n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities
Keywords:
harmonic balance method, hypertime domain, unilateral contactAbstract
The harmonic balance method is widely used for the analysis of strongly nonlinear problems under periodic excitation. The concept of hypertime allows for the generalization of the usual formulation to multi-tone excitations. In this article, the method is applied to a system involving a nonlinearity which cannot be explicitly expressed in the multi-frequency domain in terms of harmonic coefcients. The direct and inverse Discrete Fast Fourier Transforms are then necessary to alternate between time and frequency domains in order to take into account this nonlinearity. The results show the efciency and the precision of the method.
Downloads
References
Cameron T. M., Grifn J. H., An alternating frequency/time domain method for calculating
the steady state response of nonlinear dynamic systems, Journal of Applied Mechanics,
vol. 56, p. 149-154, 1989.
Ewins D. J., Von Groll G., The harmonic balance method with arc-length continuation in
rotor/stator contact problems, Journal of Sound and Vibration, vol. 241, p. 223-233, 2001.
Flechter R., Practical Methods of Optimization, John Wiley, 1987.
Gilmore R., Steer M., Nonlinear circuit analysis using the method of harmonic balance - a
review of the art. Part I. Introductory concepts, International Journal on Microwave and
Millimeter Wave Computer Aided Engineering, 1991.
Kim Y., Choi S.-K., A multiple harmonic balance method for the internal resonant vibration
of a non-linear Jeffcott rotor, Journal of Sound and Vibration, vol. 208, p. 745-761, 1997.
Lau S. L., Cheung Y. K., Wu S. Y., Incremental harmonic balance method with multiple time
scales for aperiodic vibration of nonlinear systems, Journal of Applied Mechanics, vol. 50,
p. 871-876, 1983.
Lau S., Zhang W.-S., Nonlinear vibrations of piecewise-linear systems by incremental harmonic
balance method, Journal of Applied Mechanics, vol. 59, p. 153-160, march 1992.
Legrand M., Modèles de prédiction de l'interaction rotor/stator dans un moteur d'avion, Thèse
de doctorat, École Centrale de Nantes, March, 2005.
Legrand M., Peseux B., Pierre C., Amélioration de la prédiction de l'interaction rotor/stator
dans un moteur d'avion, Actes du 6e Colloque National en Calcul des Structures, Giens,
p. 53-68, juin 2003.
Legrand M., Peseux B., Pierre C., Étude de l'interaction modale rotor/stator dans un moteur
d'avion, 14e Colloque Vibrations, Chocs et Bruit, Lyon, juin 2004.
Nayfeh A., Balachandran B., Applied Nonlinear Dynamics : analytical, computational and
experimental methods, Wiley Interscience, 1995.
Nayfeh A., Mook D., Nonlinear oscillations, Wiley Interscience, 1979.
Puenjak R. R., Oblak M. M., Incremental harmonic balance method with multiple time variables
for dynamical systems with cubic non-linearities, International Journal for Numerical
Methods in Engineering, vol. 59, p. 255-292, 2004.
Schmiechen P., Travelling Wave Speed Coincidence, Ph.d. thesis, College of Science, Technology
and Medicine, London, UK, May, 1997.
Ushida, Chua L., Frequency-domain analysis of nonlinear circuit driven by multi-tone signals
, IEEE Transactions on circuits and systems, vol. CAS-31, p. 766-778, 1984.