Abstract
We know now, in principle, how to formulate the Harmonic Balance equations and how to numerically solve them. In our experience, this alone is not sufficient to ascend from the stage of an absolute beginner to a successful user or even developer of a Harmonic Balance computer tool. Additional practical experience is required for this. The solved exercises shall illustrate the practical opportunities and limitations of computational Harmonic Balance. The homework problems are designed for self-contained studying and demonstrate typical difficulties associated with nonlinear vibrations and numerical methods. The ambitious goal is to teach the interested reader how to apply and further develop existing Harmonic Balance tools.
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Notes
- 1.
In case you encounter difficulties and for validation, the result is \(\varOmega = 1\) and \(a=2\) (independent of \(\zeta \)).
- 2.
Note that in this simple case, one could also do a phase normalization by setting, e.g., \(\hat{q}_{\mathrm s}(1)=0\), and reducing the number of unknowns.
References
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Krack, M., Gross, J. (2019). Solved Exercises and Homework Problems. In: Harmonic Balance for Nonlinear Vibration Problems. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-14023-6_5
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DOI: https://doi.org/10.1007/978-3-030-14023-6_5
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