Nonlinear modal interactions in composite thin-walled beam structures with simultaneous 1:2 internal and 1:1 external resonances

Nonlinear dynamic characteristics of a composite aircraft wing structure modeled by a geometrically nonlinear anisotropic thin-walled beam in the presence of simultaneous 1:2 internal and 1:1 external resonances are investigated. Some prominent non-classical effects such as of transverse shear strain, warping inhibition, and three-dimensional strain are considered in the beam model. Moreover, circumferentially asymmetric stiffness lay-up configuration is adapted to generate the transverse bending-twisting elastic coupling. The solution methodology is based on the Extended Galerkin's Method, and the method of multiple scales is applied to the system in order to obtain the equations of amplitude and modulation. Steady-state solutions and their stability are investigated. The peculiarity of the internal resonances and the conditions for saturation and jump phenomenon during the modal interactions are discussed and the commercial code ABAQUS is used to validate the theoretical results we have obtained. Finally, the prominent features of modal interactions in composite thin-walled beam structures are summarized and pertinent suggestions concerning safe design of the wing structures are given.