A modified frequency-time domain method for nonlinear aeroelastic systems with initial conditions

The frequency-time domain method is a very powerful tool for analyzing nonlinear aeroelastic systems; however, it is limited to obtaining steady-state solutions. To investigate nonlinear dynamic behaviors with initial conditions, a modified frequency-time domain method is proposed. Initial conditions, represented as pseudo forces, are introduced into the nonlinear feedback loops and are subsequently transformed from the time domain into the frequency domain. Hence, the proposed method allows nonlinear responses with initial conditions. Owing to the characteristics and limitations of this method, certain skills are presented to simulate both accurately and efficiently. Numerical results are provided for, in addition to the Van Der Pol equation, a two-degree-of-freedom airfoil section, and a three-degree-of-freedom aeroelastic typical section with control surface freeplay. Consequently, the feasibility of introducing initial conditions is validated. The comparison with the Runge-Kutta algorithm demonstrates the accuracy and efficiency of the proposed method, as an alternative to time-marching approaches. Furthermore, several key parameters, such as the sampling frequency and ending time of convolution integral, are investigated to explore the efficiency. The sensitivity of parameters and calculation methods of convolution integral is observed, which contributes to the strategies for adequate accuracy.