The response-frequency relationship in the vicinity of a resonant frequency, the occurrenceof travelling wave response and the presence of internal resonances are investigatedfor simply supported, circular cylindrical shells. Donnell’s nonlinear shallow-shelltheory is used. The boundary conditions on radial displacement and the continuity ofcircumferential displacement are exactly satisfied. The problem is reduced to a system offour ordinary differential equations by means of the Galerkin method. The radial deflectionof the shell is expanded by using a basis of four linear modes. The effect of internalfluid is also investigated. The equations of motion are studied by using a code based onthe Collocation Method. The present model is validated by comparison of some resultswith others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internalresonances is investigated for the first time; it shows intricate and interesting dynamics.
Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: Equations of motion and numerical results / M., Amabili; Pellicano, Francesco; A. F., Vakakis. - In: JOURNAL OF VIBRATION AND ACOUSTICS. - ISSN 1048-9002. - STAMPA. - 122:4(2000), pp. 346-354. [10.1115/1.1288593]
Nonlinear vibrations and multiple resonances of fluid-filled, circular shells, part 1: Equations of motion and numerical results
PELLICANO, Francesco;
2000
Abstract
The response-frequency relationship in the vicinity of a resonant frequency, the occurrenceof travelling wave response and the presence of internal resonances are investigatedfor simply supported, circular cylindrical shells. Donnell’s nonlinear shallow-shelltheory is used. The boundary conditions on radial displacement and the continuity ofcircumferential displacement are exactly satisfied. The problem is reduced to a system offour ordinary differential equations by means of the Galerkin method. The radial deflectionof the shell is expanded by using a basis of four linear modes. The effect of internalfluid is also investigated. The equations of motion are studied by using a code based onthe Collocation Method. The present model is validated by comparison of some resultswith others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internalresonances is investigated for the first time; it shows intricate and interesting dynamics.Pubblicazioni consigliate
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