Comparison Between the Incremental Harmonic Balance Method and Alternating Frequency/Time-Domain Method

Two widely used semi-analytical methods: the incremental harmonic balance (IHB) method and alternating frequency/time-domain (AFT) method are compared, and some long-standing discussions on frameworks of these two methods are cleared up. The IHB and AFT methods are proved for the first time to be theoretically equivalent when spectrum aliasing does not occur in the AFT method. Based on this equivalence, the minimal nonaliasing sampling rate for the AFT and fast Fourier transform (FFT)-based IHB methods can be obtained for a system with polynomial nonlinearities. While spectrum aliasing is theoretically inevitable for nonpolynomial nonlinearities, a sufficiently large sampling rate can be usually used with acceptable accuracy and efficiency for many systems. Convergence and efficiency of the IHB method, AFT method, and several FFT-based IHB methods are compared. Accuracy and convergence can be affected when the sampling rate is insufficient. This comparison can provide some insights to avoid misuse of these methods and choose which methods to use in engineering applications.