Flutter analysis based on the piecewise express of aerodynamic forces and the application of mode tracking technology

During solving the frequency domain flutter equations via the piecewise quadratic interpolation(PQI) method, this method can directly calculate the aerodynamic forces by using the piecewise aerodynamic force expression form. Thus, this method avoids the iteration process. Because of the construction of the function of the generalized aerodynamic forces depends on the choice of the reduced frequencies, a sudden jump of structural modes may occur when the PQI method is used in the flutter analysis. For this reason, a predictor-corrector scheme based on the perturbation theory of eigenvalues is developed. The scheme can determine the correspondence between the baseline and perturbed eigenvalues with parameter variation. In this paper, the present scheme is used in the flutter analysis. As an illustrative example, the developed method is applied to the whole plane flutter analysis with the axisymmetric boundary condition. By comparing with the P-K method, the numerical results show that the PQI method can accurately predict the flutter boundary and the mode tracking scheme is effective.