3-D Free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM)

In this paper, the free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using the differential quadrature method for different boundary conditions including simply supported–clamped, clamped–clamped and free–clamped ends is...

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Bibliographic Details
Published in:Acta mechanica 2012, Vol.223 (1), p.43-62
Main Authors: Yas, M. H., Tahouneh, V.
Format: Article
Language:English
Subjects:
Annular plates
Boundary conditions
Classical and Continuum Physics
Control
Dynamical Systems
Elasticity
Engineering
Engineering Thermodynamics
Foundations
Free vibration
Functionally gradient materials
Heat and Mass Transfer
Laws, regulations and rules
Mathematical models
Mechanical engineering
Mechanical properties
Methods
Quadratures
Solid Mechanics
Theoretical and Applied Mechanics
Three dimensional
Vibration
Vibration analysis
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Summary:In this paper, the free vibration of functionally graded annular plates on elastic foundations, based on the three-dimensional theory of elasticity, using the differential quadrature method for different boundary conditions including simply supported–clamped, clamped–clamped and free–clamped ends is investigated. The foundation is described by the Pasternak or two-parameter model. A semi-analytical approach composed of differential quadrature method (DQM) and series solution are adopted to solve the equations of motions. The material properties change continuously through the thickness of the plate, which can vary according to power law, exponentially or any other formulations in this direction. The fast rate of convergence of the method is demonstrated, and comparison studies are carried out to establish its very high accuracy and versatility. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-011-0543-6