Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials
TLDR
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.read more
Citations
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Size dependent nonlinear free vibration of axially functionally graded tapered microbeams using finite element method
TL;DR: In this paper, a nonlinear finite element formulation of axially functionally graded (AFG) tapered microbeams is presented, which is based on the modified couple stress and Euler-Bernoulli beam theory.
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An efficient approach for in-plane free and forced vibrations of axially functionally graded parabolic arches with nonuniform cross section
TL;DR: In this paper, an effective approach for analyzing the in-plane free and forced vibration responses of axially functionally graded (AFG) parabolic arches with a nonuniform cross section is presented.
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Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory
Yong Huang,Meng Zhang,Haiwu Rong +2 more
TL;DR: In this article, the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated and the coupled governing equations were converted into a system of linear algebraic equations.
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On the vibrations of axially graded Rayleigh beams under a moving load
TL;DR: In this paper, the forced and free vibrations of axially functionally graded (AFG) Rayleigh and Euler-Bernoulli (EB) beams subjected to a moving load are studied and compared, aiming at performance enhancement of transportation systems.
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Simple formulas for the natural frequencies of non-uniform cables and beams
TL;DR: In this paper, the authors used the asymptotic development method to obtain approximate analytical expressions for the natural frequencies of non-uniform cables and beams, by manipulating the first-order terms, they obtained the mechanical properties (mass, stiffness, etc.) of the equivalent uniform cables and beam having the same (up to the first order) frequencies of the nonuniform one.
References
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Differential Quadrature Method in Computational Mechanics: A Review
Charles W. Bert,Moinuddin Malik +1 more
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.
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Differential quadrature and long-term integration
Richard Bellman,John Casti +1 more
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A new beam finite element for the analysis of functionally graded materials
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.
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Free vibration characteristics of a functionally graded beam by finite element method
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.
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