Analysis of piecewise linear aeroelastic systems using numerical continuation

Abstract

This paper demonstrates the application of a numerical continuation method to dynamic piecewise aeroelastic systems. The aeroelastic system is initially converted into a state space form and then into a set of equations which solve the system as the motion moves between different linear zones in a free-play motion. Once an initial condition is found that satisfies these sets of equations, a continuation method is used to find all other possible solutions of the same period for a variation in any parameter. This process can then be repeated for different order systems, allowing the limit cycle behaviour of the whole system to be built up. The solutions found using this method have been shown to be the same as those found using a more traditional Runge-Kutta type of approach with a considerable time saving and added flexibility through multiple parameter variation.