Unsteady Aerodynamics and Dynamic Response of Flexible Supersonic Aircraft to Continuous Turbulence

This paper presents an analytical evaluation of unsteady aerodynamic forces and dynamic response of a flexible airplane to continuous turbulence in supersonic flight by applying the power-spectral-density (PSD) method. A brief explanation of differences in observed upwashes arising from the elastic and the gust oscillations is given. The aerodynamics for supersonic flight is described in terms of lifting-surf ace theory represented by a linear integral equation. The development is carried out for an airplane with coplanar wings of arbitrary planform subjected to a random vertical turbulence description. By applying the box technique, the aerodynamic influence coefficients are obtained for the combined elastic response and gust excitation velocity potential, which in turn determines the aerodynamic loads and the generalized forces. Choosing the flexible modes as the natural modes of the free-free airplane vibration, the frequency response functions are then determined. The interpretation of statistical results and the definition of parameters obtained by the PSD method, which are useful for design purposes, are discussed. The method of calculating the gust excitation forces and response of a flexible airplane is demonstrated by numerical examples.