Конкуренция режимов колебаний плохо обтекаемого тела в воздушном потоке

Abstract

Based on well-known mathematical models describing vibrations in the gas flow of a bluff body with one degree of freedom, a model of vibrations of a body with two degrees of freedom is proposed. The equations of transverse translational vibrations and rotational vibrations of an elastically fixed body around an axis perpendicular to the velocity vector of the incoming flow are obtained. Using the Krylov-Bogolyubov method in the first approximation, the equations are reduced to equations for slowly varying amplitudes and frequencies of vibrations. It turned out that the differential equations written for the squares of dimensionless amplitudes of translational and rotational vibrations coincide with the well-known Lotka-Volterra equations describing competition between two species of animals that eat the same food. The coefficients of the equations depend on the velocity of the incoming flow. The model is verified in the experiments in the wind tunnel.