This paper describes and illustrates two ways of performing time-correlated gust-load calculations. The first is based on matched filter theory, the second on random process theory. Both approaches yield theoretically identical results, represent novel applications of the theories, are computationally fast, and may be applied to other dynamic-response problems. A theoretical development and example calculations using both matched filter theory and random process theory approaches are presented.
Nomenclature
G(s) = transfer function of vertical velocity component of von Karman turbulence HJ(U>) = Fourier transform of h f (t) (frequency responsefunction of output variable /) hi(t) = time response of output variable / to unit impulse K = arbitrary constant L = scale of turbulence RIJ(T) = cross-correlation function between quantities / and j; autocorrelation function if / equals j Sy(<*>) = cross-spectrum between quantities / andy; autospectrum if / equals j s = Laplace variable t = time to = arbitrary time shift V = velocity of aircraft W g ((jci) = Fourier transform of w g (t) w g (t) = vertical velocity component of gust X(co) = Fourier transform of x(t) x(t) = "matched" excitation waveform Y(u>) -Fourier transform of y(t) y(t) = time response of output quantity y y y (t) = time response of output quantity y to excitation matched to y y z (t) = time response of output quantity y to excitation matched to z Z(co) = Fourier transform of z(t) z(t) = time response of output quantity z z y (t) -time response of output quantity z to excitation matched to y Z z (t) -time response of output quantity z to excitation matched to z oi = root-mean-square of quantity / T = time argument for auto-and cross-correlation functions
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