Mathematical Model Improvement for the Nonlinear Characteristics of Transonic Flutter

In order to make better agreement with transonic wind tunnel experimental data, which was obtained in the Japan Aerospace Exploration Agency (JAXA) in 1990’s, we proposed new mathematical model to improve the previous model. The bifurcation diagram was analyzed by a continuation method. The continuation method can continuously follow the solutions of dynamical system, such as a limit cycle oscillation (LCO), as one or more parameters in the systems are changed. So the continuation method enables to analyze the bifurcation diagram efficiently even through an unstable limit cycle (stability boundary) and can obtain a saddle-node point. We first analyzed the bending dominant (first) mode model and the torsion dominant (second) mode model separately, then combined the two models into one model. The final adjustment of the free parameters was performed to get the improved model. The model has a fourth order nonlinearity in the velocity of the first mode and the deflection of the second mode.