Journal ArticleDOI
Dynamic stiffness formulation and free vibration analysis of functionally graded beams
H. Su,J.R. Banerjee,C.W. Cheung +2 more
TLDR
In this article, a dynamic stiffness matrix is derived by relating the amplitudes of forces to those of the displacements at the beam ends, and the Wittrick-Williams algorithm is used to compute the natural frequencies and mode shapes.About:
This article is published in Composite Structures.The article was published on 2013-12-01. It has received 93 citations till now. The article focuses on the topics: Stiffness matrix & Direct stiffness method.read more
Citations
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Journal ArticleDOI
Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities
TL;DR: In this article, the effects of material property distribution, spring constants and porosity volume fraction on linear and nonlinear frequencies of functionally graded materials (FGMs) beams with porosity phases were investigated.
Journal ArticleDOI
Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories
TL;DR: In this article, the authors used the generalized displacement field of the Carrera Unified Formulation (CUF), including the Zig-Zag (ZZ) effect given by the Murakami's function.
Journal ArticleDOI
Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method
TL;DR: In this paper, the authors used the modified rule of mixture to approximate material properties of the FGM beams including the porosity volume fraction and the Timoshenko beam theory is used to form the coupled equations of motion for describing dynamic behavior of the beams.
Journal ArticleDOI
Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory
TL;DR: In this paper, a new higher-order shear deformation theory for buckling and free vibration analysis of isotropic and functionally graded (FG) sandwich beams is proposed.
Journal ArticleDOI
Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression
Jung Woo Lee,Jung Youn Lee +1 more
TL;DR: In this paper, an exact transfer matrix method was developed to analyze the free vibration characteristics of a functionally graded beam, which can be used to produce the natural frequencies and mode shapes for such problems in which material properties such as the elastic modulus and density are assumed to vary continuously along the height direction of the beam cross-section depending on a power-law form.
References
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Journal ArticleDOI
A general algorithm for computing natural frequencies of elastic structures
W. H. Wittrick,F. W. Williams +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.
Journal ArticleDOI
A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams
TL;DR: In this article, a unified approach for analyzing the static and dynamic behaviors of functionally graded beams (FGB) with the rotary inertia and shear deformation included is presented, where all material properties are arbitrary functions along the beam thickness.
Journal ArticleDOI
Free vibration analysis of functionally graded beams with simply supported edges
Metin Aydogdu,Vedat Taskin +1 more
TL;DR: In this article, the free vibration of simply supported FG beam was investigated and the governing equations were found by applying Hamilton's principle, and different higher order shear deformation theories and classical beam theories were used in the analysis.
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Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories
An analytical method for free vibration analysis of functionally graded beams
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Metin Aydogdu,Vedat Taskin +1 more