Nonlinear aerodynamic characteristics and modeling of a quasi-flat plate at torsional vibration: effects of angle of attack and vibration amplitude

The clarification of the nonlinear and unsteady aerodynamic characteristics of a quasi-flat plate is of great importance to predict its wind-induced post-flutter behavior. Forced motion wind tunnel tests on a quasi-flat plate sectional model with a width-over-thickness ratio of 62.5:1 are conducted using the synchronous measurement of the dynamic forces and torsional displacements at various initial angles of attack (AoAs), vibration amplitudes and incoming wind speeds. The flutter derivatives related to torsional degree of freedom (DOF) are identified and compared. The nonlinear and unsteady characteristics of self-excited forces (SEFs) in terms of the frequency components and phase lag between the force and motion are quantitatively examined. The wind-induced energy maps of the quasi-flat plate at various initial AoAs are analyzed by introducing the aerodynamic work done by the self-excited lifting moment. A polynomial model is proposed to describe the nonlinear characteristics of the SEFs. It is validated that the flutter derivatives related to the torsional DOF are almost a single-valued function with respect to the reduced frequency, even at large vibration amplitudes. At large initial AoAs and oscillation amplitudes, the high-order frequency components of SEFs are significant, and the nonlinearity of the self-excited lifting moment is stronger than that of the self-excited lift force for torsional motion. This provides a reasonable explanation for the significant amplitude dependence of the flutter derivatives related to the lifting moment. The proposed polynomial nonlinear SEF model can achieve satisfactory accuracy in reproducing the SEFs in both time and frequency domains.