Nonlinear aeroelastic analysis of an airfoil-store system with a freeplay by precise integration method

The aeroelastic system of an airfoil-store configuration with a pitch freeplay is investigated using the precise integration method (PIM). According to the piecewise feature, the system is divided into three linear sub-systems. The sub-systems are separated by switching points related to the freeplay nonlinearity. The PIM is then employed to solve the sub-systems one by one. During the solution procedures, one challenge arises when determining the vibration state passing the switching points. A predictor-corrector algorithm is proposed based on the PIM to tackle this computational obstacle. Compared with exact solutions, the PIM can provide solutions to the precision in the order of magnitude of 10⁻¹². Given the same step length, the PIM results are much more accurate than those of the Runge–Kutta (RK) method. Moreover, the RK method might falsely track limit cycle oscillations (LCOs), bifurcation charts or chaotic attractors; even the step length is chosen much smaller than that for the PIM. Bifurcations and LCOs are obtained and analyzed by the PIM in detail. Interestingly, it is found that multiple LCOs and chaotic attractors can exist simultaneously. With this magnitude of precision and efficiency, the PIM could become a solution technique with excellent potential for piecewise nonlinear aeroelastic systems.