Acta Mechanica Sinica

, Volume 9, Issue 1, pp 61–71

Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic and combination resonances of self-excited two coupled second order systems to multi-frequency excitation

Authors

  • A. M. Elnaggar
    • Mathematics DepartmentFaculty of Science
  • A. F. El-Basyouny
    • Mathematics DepartmentFaculty of Science
Article

DOI: 10.1007/BF02489163

Cite this article as:
Elnaggar, A.M. & El-Basyouny, A.F. Acta Mech Sinica (1993) 9: 61. doi:10.1007/BF02489163

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.

Key Words

resonancenonlinear oscillationmultiple-scales methodself-excited systemmulti-frequency excitation
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© Chinese Society of Theoretical and Applied Mechanics 1993