Free vibration of a cantilever annular sector plate with curved radial edges

An analysis is presented for the free vibration of a cantilever annular sector plate with curved radial edges. For this purpose, the plate is transformed into a regular sector plate with unit outer radius by a transformation of variables. The transverse deflection of the transformed plate is expressed in a power series, the dynamical energies of the plate are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to annular sector plates with symmetrically or unsymmetrically curved radial edges, and the natural frequencies and the mode shapes are calculated numerically up to higher modes. The eigenvalues obtained here are compared with experimental values of other authors.