Stability of Various Stationary Points with Small Oscillations of the Aerodynamic Pendulum in the Flow of a Quasi-Static Medium

Abstract

In the article, a mathematical model of small oscillations of an aerodynamic pendulum in the flow of a moving medium is constructed and investigated. As a model of the effect of the medium on the body, the model of quasi-static flow around the plate by the medium is adopted. According to this hypothesis, the aerodynamic forces acting on the body are applied at the center of pressure. In our problem, the pressure center is movable relative to the plate. The equations of motion for the body under consideration are obtained. The transition to new dimensionless variables has been carried out. The violation of uniqueness in determining the angle of attack is shown. The parametric analysis of the ambiguity areas is carried out. All stationary points that are solutions of the equilibrium equations are found. It is shown that there is no ambiguity in the most characteristic equilibrium position corresponding to the state of rest. A study of the stability of various non-trivial equilibrium positions in which the Hurwitz criterion is implemented, and the stability regions are depicted is carried out. It is shown that the forces of aerodynamic action for bodies with some shapes can contribute to the development of self-oscillations, and for others to attenuation. The mathematical package MATLAB 18 contains a set of programs that allows you to find stationary points, build stability regions for each of them and perform numerical integration of equations describing body vibrations in order to confirm the adequacy of the constructed mathematical model.

Keywords

• body
• stationary mode
• stability
• stability region
• flutter