The Dynamics of a Swept Wing

Abstract

I t is assumed tha t a swept wing may be represented dynamically by a plane curved rod of variable cross section with finite stiffness in torsion and in bending normal to its plane. The equations of motion for this configuration are exhibited with the restriction tha t the curvature of the elastic axis be finite. By allowing the curvature to become infinite a t a point, certain auxiliary conditions are obtained at the bend. The validity of this limiting process is examined from the physical point of view. A wing with an elastic axis consisting of a plane broken line of (n + 1) segments is denoted as an bend A method is developed for calculating the natural frequencies and modes of a single bend wing. Formulas for the natural frequencies and modes of a free-free symmetric single bend uniform rod are obtained. A generalized type of orthogonality condition between the modes of a single bend wing is proved. Based on these results, formulas are developed for the dynamic response of a single bend wing to a general system of forces. A method of generalizing the above results for a single bend wing to the n bend wing is indicated. The use of an n bend wing as an approximate representation of a wing of continuous curvature is discussed.