Dynamic response of composite beams with application to aircraft wings

In this paper, the response of composite beams to deterministic and random loads is investigated. Of particular interest is the inclusion of the (material) coupling between the bending and torsional deformation that usually exists because of the anisotropic nature of fibrous composites. First, the free vibration characteristics of a bending-torsion coupled composite beam are established using the basic governing differential equations of motion. The response problem is then formulated through the use of generalized coordinates and normal modes obtained from the free vibratory motion. The orthogonality condition of the bending-torsion coupled beam is derived to decouple the equations of motion. The overall response is then calculated by superimposing the response obtained in each mode. The developed theory is fairly general and can be applied to composite beams with any cross section, e.g., an aerofoil, as long as their rigidity and other properties are known. Numerical results are obtained for a cantilever composite aircraft wing with substantial coupling between bending and torsional modes of deformation. Both deterministic and random loads are considered in the analysis. The deterministic load is a harmonically varying concentrated flexural force at the tip, whereas the random load is that of an atmospheric turbulence, modeled by the von Karman spectra, uniformly distributed over the length of the wing.