NATURAL FREQUENCIES AND MODE SHAPES OF ELLIPTIC PLATES WITH BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS AS ASSUMED SHAPE FUNCTIONS

The natural frequencies and natural modes of vibration of uniform elli ptic plates with clamped, simply supported and free boundaries are inv estigated using the Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in the C artesian coordinate system are transformed into the modified polar coo rdinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection sha pes are classified into four basic categories, depending on their symm etrical or antisymmetrical properties about the major and minor axes o f the ellipse. The first six natural modes in each of the above catego ries are presented in the form of contour plots.