Some Nonlinear Vibration and Response Problems of Cylindrical Panels and Shells

Abstract

Large amplitude vibrations and forced responses of curved panels and shells are studied by the application of the shallow shell equation. The Galerkin procedure is used to reduce the nonlinear partial differential equations to ordinary nonlinear equations. Marked differences are found between the behavior of curved panels and cylindrical shells. Relations for the dependence of the free vibration period on amplitude are given. A two mode analysis of the cylindrical shell problem is included. The curved panel is found to exhibit a buckling phenomenon for the simple breathing Shock response methods are used to predict dynamic buckling of the curved panel and the predictions are verified by numerical integration. The cylindrical shell vibrations and responses are found to be governed by Duffing's equation and certain of the well-known properties of Duffing's equation are applied to the cylindrical shell dynamics. The two mode analysis of the cylindrical shell is shown to exhibit weak coupling, allowing the separate excitation of the coupled modes. Some numerical results are given.