Investigation of Dynamic Buckling of a Wing Model in Air Flow

The paper deals with studying a dynamic stability of the wing model in the ram airflow. As known, at a certain flow rate that is called critical, there is a phenomenon of self-excited non-damping flexural-torsional self-vibrations, named flutter. A two-mode elastic system wing model is under consideration, as is common in the literature in the field concerned. The paper continues and develops investigations of well-known scientists in this field, such as V.L. Biderman, S.P. Strelkov, Ya.G. Panovko, I. I. Gubanova, E.P. Grossman, J.Ts. Funen, etc. A great deal of papers dedicated to this problem and published by abovementioned and other scientists, give only the problem formulation and the derivation of equations, often in a fairly simplified form, do not offer solutions of these equations for specific numerical parameters of the wing model, and do not study how these parameters affect the flutter onset velocity. The paper details the derivation of linear differential equations of small vibrations of the wing model in the flow, determines the natural frequencies and shapes of flexural-torsional vibrations, checks their orthogonality, studies vibrations under the influence of aerodynamic force and moment, determines the critical flow velocity for a number of system parameters, and draws a conclusion about the influence of these parameters on the critical velocity. In particular, it studies how such a parameter as the distance between the center of gravity and the center of stiffness affects the critical velocity, as well as how the stiffness of the model's spring suspension, which simulates the stiffness characteristics of the wing impacts on bending and torsion. The calculation results allow us to draw conclusion concerning the methods of dealing with this phenomenon. One of the promising options may be, in addition to varying the geometric and rigid parameters of the system, the introduction of additional mass to be an analogue of the vibration damper. The paper may be of interest both for engineering students who learn the theory of mechanical vibrations, and for engineering-specialists in aero-elasticity and dynamic stability of elements in mechanical systems.