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Keywords:

  • Parametric instability;
  • combination resonance;
  • cantilever beam;
  • non-linearity

The effects of parametric excitation of a simple structure are such that very large responses may be generated in a plane perpendicular to that of the excitation as a result of relatively small accelerations, provided that the frequency of the excitation is related to that of the excited mode or modes in a certain manner. It is shown that it is possible for two or more resonances to be excited simultaneously, and that an effect generated by a weaker type of coupling can in fact modify that of a stronger coupling to a significant extent. A vertically oriented, thin and flexible cantilever beam of rectangular uniform cross-section with a lumped end inertia, is modelled both to first and second order of approximation, and theoretical and experimental results for the stability zoning of the resonances are presented. An additional model is proposed which examines the combined effect of two resonances for two tuning cases, and this is compared with measurements of vibratory responses and strain on an experimental system. It is thus shown that the theoretical model postulated for the simultaneous excitation of two resonances accurately predicts the observed behaviour of the laboratory system within a specific range of excitation accelerations.