An analytic model for the frequencies of resonance of rectangular plates of variable curvature and thickness

A flexible and powerful model is developed for the frequencies of resonance of a curved plate with a rectangular planform and arbitrary but smoothly varying curvature and thickness. The model is a classical one. The curvature and thickness are fitted to biquartic polynomials in terms of the centerline arc lengths. The coefficients of the polynomial fits are carried throughout the derivation of the solution so that a new set of coefficients is all that is required for the solution of each new plate geometry. Solutions for the frequencies of resonance are developed using a combination of the Galerkin and Rayleigh–Ritz methods. For several selected geometries, comparisions are made to published results to validate the model. Finally, a study of the dependence of the frequencies of resonance on variations in curvature and thickness is presented for cantilevered plates.