Using a quasi-static analysis, (Connors & Parrondo, 1970) and later (Dalton & Helfinstine, 1971) developed the fluid-elastic instability prediction for cylinders (single row of cylinders) subjected to cross-flow. Connors measured the fluid forces instead of predicting these using pitch to dia. ratio of P/D=1.41. He observed many different model patterns at instability, but suggested that the most dominant was elliptical motion (whirling). Using the measured fluid stiffness, Connors obtained energy balances in the in-and cross-flow directions, which must be satisfied simultaneously giving

where K is the so-called Connors constant, fn is the frequency of oscillation. Vpc is the so — called pitch velocity given by

VP

P — D

where P being the centre-to-centre inter cylinder pitch

(Blevins, 1974) has derived Equation 3 by assuming that the fluid forces on any cylinder are due to relative displacements between itself and its neighboring cylinders. Later, (Blevins, 1979) modified his original analysis to account for flow dependent fluid damping giving

where and ^y are total damping factors in the in-and cross-flow directions.