Nonlinear analysis of an aeroelastic response generated on a flexible sheet under periodic aerodynamic excitation

This study presents a nonlinear analysis of the aeroelastic response of a cantilevered flexible sheet under periodic aerodynamic excitation. The aerodynamic excitation is generated by upstream excitation plates (oscillating thin and rigid plates). Periodically fluctuating flow is generated by oscillating the excitation plates in uniform flow, and the downstream sheet is subjected to aerodynamic excitation driven by the sinusoidally oscillating wake of the excitation plates. The response of the sheet under the influence of periodic aerodynamic excitation is investigated by numerical simulations, considering the nonlinearity of the fluid force due to aerodynamic excitation varying the flow velocities and forcing frequencies. The calculation results obtained from the nonlinear analysis are compared with the previous experimental data and linear analyses. Furthermore, the underlying excitation mechanism, that is the factor triggering the vibration, is discussed. The amplitude calculated by the nonlinear analysis shows closer agreement with the previous experimental results than those obtained from the previous linear analysis. Moreover, it is found that the fluid force acting around the leading edge of the sheet due to aerodynamic excitation can trigger the initial vibration. The present study demonstrates that capturing the nonlinearity of wake dynamics and fluid-structure interactions is indispensable for accurately predicting large-amplitude responses, revealing the limitations of the conventional linear approach. Furthermore, the nonlinear analysis successfully clarifies the physical transition of the excitation mechanism: while the vibration is initially triggered by periodic aerodynamic forces concentrated near the leading edge, it subsequently evolves into a traveling-wave-type mode sustained by motion-induced self-excited fluid forces as the response reaches a steady state.