This article deals with the new generation of proper Mach dependent exponential approximations of the indicial aerodynamic functions toward the aeroelastic formulation of 2-D lifting surface in the subsonic compressible flow. The indicial lift response is a useful starting point in the development of a general time-domain unsteady aerodynamic theory. By definition, an indicial function is the response to a disturbance that is applied instantaneously at time zero and held constant thereafter; that is a disturbance given by a step function. If the indicial response is known, then the unsteady loads to arbitrary changes in angle of attack can be obtained through the superposition of indicial responses using Duhamel’s integral. The indicial functions have been used to modify the circulatory part of the lifting force and pitching moment in unsteady compressible aerodynamic models. The coefficients of the approximation are obtained with an indirect approach by relating numerical results obtained for oscillating airfoil in the frequency domain back into the time domain. compressible and supersonic flight speed regimes. Exponential approximations of the subsonic compressible indicial functions in the existing research works are available only in limited Mach numbers (M = 0.5, 0.6, 0.7, 0.8). In the present study, a novel exponential approximation is developed which represent the coefficients of approximations as functions of Mach number (0.5 < M < 0.8).

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