Free vibration of isotropic half-elliptic plates of linearly varying thickness with clamped curved boundary

Two-dimensional boundary characteristic onltonormal polynomials are used in Rayleigh-Ritz method to study thc title problem. ln general, it is found that this method gives beller results than the other traditional method such as boundary integral equation methods, Spline methods, Chebyshev collocation method, Frobenius method etc. The thickness is taken to he linearly varying in two orthogonal directions. Comparisons in particular cases have been made with the existing results in the literature. Convergence of frequencies of at least up to live signilieant ligurcs is obtained. Results showing the variation in frequencies with taper parameters and aspect ratios are presented in tabular form. Mode shapes are shown using three-dimensional graphs of plates in displaced configurations