Abstract:
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.
