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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Nonlinear vibrations of non-uniform beams by the MTS asymptotic expansion method
TL;DR: In this paper, the frequency response curves of a non-uniform beam undergoing nonlinear oscillations are mined analytically by the multiple time scale method, which provides approximate, but accurate results.
Journal ArticleDOI
Free Vibration Analysis of Rotating Axially Functionally Graded Tapered Timoshenko Beams
TL;DR: In this article, the free vibration of rotating tapered Timoshenko beams (TBs) made of the axially functionally graded materials (FGMs) is studied, and the Chebyshev polynomials multiplied by the boundary functions are selected as the admissible functions in the Ritz minimization procedure.
Journal ArticleDOI
On vibration behavior of rotating functionally graded double-tapered beam with the effect of porosities:
Farzad Ebrahimi,Mahmud Hashemi +1 more
TL;DR: In this article, the free vibration characteristics of a rotating double-tapered functionally graded (FG) beam made of porous material were investigated using a semi-analytical technique called the differential transform method (DTM).
Journal ArticleDOI
Bending, buckling and vibration analysis of functionally graded non-uniform nanobeams via finite element method
TL;DR: In this paper, bending, buckling and vibration behaviors of functionally graded in depth direction non-uniform nanobeams are investigated in the framework of nonlocal strain gradient theory, where material variation is assumed through the thickness and modelled using exponential, sigmoid and power-law functions.
Journal ArticleDOI
Initial value method for free vibration of axially loaded functionally graded Timoshenko beams with nonuniform cross section
Dong Liang Sun,Xian-Fang Li +1 more
TL;DR: In this paper, free vibration of nonuniform axially functionally graded Timoshenko beams subjected to combined axially tensile or compressive loading is studied and an emphasis is placed on the effect of tip tilt on the free vibration.
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
Journal ArticleDOI
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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