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1 Journal of Theoretical and Applied Mechanics

1 2024

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Error measures and solution artifacts of the harmonic balance method on the example of the softening Duffing oscillator

Dänschel Hannes, Lentz Lukas, von Wagner Utz

Journal of Theoretical and Applied Mechanics

2024

Vol. 62 nr 2

435--455

The Harmonic BalanceMethod (HBM) is one of the most often applied semi-analytic approximation methods in nonlinear dynamics. In earlier publications, the two coauthors already observed for the softening Duffing oscillator and other systems that especially low ansatz order HBM solutions may contain larger errors for some solution branches, and called this artifacts. In the present work, this problem is studied systematically with a new implementation of the method and applied again to the example of the softening Duffing oscillator. In conjunction with a mathematical definition for HBM artifacts we discuss and present possible a posteriori and a priori HBM error measures.