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
Analysis of axially temperature-dependent functionally graded carbon nanotube reinforced composite plates
Ahmed Amine Daikh,Mohammed Sid Ahmed Houari,Mohamed Oujedi Belarbi,Snehashish Chakraverty,Mohamed A. Eltaher,Mohamed A. Eltaher +5 more
TL;DR: In this article, the static buckling stability and static deflection of axially single-walled (SW) functionally graded (FG) carbon nanotubes reinforced composite (CNTRC) plates with temperature-dependent material properties and graded by different functions were investigated.
Journal ArticleDOI
Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate
TL;DR: In this article, the free vibration of a rotating variable thickness two-directional FG circular microplate is studied and the solution of equations is presented utilizing the differential quadrature method, showing that the increase of the size dependency would lead to the reduction of the non-dimensional natural frequency as well as the critical angular velocity.
Journal ArticleDOI
Dynamics of an axially functionally graded beam under axial load
TL;DR: In this article, the dynamics of a simply supported beam under axial time-dependent load was considered and the motion equations were deduced from the equilibrium in deformed configuration and no restriction was made on the amplitude of the transversal displacement, but that naturally imposed by the inextensibility assumption that is adopted in the present study.
Journal ArticleDOI
Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams
TL;DR: Free vibration of functionally graded (FG) beams is presented based on a newly proposed shear deformation theory, PESDBT, which exactly satisfies the transverse stress boundary conditions on the bottom and top surfaces of the beam.
Journal ArticleDOI
Free vibration of non-uniform axially functionally graded beams using the asymptotic development method
Dongxing Cao,Yanhui Gao +1 more
TL;DR: In this paper, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform axially functionally graded (AFG) beams with different boundary conditions.
References
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Journal ArticleDOI
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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