Mathematical model of fuselage oscillations at transonic flight speeds

Abstract

Ensuring the safety of supersonic aircraft flights and aerospace systems in the transonic range of M flight numbers still remains an urgent scientific and applied problem. This is caused by the peculiarities of the aerodynamic surfaces flow by inhomogeneous (transonic) air and is due to the emergence of various aeroelastic phenomena in these flight modes and the current lack of a generally accepted model of transonic flutter, even for aerodynamic control surfaces. Based on a joint analysis of the conditions for the formation of shock waves on the surface of the aerodynamic profile, changes in the parameters of supersonic flow across the Prandtl-Meyer expansion fan, and the hypothesis of dynamic curvature of the aerodynamic profile , the approximate laws of interaction of elastic bending vibrations of the fuselage with fluctuations in shock waves were obtained. The obtained regularities are used to substantiate a mathematical model for estimating excited forces and excited bending moments of the fuselage. The analysis of the obtained mathematical model confirms the theoretical possibility of the appearance of fuselage forms of transonic flutter in supersonic aircraft, which was observed in the flight experiment and which is due to the interaction of shock waves with the angular velocity of the fuselage elastic bending vibrations. With the accepted in the article input geometrical data of a fuselage aerodynamic surfaces’ profile, the maximum possible values of fuselage bending moments are obtained using the developed mathematical model. The obtained mathematical model can be used for a preliminary approximate assessment of the transonic flutter fuselage forms characteristics in supersonic aircraft and aerospace systems.