(Price, 1995) remarks that Fung and Blevins have concluded that quasi-steady fluid

V

dynamics is valid provided fD -10 ; however, experiments by Price, Paidoussis and

Sychterz and others suggest that for closely spaced bodies the restriction on the use of quasi­steady fluid dynamics is much more severe than that suggested by Fung or Blevins. (Gross, 1975) carried out first quasi-steady analysis of cylinder arrays subjected to cross-flow concluding that instability in cylinder arrays is due to two distinct mechanisms: negative damping and stiffness controlled instability.

1.1.3 Computational fluid dynamic (CFD) models

The CFD solutions applicable to fluid-elastic instability and other problem areas of flow- induced vibrations are increasing. These include (Marn and Catton, 1991) and (Planchard & Thomas, 1993).

1.1.4 Non-linear models

The first non-linear model was given by (Roberts, 1962, 1966), who employed Krylov and Bogoliubov method (Minorsky, 1947) of averaging to solve the non-linear equations. Two — motivating forces have been remarked by (Price, 1995) for non-linear analyses. Firstly because of manufacturing tolerances and thermal constraints, there are likely to be small clearances between heat exchanger tubes and intermediate supports. Hence, large lengths of unsupported tubes, having very low natural frequencies. These low-frequencies may suffer from fluid-elastic instability at relatively low Vpc. A second and more academic motivating force for these non-linear analysis has been to investigate the possibility of Choatic behavior of tube motion.