Experiments and theory on the nonlinear dynamics and stability of clamped shells subjected to axial fluid flow or harmonic excitation

This thesis presents experimental and theoretical results on the nonlinear dynamics and stability characteristics of thin-walled clamped-clamped circular cylindrical shells in contact with flowing fluid. Additionally, the large-amplitude vibrations of clamped shells subjected to an external radial harmonic force excitation are also investigated theoretically.The experiments were conducted with three experimental set-ups: one for experiments with elastomer shells in annular air-flow, the second for elastomer shells with internal air-flow, and the last one for aluminum or plastic cylindrical shells with internal water-flow. In all cases the interaction between the shell and the fully developed flow gives rise to instabilities in the form of static or dynamic divergence at sufficiently high flow velocities. The experimental results show a softening type nonlinear behaviour, with a large hysteresis in the velocity for the onset and cessation of divergence. Only static solutions were observed.In the theoretical study, the standard form of the Donnell's nonlinear shallowshell equations is used. The solution expansion includes both driven and companion modes, thus allowing for a traveling wave in the circumferential direction; it also includes axisymmetric modes to capture the nonlinear inward shell contraction and the correct type (softening) nonlinear behaviour observed in the experiments. The clamped-clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The theoretical results indicate loss of stability by divergence, and a strong nonlinear subcritical response. In the case of external excitation the shell exhibited a softening type of nonlinearity.The results from the theoretical model are compared with experimental data, and in all cases good qualitative and quantitative agreement is observed. In addition, a parametric analysis investigates the effect of the length/radius and thickness/radius ratios and transmural pressure on the nonlinear response of the shell with internal flow