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Nonlinear stability analysis of rotational dynamics and transversal vibrations of annular circular thin plates functionally graded in radial direction by differential quadrature
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In this article, the nonlinear analysis of free vibrations, dynamic stability, and rotational dynamics of rotating annular circular thin plates, made of functionally graded material (FGM), is studied.Abstract:
In this article, the nonlinear analysis of free vibrations, dynamic stability, and rotational dynamics of rotating annular circular thin plates, made of functionally graded material (FGM), is studied. Based on classical plate theory, von Karman’s nonlinear plate theory, and assuming the FGM mechanical properties vary in the radial direction, the governing equations of motion are obtained by direct use of Newton’s laws. A 1-D differential quadrature is used to solve the governing equations determining the natural frequencies, corresponding transverse mode shapes, and the critical speeds of rotation. The accuracy and convergence of the method are studied by comparing the results with the similar results whenever available in the literature. The influence of different parameters such as inner-to-outer radii ratio, thickness-to-outer radius ratio, graded index, angular velocity of the plate, and different boundary conditions on the natural frequencies of FG rotating plate are demonstrated by numerical example...read more
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Journal ArticleDOI
Free Vibration Analysis of Rotating Functionally Graded Annular Disc of Variable Thickness Using Generalized Differential Quadrature Method
TL;DR: In this article, free vibration analysis of rotating annular disc made of functionally graded material (FGM) with variable thickness is presented, where elasticity modulus, density and thickness of the disc are assumed to vary radially according to a power low function.
Journal ArticleDOI
Free vibration behavior of rotating bidirectional functionally-graded micro-disk for flexural and torsional modes in thermal environment
Suman Pal,Debabrata Das +1 more
TL;DR: In this article, a mathematical model for investigating the asymmetric as well as the axisymmetric free vibration behavior of a rotating annular micro-disk is presented for the first time, where the disk is assumed to be functionally-graded along the radial and thickness directions, and is considered to be operating in high-temperature environment.
Journal ArticleDOI
Elastic Stress Analysis of Rotating Functionally Graded Annular Disk of Variable Thickness Using Finite Difference Method
TL;DR: In this article, an analysis of rotating variable thickness annular disk made of functionally graded material (FGM) is presented, and the effects of the graded index, thickness variation, and rotating speed on the stresses and deformation are evaluated.
Journal ArticleDOI
Vibration analysis of a rotating variable thickness bladed disk for aircraft gas turbine engine using generalized differential quadrature method
TL;DR: In this article, free vibration analysis of rotating variable thickness annular bladed disk suitable to be used in aircraft gas turbine engine is investigated, and the numerical generalized differential analysis is performed.
Journal ArticleDOI
Nonlinear vibration and stability of a moving printing web with variable density based on the method of multiple scales
TL;DR: An axially moving printing web with variable density in a printing process causes a geometric nonlinear vibration, and a non linear vibration system is established using the von Karman nonlinear pla... as discussed by the authors.
References
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Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Journal ArticleDOI
Theory of Elasticity (3rd ed.)
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Differential Quadrature and Its Application in Engineering
TL;DR: A Differential Quadrature Hierarchical Finite Element Method (DQEEM) based on Bernstein Polynomials is proposed in this paper for the analysis of doubly-curvel shell structures.
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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Energy principles and variational methods in applied mechanics
TL;DR: In this paper, the authors present a review of the work, energy, and variational calculus of solid mechanics and their application in the analysis of plate models. But their focus is on the theory and analysis of plates.
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