Suppression of super-harmonic resonance response using a linear vibration absorber

Super-harmonic resonances may appear in the forced response of a weakly nonlinear oscillator having cubic nonlinearity, when the forcing frequency is approximately equal to one-third of the linearized natural frequency. Under super-harmonic resonance conditions, the frequency–response curve of the amplitude of the free-oscillation terms may exhibit saddle-node bifurcations, jump and hysteresis phenomena. A linear vibration absorber is used to suppress the super-harmonic resonance response of a cubically nonlinear oscillator with external excitation. The absorber can be considered as a small mass-spring-damper oscillator and thus does not adversely affect the dynamic performance of the nonlinear primary oscillator. It is shown that such a vibration absorber is effective in suppressing the super-harmonic resonance response and eliminating saddle-node bifurcations and jump phenomena of the nonlinear oscillator. Numerical examples are given to illustrate the effectiveness of the absorber in attenuating the super-harmonic resonance response.

► Linear absorber to suppress super-harmonic resonance response.
► Saddle-node bifurcations and jump phenomena can also be eliminated.
► The absorber can be considered as a small perturbation to the primary system.
► No need to tune the absorber natural frequency to be close of the forcing frequency.
► No optimal values of stiffness and damping of absorber exist.