Investigation of Additional Mass Effect on Dynamic Wing Model Stability in Airflow

Abstract

The paper investigates a dynamic stability of the wing model in the flow of incoming air. As is known, at a certain flow rate, called critical, there occurs a phenomenon of self-excited non-damping flexural-and-torsional self-vibrations, called flutters. The paper considers an anti-flutter approach that is the placement of additional weight on the elastic elements (springs) in the wing model. Thus, a three-stage wing model is under consideration while the publications concerning this problem more often describe a two-stage wing model. The paper is a natural sequel to the authors’ first paper [9] where a two-stage wing model was considered in detail. It continues and develops research in this area, conducted by many famous scientists, such as V.L. Biderman, S.P. Strelkov, Ya.G. Panovko, I.I. Gubanova, E.P. Grossman, J.C. Fyn and many others who have investigated this phenomenon. It is also necessary to mention the scientists, namely Keldysh M.V., Reese P.M., Parkhomovsky Y. M., etc. who not only studied this phenomenon, but developed anti-flutter methods for it.It should be noted that not only scientists-theoreticians, but also test pilots, in particular M.L. Gallay [8], contributed to the solution of the flutter problem. The paper describes in detail a derivation of the linear differential equations of small vibrations of a wing model with additional weight in the flow, determines the eigenfrequencies and forms of flexural-and-torsional vibrations, checks their orthogonality, explores the forced vibrations under aerodynamic force and moment, and estimates a critical flow rate for a number of system parameters, namely a mass of the additional weight and the rigidity of its suspension. The conclusion is drawn that these parameters effect on the critical rate. Based on the calculation results, one can come to the conclusion on the additional weight effect on the critical flutter speed and on how relevant the anti-flutter method is. The given paper may be of interest both for students of technical specialties who learn the theory of mechanical vibrations, and for engineers majoring in aero-elasticity and dynamic stability of the elements of mechanical systems.