Harmonic Balance Methods: A Review and Recent Developments

The harmonic balance (HB) method is one of the most commonly used methods for solving periodic solutions both weakly and strongly nonlinear dynamical systems. However, it confined to low-order approximations due complex symbolic operations. Many variants have been developed improve HB method, among which time domain HB-like are regarded as crucial improvements because their fast computation simple derivation. So far, there two problems remaining be addressed. i) A dozen different versions methods, in frequency or hybrid, developed; unfortunately, misclassification pervades them unclear borderlines methods. ii) suffer from non-physical solutions, shown caused by aliasing (mixture high-order into harmonics). Although a series dealiasing techniques over past decades, mechanism final solution still not well known academic community. This paper aims provide comprehensive review development enunciate principal differences. In particular, emphasized with famous phenomenon clearly