Free vibration analysis of discrete-continuous functionally graded circular plate via the Neumann series method

Krzysztof Kamil Żur


The Neumann series method has been used for the first time to solve the boundary value problem of free axisymmetric and nonaxisymmetric vibrations of continuous and discrete-continuous functionally graded circular plate on the basis of the classical plate theory. The equation of motion and the general solution for a functionally graded circular plate with a very complex system of a discrete elements attached, such as concentric ring masses, elastic supports, rotational springs, and damping elements are presented for the first time. The particular continuous solutions to the defined differential equations are obtained as the Neumann power series rapidly, absolutely, and uniformly convergent to the exact eigenfrequencies for any physically justified values of the plate's parameters on the basis of the properties of the obtained closed-form kernels of the Volterra integral equations. The multiparametric nonlinear characteristic equations for plate with classical and nonclassical boundary conditions are defined and numerically solved to obtain the full spectrum of eigenfrequencies in a simple way. The effects of the position and stiffness of ring supports and of singularities as the radii of supports shrink to the center of the plate on the dimensionless eigenfrequencies of homogeneous and functionally graded circular plate with sliding support and elastic constraints are comprehensively studied and presented for the first time. The accuracy of the proposed low-computational-cost method is demonstrated by comparison of the numerical results with those available in the literature.
Author Krzysztof Kamil Żur (FME / DMACS)
Krzysztof Kamil Żur,,
- Department of Mechanics and Applied Computer Science
Journal seriesApplied Mathematical Modelling, ISSN 0307-904X, (N/A 100 pkt)
Issue year2019
Publication size in sheets1.15
Keywords in EnglishNeumann series, Volterra integral equations, Functionally graded material, Circular plate, Complex system of discrete elements
ASJC Classification2604 Applied Mathematics; 2611 Modelling and Simulation
Internal identifierROC 19-20
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreBUT score = 42.0, 17-06-2019, manual
Ministerial score = 100.0, 12-02-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.495; WoS Impact Factor: 2018 = 2.841 (2) - 2018=3.112 (5)
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