Free asymmetric transverse vibration of polar orthotropic annular sector plate with thickness varying parabolically in radial direction

Abstract

In the present paper, free asymmetric transverse vibrations of a non-uniform polar orthotropic annular sector plate, with parabolically varying thickness in the radial direction, have been studied on the basis of classical plate theory. The circular edges of the plate are elastically restrained against translation and rotation while the straight (radial) edges are simply-supported. Fourth-order linear differential equations with variable coefficients governing the motion have been solved by using the collocation interpolation technique with Chebyshev points as the interpolating nodes. Frequency parameters of the plate with flexible boundary conditions at the circular edges for some typical values of the taper parameters, the rigidity ratios and the radii ratio have been presented.