Attenuation of primary resonance vibrations of a non-linear system using a non-linear vibration absorber

Engineers Media for Engineers Australia
Publication Type:
Journal Article
Australian Journal of Mechanical Engineering, 2011, 8 (2, Special Issue on ACAM6), pp. 113 - 119
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In a single degree-of-freedom weakly nonlinear oscillator subjected to a periodic external excitation, a small-amplitude excitation may produce relatively large-amplitude vibrations under primary resonance conditions, when the forcing frequency is in the neighbourhood of the linearized natural frequency of the nonlinear oscillator. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state forced response. A nonlinear vibration absorber is thus used to suppress the primary resonance vibrations. The two linearized natural frequencies of the resultant system formed by the nonlinear primary system and nonlinear absorber are not under any internal resonance conditions. The method of multiple scales is used to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions. Illustrative examples are given to show the effectiveness of the nonlinear vibration absorber for suppressing nonlinear vibrations of the forced oscillator under primary resonance conditions.
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