Open Access
REVIEW
Harmonic Balance Methods: A Review and Recent Developments
Zipu Yan1,2, Honghua Dai1,2,*, Qisi Wang1,2, Satya N. Atluri3
1
School of Astronautics, Northwestern Polytechnical University, Xi’an, 710072, China
2
National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi’an, 710072, China
3
Department of Mechanical Engineering, Texas Tech University, Lubbock, 79401, USA
* Corresponding Author: Honghua Dai. Email:
Computer Modeling in Engineering & Sciences 2023, 137(2), 1419-1459. https://doi.org/10.32604/cmes.2023.028198
Received 04 December 2022; Accepted 13 February 2023; Issue published 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, have been developed; unfortunately, misclassification
pervades among them due to the unclear borderlines of different methods. ii) The time domain HB-like methods
suffer from non-physical solutions, which have been shown to be caused by aliasing (mixture of the high-order
into the low-order harmonics). Although a series of dealiasing techniques have been developed over the past two
decades, the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic
community. This paper aims to provide a comprehensive review of the development of HB-like methods and
enunciate their principal differences. In particular, the time domain methods are emphasized with the famous
aliasing phenomenon clearly addressed.
Keywords
Cite This Article
APA Style
Yan, Z., Dai, H., Wang, Q., Atluri, S.N. (2023). Harmonic balance methods: A review and recent developments. Computer Modeling in Engineering & Sciences, 137(2), 1419-1459. https://doi.org/10.32604/cmes.2023.028198
Vancouver Style
Yan Z, Dai H, Wang Q, Atluri SN. Harmonic balance methods: A review and recent developments. Comput Model Eng Sci. 2023;137(2):1419-1459 https://doi.org/10.32604/cmes.2023.028198
IEEE Style
Z. Yan, H. Dai, Q. Wang, and S.N. Atluri "Harmonic Balance Methods: A Review and Recent Developments," Comput. Model. Eng. Sci., vol. 137, no. 2, pp. 1419-1459. 2023. https://doi.org/10.32604/cmes.2023.028198