Non-linear vibrations of circular cylindrical shells with flow

The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. Nonlinearities due to moderately large amplitude of vibration are considered by using the nonlinear Donnell shallow shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using a model proposed by Paidoussis and Denise. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to the bifurcated equilibrium positions. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincare maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude modulated motions, multi-periodic oscillations, and chaotic responses have been observed. A parametric analysis of the chaotic motion has shown a cascade of bifurcations as the route to chaos and the "blue-sky catastrophe", which are predicted here probably for the first time for dynamics of circular cylindrical shells.