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 shel ls. Donnell's nonlinear shallow-shell theory is used. The boundary conditio ns on radial displacement and the continuity of circumferential displacemen t are exactly satisfied. The problem is reduced to a system of forts ordina ry differential equations by means of the Galerkin method The radial deflec tion of the shell is expanded by using a basis of four linear modes. The ef fect of internal fluid is also investigated The equations of motion are stu died by using a code based on the Collocation Method. The present model is validated by comparison of some results with others available. A water-fill ed shell presenting the phenomenon of 1:1:1:2 internal resonances is invest igated for the first time; it shows intricate and interesting dynamics. [S0 739-3717(00)01204-6].