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From:
M. Amabili, F. Pellicano and M.P. Païdoussis
(1) Dipartimento di Ingegneria Industriale, Università di Parma, Parco Area delle Scienze 181/A, 43100, Parma, Italy
(2) Dipartimento di Scienze dell'Ingegneria, Università di Modena, Via Campi 213b, Modena, I - 41100, Italy
(3) Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street W. Montreal, Québec, Canada, H3A 2K6
“Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part 1: Stability”, Journal of Sound and Vibration, Vol. 225, No. 43, 26 August 1999, pp 655-699, doi:10.1006/jsvi.1999.2255
ABSTRACT: The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid–structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
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