Aeroelastic Vibrations of a Thin Ribbon in a Laminar Air Flow

— The nonlinear aeroelastic vibrations of a thin flat ribbon in a laminar air flow are investigated. The analytical model is a long flat membrane with two strings fixed along its long edges, to which tensile forces are applied. The air flow is directed along the plane of the membrane. The transverse torsional vibrations caused by aerodynamic forces are investigated. Coupled differential equations are obtained in dimensionless form, in which the flexural and torsional stiffnesses of the system are provided by the tension of the strings and the torque from the lifting force. The solution to the problem is presented in accordance with the Galerkin method. The conducted stability analysis revealed the Poincaré–Andronov–Hopf bifurcation (development of ribbon flutter in the air flow) and the Euler bifurcation (ribbon divergence). The dependence of the critical velocity and frequency of vibrations in the case of flutter as a function of the ribbon tension force has been determined. The supercritical behavior of the system and the establishment of a self-oscillating regime are investigated, and for the latter its frequency and amplitude of vibrations are determined.