A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator

• Published in: Journal of computational physics Vol. 215; no. 1; pp. 298 - 320
• Main Authors: Liu, L., Thomas, J.P., Dowell, E.H., Attar, P., Hall, K.C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 10.06.2006; Elsevier
• Subjects: Algorithms; Computation; Computational techniques; Duffing oscillators; Duffing’s oscillator; Dynamical systems; Exact sciences and technology; Harmonic balance method; Harmonics; Limit cycle oscillations; Mathematical methods in physics; Mathematical models; Nonlinearity; Numerical analysis; Physics; 74H15; Duffing’s oscillator; 65P99; Numerical analysis; 74S25; Limit cycle oscillations; Harmonic balance method; Dynamical systems; Algorithms; Non linear model; Limit cycles; Mathematical models; Calculation; 65P99; 74H15; 74S25; Oscillators; Calculation methods; Duffing's oscillator; Harmonic balance method; Limit cycle oscillations; Numerical analysis; Dynamical systems
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2005.10.026

The present study focuses on a novel harmonic balance formulation, which is much easier to implement than the standard/classical harmonic balance method for complex nonlinear mathematical models and algorithms. Both harmonic balance approaches are applied to Duffing’s oscillator to demonstrate the advantages and disadvantages of the two approaches. A fundamental understanding of the difference between these two methods is achieved, and the properties of each method are analyzed in detail.