Improved Implementation of the Harmonic Balance Method

Harmonic Balance (HB) methods have been applied to non-linear aeroelastic problems
since the 1980s. As the computational power available to researchers has increased, so has
the order of calculated HB solutions. However, the computational cost of a HB solution
increases with the square of the order. Additionally, the traditional Newton-Raphson,
Broyden, Toeplitz Jacobian and other techniques used for the solution of the non-linear
algebraic problem at the heart of the HB methodology rely on a good initial guess for
the unknown coefficients. If there are many such coefficients the probability that a good
guess will be available is very low and the HB scheme may well fail. In this paper a search
procedure using Genetic Algorithms (GA) is introduced to evaluate the coefficients of a
harmonic balance solution. It is shown that the GA can provide high quality initial guesses
for the HB coefficients. The method is applied to an aeroelastic galloping-type problem.