Bending-torsion transfer matrices associated with swept surfaces.

Abstract

I an earlier paper Lin discussed the advantages to be gained from using transfer matrices for calculating the steady response of flexible aircraft structures. For coupled bending-torsion of swept wing and tail surfaces it is desirable from the standpoint of the aerodynamic calculations to offset the mass elements in a streamwise direction rather than perpendicular to the elastic axis. The mass point transfer matrix for such an arrangement is derived below. The streamwise offset mass element is shown in Fig. 1, in which the notation and positive sign conventions follow those of Pestel and Leckie. Forcing functions may be applied at the elastic axis 0 (/i, Qi, ft), at the mass element A (/2, 62, ft)> or at some point along the streamwise strip B (/3, Qs, ft), depending upon the application. If L is taken to be the downward displacement of the mass element, F and A its rotations about the axes indicated, then the equations of motion are