## Twc

This expression also gives the flapwise damping coefficient per unit length if 6* is replaced by 6* + 90° throughout.

The variation of the damping coefficient cY* per unit length at 14 m radius with vibration direction, 6*, at three different wind speeds is illustrated in Figure 7.17 for a specimen aerofoil section on a 20.5 m tip radius blade rotating at 29 r.p.m. The data are taken from Petersen et al. (1998), and do not include allowance for the axial induction factor. It can be seen that negative damping is worst at 20 m/s, and that negative edgewise damping is ameliorated by increasing 6* at the expense of increasing negative flapwise damping.

Although a plot of the local damping coefficient at ca 70 percent radius can provide a useful indication of trends, the best guide to the likelihood of divergent oscillations is provided by the modal damping coefficient for the mode under consideration. This is obtained by multiplying the right-hand side of Equation (7.26) by the square of the local modal amplitude and integrating over the length of the blade.

If comparison of the first mode edgewise and flapwise modal damping coefficients shows there is a benefit to be gained from altering the direction of vibration, small changes can be made by redistributing material within the blade cross section. Alternatively the blade pitch could be altered in conjunction with a compensatory change in aerofoil camber so that the aerodynamic properties for any given inflow angle are unchanged.

The prediction of edgewise vibrations in stall is examined in detail by Petersen et al. (1998), whose work provides the basis of the introductory survey given here.

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