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
Two-Dimensional Free Vibration Analysis of Axially Functionally Graded Beams Integrated with Piezoelectric Layers: An Piezoelasticity Approach
Agyapal Singh,Poonam Kumari +1 more
TL;DR: In this article, a two-dimensional (2D) piezoelasticity-based analytical solution is developed for free vibration analysis of axially functionally graded (AFG) beams integrated with piezoelectri...
Journal ArticleDOI
Generating mechanism of mode localization for the beams and its application in the passive vibration control
TL;DR: In this paper, an axially functionally graded design method is proposed to adjust the configuration of mode localization for the structures, which can suppress the vibration of a certain span of the beam and enlarge the length of the controlled part.
Book ChapterDOI
Functionally Graded Beams
TL;DR: In this article, free vibration of functionally graded (FG) beams based on various shear deformation beam theories is considered and alternate forms of newly proposed deformation theories are also included, based on certain assumptions.
Journal ArticleDOI
A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings
Amlan Paul,Debabrata Das +1 more
TL;DR: In this article, the non-linear postbuckling load-deflection behavior of a tapered functionally graded material beam for different in-plane thermal loadings was studied for two different thermal loads.
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.
Journal ArticleDOI
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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