Effect of Boundary Conditions of Flexural Vibrations of Thin Orthogonally Stiffened Cylindrical Shells

Abstract

The flexural vibrations of thin orthogonally stiffened cylindrical shells are discussed considering the effect of different boundary conditions. The orthotropic shell theory of W. H. Hoppmann, II, was usect to derive the orthotropic stress-strain law, and the equations of motion were formulated for the shell element in three partial differential equations. The equations were reduced to a single eighth-order ordinary differential equation. This equation yielded a fourth-order frequency equation by considering a relatively long cylinder. The following three boundary conditions were applied: clamped-clamped, clamped-simply supported, and both edges simply supported. The author's theory was compared with Hoppmann's theory and test results for the case of simple supports. The errors are about the same for both theories. The author's theory shows that the clamped-clamped and clamped-simply supported boundary conditions can affect the frequencies seriously in the case of longitudinal stiffeners; however, the effect is smaller with radial stiffeners. For the isotropic case, the theory simplifies to the solution of Yi Yuan Yu.