An analytic model for the vibrations of rectangular shells of variable curvature and thickness

A flexible and powerful model is developed for analyzing the vibration of a rectangular platform shell whose curvature and thickness are arbitrary. The shape of the shell can have almost any conceivable representation, since the curvature and thickness are represented by bicubic polynomials of the centerline arc length. The vibration model includes the effects of shear deformation, rotary inertia, and centerline extension. The equations of motion are solved by an alternative form of the Rayleigh–Ritz method. The resulting integral formulas for the stiffness and mass matrix elements are evaluated by a set of simple computer routines that do symbolic manipulations of algebra and calculus. Predictions of the natural frequency for the several shell geometries are compared to published data, with good agreement. A parameter study shows the dependence of the resonance frequencies and mode shapes on the curvature and the thickness of the shell.