Journal ArticleDOI
Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green's function method
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TLDR
In this paper, the quasi-Green's function has been employed to solve boundary value problem of free vibration of functionally graded annular plate with free outer edge and clamped, simply supported and free inner edges.Abstract:
Analysis and numerical results for the free axisymmetric and non-axisymmetric vibrations of functionally graded annular plates elastically supported on the ring support have been presented on the basis of classical plate theory. The quasi-Green's function has been employed to solve to boundary value problem of free vibration of functionally graded annular plate with free outer edge and clamped, simply supported and free inner edges. Additional properties of the quasi-Green's function were presented and discussed for the functionally graded annular plate. The influence of volume fraction index, core radius, selected boundary conditions, position and stiffness of ring supports on natural frequencies of an annular plate has been comprehensively studied. Singularities as the core and support radii shrink to zero are calculated for different values of volume fraction index and stiffness of the support. The quasi-Green's function method allows us to obtain universal non-linear multiparametric characteristic equations functional dependent on radius of core, volume fraction index, position and stiffness of any amount of elastic supports or other discrete elements without necessity considering new boundary value problem or find scaling factors. Additionally, the continuity conditions between the supports and plate can be omitted in the obtained solutions of boundary value problem. The presented investigation has not been reported previously. The exact frequencies of vibration presented in non-dimensional form can serve as benchmark values for researchers and engineers to validate their numerical methods applied in many fields of engineering such us mechanical, aeronautical or production engineering.read more
Citations
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Trigonometric Solution for the Bending Analysis of Magneto-Electro-Elastic Strain Gradient Nonlocal Nanoplates in Hygro-Thermal Environment
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Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule
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TL;DR: In this paper, free axisymmetric vibrations of functionally graded circular plates subjected to a non-linear temperature distribution along the thickness direction have been studied on the basis of classical plate theory.
Journal ArticleDOI
Free vibration analysis of discrete-continuous functionally graded circular plate via the Neumann series method
TL;DR: In this paper, the boundary value problem of free axisymmetric and nonaxisymetric vibrations of continuous and discrete-continuous functionally graded circular plate on the basis of the classical plate theory was solved using the Neumann series method.
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Natural frequency analysis of imperfect GNPRN conical shell, cylindrical shell, and annular plate structures resting on Winkler-Pasternak Foundations under arbitrary boundary conditions
Emad Sobhani,Mehmet Avcar +1 more
TL;DR: In this article , the Natural Frequencies (NFs) of perfect and imperfect Graphene Nanoplatelet Reinforced Nanocomposite (GNPRN) structures of revolution (conical and cylindrical shells and annular plate structures) resting on elastic foundations under general boundary conditions (BCs).
References
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Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates
G. N. Praveen,J. N. Reddy +1 more
TL;DR: In this paper, the static and dynamic response of the functionally graded material (fgm) plates are investigated by varying the volume fraction of the ceramic and metallic constituents using a simple power law distribution.
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Journal ArticleDOI
Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution
TL;DR: In this article, a generalization of the power-law distribution presented in literature is proposed for the volume fraction of conical shells, where materials are assumed to be isotropic and inhomogeneous through the thickness direction.