The Influence of Initial Stresses and Boundary Restraints on the Nonlinear Vibrations of Cylindrical Shells

Abstract

Abstract A Rayleigh-Ritz procedure is used in conjunction with nonlinear shallow shell theory to study the influence of axisymmetric initial stresses on the nonlinear flexural vibrations of thin-walled cylindrical shells. A similar formulation is used to determine the effect of in-plane boundary conditions on the nonlinear vibrations. Both analyses make use of an assumed vibration mode which possesses a moment restraint at the edges of the shell. The results show that compressive initial stresses cause the vibrations to become increasingly nonlinear as buckling is approached. Initial tensile stresses generally cause the vibrations to become more nearly linear. In-plane restraints on the axial displacement at the ends of the shell have a hardening influence on the nonlinear behavior. This influence is most pronounced for vibration modes with high axial wave numbers. A study of the moment restraint at the boundary shows that for thin shells, the conditions of simple-support are closely approximated by the present analysis.