NONLINEAR BEN DING-TORSION FLUTTER OF A CANTILEVER WING SUBJECTED TO PARAMETRIC EXCITATION

摘要

This study deals with the nonlinear flutter of a cantilever wing in the absence and presence of parametric excitation that acts in the plane of highest rigidity. The nonlinear equations of motion in the presence of an incompressible fluid flow are derived using Hamilton's principle. The regions of parametric instability are obtained for different values of flow speed. In the neighborhood of combination parametric resonance, the nonlinear response is determined using the multiple scales method for different values of flow speed. In the absence of parametric excitations, numerical simulation is performed for flow speeds at the critical flutter speed. It is found that the nonlinear flutter of the two modes depends on initial conditions, and exhibits symmetric periodic oscillations. Under parametric excitation and in the absence of air flow, each mode oscillates at its own natural frequency. In the presence of air flow, the two modes possess the same frequency response. Depending on the flow speed the response could be periodic, quasi-periodic, or chaotic.