Efficient Method for Limit Cycle Flutter Analysis by Nonlinear Aerodynamic Reduced-Order Models

Nonlinearities can be present in an aeroelastic system because of some aerodynamic factors that occur in transonic flight regimes or at a large angle of attack. The sources are shock wave motions and separated flows. Complex aeroelastic problems due to the aerodynamic nonlinearity can be studied using high-fidelity computational fluid dynamics (CFD) codes. However, the computational cost may be very high. Hence, this kind of problem is conveniently solved using the reduced-order model (ROM) for unsteady aerodynamic analysis. Many studies have been done using reduced-order modeling for aeroelastic analysis. However, most of the reduced-order aerodynamic models are dynamic linear models and have loads proportional to the structural motions. In the current paper, a nonlinear unsteady reduced-order aerodynamic model is constructed using the radial basis function neural network model. This kind of ROM is used to analyze the limit cycle oscillation (LCO) for two linear structural models with large shock motions in transonic flow. Unlike the input signals in the traditional design method, the signals of the self-excited vibration of the aeroelastic system are designed as the input signals in the current paper. Coupling the structural equations of motion and nonlinear aerodynamic ROM, the system responses are determined by time marching the governing equations using a hybrid linear multistep algorithm. Then, the LCO change with velocities (dynamic pressure) was analyzed. The two transonic aeroelastic examples show that both the structural responses and the LCO characteristics simulated using the nonlinear ROM agree well with those obtained using the direct CFD method. Moreover, the computational efficiency of the nonlinear ROM-based method is improved by one to two orders of magnitude compared with that of the direct CFD method.