Resonant Displacement Response Ignoring Wind Variations along the Blade

A5.3.1 Linearization of wind loading

For a fluctuating wind speed U( t) = U + u( t), the wind load per unit length on the blade is ±CfpU2(t)c(r) = ±Cfp[U2 + 2Uu(t) + u2(t)]c(r), where Cf is the lift or drag coefficient, as appropriate, and c( r) is the local blade chord dimension. In order to permit a linear treatment, the third term in the square brackets, which will normally be small compared to the first two, is ignored, so that the fluctuating load q( r, t) becomes CfpUu(t)c(r).

A5.3.2 First mode displacement response

Setting q(r, t) = CfpUu(t)c(r), the first mode tip displacement response to a sinusoidal wind fluctuation of frequency n (= mj2n) and amplitude uo(n) given by Equation (A5.3) becomes fi( t)


Hence power spectrum of first mode tip displacement is

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