically graded beam.

458 citations