Some Studies on the Flutter of Airfoils and Propellers

Abstract

Abstract During the last few years there has been considerable interest in the study of vibration of airfoils and propellers, both in Europe and in this country, and most of the literature regarding it is of fairly recent date. A complete solution to the problem has not yet been attained, the complicated mathematics having proved too involved. Again, some of the factors are only now the subject of research. This paper deals with a few of the many interesting phases of the problem. Because of the complexity of the mathematical expressions for the airfoils in common use, a flat plate has been used. It has also been assumed that the angle of attack in the range to be covered is below the burble point and that the amplitude of the vibrations is considered small. The paper is divided into three main parts: (a) A theoretical development of the deflection curve of a cantilever flat bar of uniform cross-section, by air forces distributed according to an elliptic-load grading curve, to show the effect of the warping produced by such loading in the strain energy of the bar so loaded. (b) An approximate solution of the free torsional vibrations of a cantilever bar of thin rectangular cross-section. (c) An analysis of the problem of self-induced torsional vibrations which will apply for any airfoil.