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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Journal ArticleDOI
Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume
Joon Kyu Lee,Byoung Koo Lee +1 more
TL;DR: In this paper, the transverse free vibration of axially functionally graded (AFG) cantilever columns under the influence of axial compressive load was investigated. But the columns possessing a regular polygon in their cross-section are tapered and their material properties vary along the axis of the column.
Journal Article
On the response of a simply supported non-uniform rayleigh beam to travelling distributed loads
S. T. Oni,E. Ayankop-Andi +1 more
TL;DR: In this paper, a simply supported non-uniform Rayleigh beam under traveling distributed loads is investigated and the solution of the problem, the Galerkin's Weighted Residual (GWR) method and Struble's asymptotic technique are employed.
Proceedings ArticleDOI
1:6 Internal Resonance in CMOS-MEMS Multiple-Stepped CC-Beam Resonators
TL;DR: In this paper , the Euler-Bernoulli beam equation was transformed into algebraic expressions based on the Adomian decomposition method (ADM), and then the initial combination using contour plots for the following fine tune in FEA.
Journal ArticleDOI
Design optimization of FGM beam in stability problem
TL;DR: In this paper, an optimized structural topology of the simply supported beam made from functionally graded material (FGM) enabling achievement of a maximum buckling load was defined and solved by using the homogenization method, and the target functions belong to the class of piece-wise continuous functions.
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.
Journal ArticleDOI
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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