Linear Analysis on Vibrations of a Thin Shell-panel including Clamped Edge with a Coupling between In-plane Deformation and Deflection

Abstract

In this study, a new analytical method on natural frequencies and vibration modes of a thin shell-panel with clamped edge is presented. At the boundaries of two opposite edges, the shell panel is simply supported, and at the other two edges the panel is simply supported or clamped. Coordinate function of deflection is assumed with the product of power series and trigonometric function. Neglecting the effect of in-plane inertia force, the Donnell type equations are applied as the governing equation of the shell-panel. Stress function is obtained which satisfies exactly the compatibility equation with the inhomogeneous term due to the coupling with deflection and the in-plane boundary conditions. Applying Galerkin method to equation of motion, natural frequencies and vibration modes are calculated and compared with the exact result.