Abstract
Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Elnaggar, A. Détermination de solutions harmoniques et sousharmoniques de L'Equation\(\ddot X + K_1 X + K_2 \cos t)X^3 = 0\). These, strasbourg, France, 1976.
Elnaggar A and Elbouhy T. Harmonic and subharmonic solution of a weakly non-linear conservative differential equation with a periodically varying coefficients.J. Proc. Math, phys. soc. Egypt, 1981, 52.
Prosper H A. subharmonic and ultraharmonic in the forced oscillators of weakly non-linear system.Am. J. Phys., 1976, 44, 548, 74.
Lindsay W C. synchronization systems in communication and control. Englewood cliffs. Nj Practice Hall, 1972.
Pavlidis T. Biological oscillators, their Mathematical Analysis. New York: Academic press, 1962.
Minorsky N. Non-linear Oscillations. Princeton NJ Vannostrand, 1962.
Andronov A A, Vitt A. A. and Kaikin S E. Theory of oscillators. England: Pergaman press, Oxford, 1966.
Asfar K R Nayfeh A. H. and Mook D. T. Response of self-excited two-degree of freedom systems to multi frequency excitation.J. of sound and vibration, 1982, 84(2), 199.
Nayfeh A H and Mook D T. Non-linear Oscillations. New York: Wily Interscience, 1980.
Vasilenko N V. The analysis of self-excited vibrations in metal cutting.Soviet Applied Mechanics, 1969, 3, 47.
Kononenko V. O. and Kovalchak P S. Interaction of self-excited vibrations in Mechanical vibrating systems.Soviet Applied Mechanics, 1973, 9: 699.
Hayashi C. Non-linear oscillation in physical systems. New York: MG Graw-Hill, 1964.
Iwan W D. Generalization of the concepts of equivalent linearilation.International Journal of non-linear Mechanics. 1973, 8, 279.
Balbi J. H. Généralization de la method de la moyenne.International Journal of non-linear mechanics, 1973, 8, 3130.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Elnaggar, A.M., El-Basyouny, A.F. Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic and combination resonances of self-excited two coupled second order systems to multi-frequency excitation. Acta Mech Sinica 9, 61–71 (1993). https://doi.org/10.1007/BF02489163
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02489163