Suppression of Super-harmonic Resonance Response of a Forced Nonlinear System Using a Linear Vibration Absorber

University of Canterbury
Publication Type:
Conference Proceeding
Proceedings of the 13th Asia-Pacific Vibration Conference (APVC 09), 2009, pp. 1 - 7
Issue Date:
Full metadata record
Files in This Item:
Filename Description Size
Thumbnail2009003170OK.pdf191.37 kB
Adobe PDF
Super-harmonic resonances may appear in a forced weakly nonlinear system of cubic nonlinearity, when the forcing frequency is approximately equal to one-third of the linearized natural frequency. In contrast with the corresponding linear oscillator, the free-oscillation term does not decay to zero despite of the presence of damping and the nonlinearity adjusts the frequency of the free-oscillation term to exactly three times the frequency of the excitation. Saddle-node bifurcations may appear in the frequency-response curve for the amplitude of the free-oscillation terms, which may lead to jump and hysteresis phenomenon. A small linear vibration absorber is designed to suppress the super-harmonic resonance response of the forced oscillator of cubic onlinearity. The absorber can be considered as a small mass-spring-damper oscillator in the sense that the mass and stiffness of the absorber are less than one-tenth of the values of the mass and linear stiffness of the forced nonlinear oscillator. It is shown that a small linear vibration absorber is effective in suppressing the super-harmonic resonance response of the system by transferring the vibrational energy from the main nonlinear oscillator to a small mass-spring-damper oscillator. Saddle-node bifurcations and jump phenomena can be easily eliminated by adding the small linear vibration absorber to the forced oscillator.
Please use this identifier to cite or link to this item: