Bending-torsional flutter of a cantilevered wing containing a tip mass and subjected to a transverse follower force

Abstract

This paper is a study of the bending-torsional flutter of a cantilevered wing subjected to a follower force, and containing a lumped mass, at the free end. In addition, a distributed aerodynamic loading is introduced along the wing. This results in a set of nonself-adjoint differential equations with variable, complex coefficients whose solutions are obtainable only in series form. Using the Frobenius method, a direct procedure is employed which retains the exact expression of the Theodorsen function and the unknown coefficients are evaluated on a computer which numerically converge to any prescribed accuracy. It is found that, as a result of the interaction of the two sources of non-conservative loadings, the follower force reduces considerably the critical speed of flows in all cases studied. An increase in the tip mass, however, has a stabilizing influence. The effect of structural damping is also examined and it is shown that internal damping forces may have pronounced influences on the flutter speed of the system.