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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On the study of element modal strain energy sensitivity for damage detection of functionally graded beams
TL;DR: In this paper, a modeling framework based on element modal strain energy sensitivity is developed for identifying damage of functionally graded beams, which can give a valid way to accurately detect the damage of beam-like structures, also has excellent resistance to measurement noise.
Journal ArticleDOI
The vibration analysis of the elastically restrained functionally graded Timoshenko beam with arbitrary cross sections
TL;DR: In this paper, an investigation on the free vibration of the beam with material properties and cross section varying arbitrarily along the axis direction is studied based on the so-called Spectro-G...
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Free high-frequency vibrations of nonlocally elastic beam with varying cross-section area
TL;DR: In this article, the boundary value problem is solved in the form of superposition of the outer expansion and edge effect integrals with high variability along the beam axis, and a clamped nanobeam with a shape matching to the shape of a slab waveguide in a photonic crystal beam laser is considered.
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Bi-directional functionally graded thin-walled non-prismatic Euler beams of generic open/closed cross section Part II: Static, stability and free vibration studies
TL;DR: In this paper, deflections, buckling loads, natural frequencies and the corresponding mode shapes and forms for BDFG thin-walled tapered beams of generic open/closed/open-closed sections are examined using the finite element method.
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A Unified Approach for Out-of-Plane Forced Vibration of Axially Functionally Graded Circular Rods
TL;DR: In this article, the Complementary Functions Method (CFM) was applied to axially functionally graded (AFG) circular rods with different variations of material properties along the rod axis.
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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