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A. Di Blasio

Bio: A. Di Blasio is an academic researcher from University of Western Ontario. The author has contributed to research in topics: Orthogonal polynomials & Orthotropic material. The author has an hindex of 1, co-authored 1 publications receiving 165 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, orthogonal polynomial functions are used in the Rayleigh-Ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates.

169 citations


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Book
16 Dec 2008
TL;DR: Vibration of Plates as discussed by the authors provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates, including boundary characteristically orthogonal polynomials (BCOPs).
Abstract: Plates are integral parts of most engineering structures and their vibration analysis is required for safe design. Vibration of Plates provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates. Reflecting the author's more than 15 years of original research on plate vibration, this book presents new methodologies and demonstrates their effectiveness by providing comprehensive results. The text also offers background information on vibration problems along with a discussion of various plate geometries and boundary conditions, including the new concepts of Boundary Characteristic Orthogonal Polynomials (BCOPs).

465 citations

Journal ArticleDOI
TL;DR: In this paper, the Rayleigh-Ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges, and a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions is developed.

212 citations

Journal ArticleDOI
TL;DR: In this paper, the displacement solution is expressed as a two-dimensional Fourier series supplemented with several one-dimensional series, which is capable of representing any function (including the exact displacement solution) whose third-order partial derivatives are (required to be) continuous over the area of the plate.

184 citations

Journal ArticleDOI
TL;DR: In this paper, the authors used the four variable refined plate theory for free vibration analysis of plates made of functionally graded materials with an arbitrary gradient, where the material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents with a given gradient.
Abstract: The novelty of this paper is the use of four variable refined plate theory for free vibration analysis of plates made of functionally graded materials with an arbitrary gradient. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents with an arbitrary gradient. The equation of motion for FG rectangular plates is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. In the case of FG clamped plates, the free vibration frequencies are obtained by applying the Ritz method where the four displacement components are assumed as the series of simple algebraic polynomials. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of FG plates. Illustrative examples are given also to show the effects of varying gradients, aspect ratios, and thickness to length ratios on the free vibration of the FG plates.

183 citations

Journal ArticleDOI
TL;DR: In this article, a set of mathematically complete two-dimensional polynomials are assumed in the displacement and rotational functions to approximate the appropriate mode shapes, and the energy function derived using Mindlin's plate theory is minimized using the Rayleigh-Ritz procedure which leads to the governing eigenvalue equations.

164 citations