Instabilities of Nonconservative Fluid-Loaded Systems

Abstract

Nonlinear bifurcations and instabilities of autonomous nonconservative systems, mainly involving the fluid loading of a solid or structure, are reviewed and described in this accessible, pictorial overview. In contrast to the earlier papers in this series (focusing on the instability of elastic deformable systems, and low-order periodically-forced mechanical systems), we focus on a handful of case studies in which the loss of stability is primarily driven by nonconservative forces, i.e. path-dependent forces not associated with a potential. Many systems involving fluid-structure interaction can lose stability under changing conditions in which there is a net flow of energy from the fluid to the structure, sometimes resulting in growing oscillatory behavior. Again, the generic manifestations of instability typically occur within the framework of bifurcation theory. Progression is from simple local bifurcations to more complex global events, and all are related to instructive and intriguing applications. Hopf bifurcations are presented in the context of the galloping and flutter of cables and pipes. Next, Neimark bifurcations appear in aircraft applications involving the free-play fluttering of aerofoils and the wing rock of the Harrier jump-jet. Turning to ships in wind and waves, a homoclinic saddle connection governs the surging and surf-riding of a vessel in stern seas, while an omega flow explosion can compromise the course-keeping of a passenger ferry in a side wind. Recent work on the dynamic step-buckling of a spherical shell illustrates the role of a center manifold, and the paper ends with a careful study of dissipation-generated instabilities, drawing on the historical struggles to understand the evolution of spinning liquid planets.