The Mechanisms

The mechanisms of wake-induced instabilities of pairs and small groups of cylinders, on the one hand, and cylinder arrays involving perhaps hundreds of cylinders, on the other, are fundamentally similar. Therefore, in principle, one could conceive of a common introduction for both Chapters 4 and 5; in practice, however, there are sufficient peculiarities in both, in particular with regard to sign conventions, to make it desirable to have different introductory sections in the two chapters, despite the repetitiousness in terms of the basic ideas involved. Wake-induced flutter is discussed in Section 4.2.

As in the introductory sections for other chapters, what is presented here is highly simplified, leaving most of the complexities and refinements to the sections that follow. Specifically, following Païdoussis & Price (1988), in Section 4.1.1, a modified form of quasi-steady theory is presented, suitable for the subject matter of Chapters 4 and 5. In Section 4.1.2, the damping-controlled instability mechanism is revisited in the context of this modified quasi-steady theory.

In terms of systems to which this work can be related, the main ones are overhead transmission lines subjected to wind and clustered offshore oil and gas production risers subjected to ocean currents.

Modified quasi-steady theory

Consider a small group of cylinders subjected to cross-flow, as shown in Figure 4.1.