Mathematical modeling of self-excited oscillations over the pitch of a conical-spherical body at Mach number M = 1.75 using the forced-oscillation hypothesis

With the aim to model the self-excited oscillations of a body, a hypothesis is proposed for the formation of periodic bottom-wake vortex structures whose frequency coincides with the natural frequency of oscillations of the body, and the force effect of the oscillations on the body is mathematically described with a harmonic function of time. Analytical formulas for aerodynamic derivatives and equivalent aerodynamic derivatives are obtained. It is shown that the mathematical model satisfactorily describes the dependence of the pitch angle on time and the dependence of the equivalent aerodynamic derivatives on the amplitude of oscillations for two moments of inertia of the body. The mathematical model predicts a hyperbolic law for the dependence of the amplitude of self-excited oscillations on the reduced frequency.