Vibration of elliptic plates using characteristic orthogonal polynomials in the Rayleigh-Ritz method

Abstract

The vibrations of uniform elliptic plates with clamped, simply-supported and free boundary conditions are investigated using boundary-characteristic orthogonal polynomials in the Rayleigh-Ritz method. Deflection shapes in the form of products of functions in the radial coordinate and the angular coordinate, respectively, using modified polar coordinates, are assumed. Boundary-characteristic orthogonal polynomials are used in the radial direction, whereas trigonometric functions are employed along the angular coordinate. Six natural frequencies corresponding to each of the four basic categories of natural modes, such as symmetric-symmetric, symmetric-antisymmetric, antisymmetric-symmetric, antisymmetric-antisymmetric modes about the major and minor axes of the ellipse, are presented.