Dynamics of flat plate complete motion in air flow with variable velocity

The research presents the mathematical model of non-stationary movement of an object in the air, considering that the wind flow might not be constant, as in the example of the vertical wind tunnel. The air flow rate might change its direction and magnitude over time, having variable velocity – a problem not solvable using conventional methods of aerodynamics, drag and lift force. Instead, the air flow around the object is divided into pressure and suction zones, and the angle of attack is variable. A thin flat plate is chosen as the moving object to allow the object not only translational movement, but also one rotational degree of freedom. Differential equations corresponding to a system with three degrees of freedom are presented in the article. Differential-integral equations are obtained and solved numerically using MathCAD software and explicit Euler step integration method. The developed method of motion analysis has been used for solving specific tasks: 1) vertical free fall of the plate in variable wind flow; 2) oscillations of the plate around a stationary base if additional elastic forces of the suspension reaction are applied. In addition, the case of a flapping wing structure in which energy is extracted from the air flow is considered. The obtained results can be used in practice to reduce or increase the interaction of other similar surface objects with air, for example, for sports equipment in competitions and everyday vehicles, as well as for obtaining energy from variable air flow in wind generators.