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    REVIEW

    Harmonic Balance Methods: A Review and Recent Developments

    Zipu Yan1,2, Honghua Dai1,2,*, Qisi Wang1,2, Satya N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.2, pp. 1419-1459, 2023, DOI:10.32604/cmes.2023.028198 - 26 June 2023

    Abstract The harmonic balance (HB) method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems. However, it is confined to low-order approximations due to complex symbolic operations. Many variants have been developed to improve the HB method, among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation. So far, there are two problems remaining to be addressed. i) A dozen of different versions of HB-like methods, in frequency domain or time domain or in hybrid,… More >

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