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Figure 3.10 Stability envelope for bluff section bridge.

empirical evidence, mostly obtained from section model wind tunnel testing although
‘discrete vortex’ computational fluid dynamics is now adding to such studies (Larsen, 2000).
The critical speed is also likely to show increased sensitivity to structural damping, as shown
on Figure 3.10.

3.3.4 Comprehensive description of motion dependent forces: Scanlan’s notation

The calculation procedures developed to evaluate flutter speeds from the aerofoil solution for
forces can be extended to accept empirical values of the derivatives. A number of notations
have been proposed, with the system developed over many years by Scanlan (Simiu and
Scanlan, 1986) gaining widest acceptance. The lift (L) and torsional couple (M) resulting from
)
harmonic vertical motion y and rotation α(and their time differentials ÿ, αare commonly
written as

(3.53a)

(3.53b)

defining the eight derivatives and . It will be noted that an adaptation of
aeronautical notation is used; great care is needed in interpretation of papers on this topic in
view of numerical factors arising from the usage of b or B and sign changes according to
whether the positive direction of displacement is the same or opposing that of the respective
/
force. If the normalized frequency is taken as K=BωV (2k in the aeronautical usage given
above) and forces are taken positive in the same direction as the respective displacements, the
values of the derivatives agree with those given in Dyrbye and Hansen (1997).
The forms taken by these derivatives in terms of Theodorsen’s function for the case of ideal
aerofoil behaviour are set out in full by Dyrbye and Hansen (1997:151), who also provide a
valuable critique of this increasingly prominent approach. In the wind tunnel, the derivatives
can be measured directly on a section model which is externally driven in harmonic motion,
but estimates can