Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: Equations of motion and numerical results

The response-frequency relationship in the vicinity of a resonant frequency the occurrence of travelling Ir ave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell's nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of forts ordinary differential equations by means of the Galerkin method The radial deflection of the shell is expanded by using a basis of four linear modes. The effect of internal fluid is also investigated The equations of motion are studied by using a code based on the Collocation Method. The present model is validated by comparison of some results with others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated for the first time; it shows intricate and interesting dynamics. [S0739-3717(00)01204-6].