Study on coupled modes panel flutter stability using an energy method

In this paper, an energy method is presented to study the coupled modes type panel flutter stability. The aeroelastic system continuous motion equation is built by adopting the first order piston theory aerodynamic loading. This continuous motion equation can be transformed by applying Galerkin method and constructed into a two-degree-of-freedom reduced order model (2-DOF ROM). Based on this ROM consisting of the first two structural modes, energy method is presented to investigate the system coupled modes type panel flutter stability. The obtained stability condition can be validated by comparing with its counterpart derived by Routh-Hurwitz criteria. Additionally, the critical system parameters can be evaluated and validated. Comparing with previous Ritz averaging method, the relationship between the modal coordinate amplitudes ratio and the modal damping coefficients ratio is believed to be firstly derived. The system damping paradoxical effect on coupled modes type panel flutter stability can be investigated after introducing the parameter, modal damping coefficients ratio. For given system modal damping coefficients, the phase difference and the modal coordinate amplitudes ratio of the first two modal coordinates can be specified. Based on the system power flow equations and the calculated parameters, the energy transfer characteristic between the supersonic airflow and the first two structural modes can be clarified. Such energy transfer procedure can be done within a half of oscillation period to sustain a neutrally stable single period oscillation.