Quasi-periodic motions and their stability are addressed from the point of view of different harmonic balance-based approaches. Two numerical methods are used: a generalized multidimensional version of harmonic balance and a modification of a classical solution by harmonic balance. The application to the case of a nonlinear response of a Duffing oscillator under a bi-periodic excitation has allowed a comparison of computational costs and stability evaluation results. The solutions issued from both methods are close to one another and time marching tests showing a good agreement with the harmonic balance results confirm these nonlinear responses. Besides the overall adequacy verification, the observation comparisons would underline the fact that while the 2D approach features better performance in resolution cost, the stability computation turns out to be of more interest to be conducted by the modified 1D approach.
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e-mail: mikhail.guskov@paris.ensam.fr
e-mail: fabrice.thouverez@ec-lyon.fr
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June 2012
Research Papers
Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis
Mikhail Guskov,
Mikhail Guskov
Associate Professor
Processes and Engineering inMechanics and Materials Laboratory, (PIMM, CNRS UMR 8006), Arts & Métiers ParisTech, 151 boulevard de l’Hôpital, 75013 Paris,
e-mail: mikhail.guskov@paris.ensam.fr
France
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Fabrice Thouverez
Fabrice Thouverez
Professor
Laboratory of Tribology and Dynamics of Systems, (LTDS, CNRS UMR 5513), Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69130 Ecully cedex,
e-mail: fabrice.thouverez@ec-lyon.fr
France
Search for other works by this author on:
Mikhail Guskov
Associate Professor
Processes and Engineering inMechanics and Materials Laboratory, (PIMM, CNRS UMR 8006), Arts & Métiers ParisTech, 151 boulevard de l’Hôpital, 75013 Paris,
France
e-mail: mikhail.guskov@paris.ensam.fr
Fabrice Thouverez
Professor
Laboratory of Tribology and Dynamics of Systems, (LTDS, CNRS UMR 5513), Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69130 Ecully cedex,
France
e-mail: fabrice.thouverez@ec-lyon.fr
J. Vib. Acoust. Jun 2012, 134(3): 031003 (11 pages)
Published Online: April 24, 2012
Article history
Received:
July 23, 2010
Revised:
October 1, 2011
Published:
April 23, 2012
Online:
April 24, 2012
Citation
Guskov, M., and Thouverez, F. (April 24, 2012). "Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis." ASME. J. Vib. Acoust. June 2012; 134(3): 031003. https://doi.org/10.1115/1.4005823
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