An efficient multiple harmonic balance method for computing quasi-periodic responses of nonlinear systems

Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The harmonic balance (MHB) method is one the most commonly used approaches for such However, it limited by low-order estimations due to complex symbolic operations practical uses. Many variants have been developed improve MHB method, among which time domain MHB-like methods are regarded as crucial improvements because their high efficiency simple derivation. But there still main drawback remaining be addressed. negatively suffer from non-physical solutions, shown caused aliasing (mixtures high-order into harmonics). Inspired collocation-based balancing framework recently established our group, we herein propose a reconstruction (RMHB) reconstruct conventional using discrete collocations. Our study shows that relation between determined an matrix, non-zero when occurs. On this basis, conditional equivalence form RMHB method. Three numerical examples demonstrate new more robust efficient than state-of-the-art methods.