The Problem of Studying the Self-Oscillations of an Aerodynamic Pendulum in the Flow of a Medium
Abstract
The paper is devoted to the construction and research of a mathematical model of self-oscillations of an aerodynamic pendulum in the flow of a medium. As a model of the influence 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 this problem, the center of pressure is mobile relative to the plate. The equations of motion for the body under consideration are obtained. The transition to new dimensionless variables is performed. Violation of uniqueness in determining the angle of attack is shown. Parametric analysis of ambiguity areas is performed. 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 equilibrium positions in which the Hurwitz criterion is implemented and the stability regions are depicted. 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 damping. In the Matlab 18 mathematical package, a set of programs is written that allows you to build stability regions and perform numerical integration of equations describing body vibrations in order to confirm the adequacy of the constructed model.
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