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 …

Quasi-periodic responses composed of multiple base frequencies widely exist in science
and engineering problems. The multiple harmonic balance (MHB) method is one of the most …

Rotor–stator interaction (RSI) is an inherent phenomenon in multi-row turbomachinery.
Unsteady reduced-order methods, such as the harmonic balance (HB) method and the …

Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic
balance (HB) method and its variants have been the most widely‐used approaches for such …

In this work, the application of the harmonic balance technique is demonstrated for transonic
buffet cases. The harmonic balance method represents an alternative to time-marching …

This paper extends the use of frequency-domain flow solvers to transonic buffet in turbulent
flow regime. To do so, a time-spectral method with frequency adaptation is developed for the …

The harmonic balance method has emerged as an efficient and accurate approach for
computing periodic, as well as almost periodic, solutions to nonlinear ordinary differential …

Presented in this work is a novel and easy-to-implement supplemental-frequency harmonic
balance (SF-HB) approach to efficiently compute dynamically aperiodic systems, which can …

Abstract The Harmonic Balance method for simulating unsteady nonlinear periodic flows is
presented in this paper. Its recent, yet rapid development was motivated by the possibility of …

ABSTRACT A new pseudo-spectral operator is developed for time-spectral harmonic
balance solutions of periodic unsteady flows. The method utilises a mechanism similar to …