Open Access

REVIEW

Harmonic Balance Methods: A Review and Recent Developments

Zipu Yan^1,2, Honghua Dai^1,2,*, Qisi Wang^1,2, 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.

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Keywords

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