Axisymmetric vibrations of annular plates of variable thickness

Abstract

Free axisymmetric vibrations of annular plates of variable thickness have been studied on the basis of the classical theory of plates. The Chebyshev collocation method has been employed to solve the differential equation governing the transverse motion of such plates. The displacement of the plate element is expressed as a Chebyshev polynomial in terms of the radial co-ordinate. Frequencies and mode shapes have been computed for different values of taper constant and radii ratio, for the first two modes of vibration of a plate with a linearly varying thickness, treated as an example.