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

Free vibrations of beams with general boundary conditions

Finite element models in tissue mechanics and orthopaedic implant design.

The eigenvalue problem for the Laplace operator in two dimensions is classical in mathematics and physics. Nevertheless, computational methods for estimating the eigenvalues are still of much current interest, particularly in applications to acoustic and electromagnetic waveguides. Although our primary interest is with the computational methods, there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and, in addition, are of interest in themselves. These results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds. Some of the more powerful techniques available are illustrated by applying them to a model problem.

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Eigenvalues of the Laplacian in Two Dimensions

M.J. Maurizi

Papers

Recent research on vibrations of arch-type structures

Literature Review : Recent Research On Vibrations of Arch-Type Structures

Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end

A note on the dynamic analysis of an elastically restrained-free beam with a mass at the free end

On the analysis of waveguides of doubly-connected cross-section by the method of conformal mapping