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).

Vibration of Plates

Vibration analysis of rectangular plates with general elastic boundary supports

An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports

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.

A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient

Transverse vibration of thick rectangular plates—I. Comprehensive sets of boundary conditions

On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates

A. Di Blasio

Papers

On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates