Bending-Torsion Divergence of a Clamped-Clamped Composite Wing

Abstract

Based on inviscid, incompressible, two-dimensional, strip theory aerodynamics and a beam structural model, a single, third-order, ordinary differential equation is derived for the bending-torsion divergence of a spanwise-uniform composite wing with bending-twist coupling. The exact divergence dynamic pressure and mode shapes are presented for the clamped-clamped case. Unlike the clamped-free case, the solution of which is well known and straightforward, this problem is more challenging because one boundary condition involves both ends. The divergence dynamic pressure is found to be dependent on only two non-dimensional parameters, one of which is driven primarily by the bending-twist coupling, and the other by a ratio involving torsional and bending stiffnesses and the offset between the aerodynamic and generalized shear centers. It is shown that the divergence dynamic pressure increases with the absolute value of the bending-twist coupling and that sensitivity of the divergence dynamic pressure to the coupling parameter is larger for larger values of torsional stiffness and for smaller values of the offset or bending stiffness. Finally, the divergence mode shape, symmetric about the mid-span for the uncoupled case, is shown to become more non-symmetric as the sensitivity to bending-twist coupling increases.