Adaptive Harmonic Balance Methods, A Comparison

Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is greatly affected by the number of harmonics included in the solution; hence, increasing the number of harmonics increases the accuracy of the solution at the expense of computational effort. Therefore, it is desirable to use an adaptive algorithm where the number of harmonics can be optimized in terms of both accuracy and computational effort. Until now, various adaptive harmonic balance methods have been formulated to perform this task. This paper presents an overview and a comparison of these adaptive harmonic balance methods in terms of their effectiveness.