High Dimensional Harmonic Balance Analysis for Dynamic Piecewise Aeroelastic Systems

Abstract

This paper describes the extension and application of a novel solution method for the periodic nonlinear oscillations of an aeroelastic system. This solution method is a very attractive alternative to time marching algorithms in that it is much faster and may track unstable as well as stable limit cycles. The method is employed to analyze the nonlinear aeroelastic response of a two dimensional airfoil including a control surface with freeplay placed in an incompressible flow. The mathematical model for this piecewise aeroelastic system is initially formulated as a set of first order ordinary differential equations. A frequency domain solution for the limit cycle oscillations is derived by a novel high dimensional harmonic balance (HDHB) method. By an inverse Fourier transformation, the system in the frequency domain is then converted into the time domain. Finally, the airfoil motions are obtained by solving the system in the time domain for only one period of limit cycle oscillation. This process can be easily implemented into computer programs without going through the complex algebraic manipulations for the nonlinearities typical of a more conventional harmonic balance solution method. The solutions found using this new HDHB method have been shown to be the same as those found using a more traditional time marching (e.g. Runge-Kutta) approach and also a conventional harmonic balance approach in the frequency domain with a considerable computational time saving.