Dynamics of a cubic nonlinear vibration absorber (Q1974264)

This paper deals with the practically important phenomenon of vibration absorption, i.e. the dissipation-free suppression of a forced vibration. This effect is usually achieved making use of the fact that oscillatory systems coupled with quadratic nonlinearities possess a 2:1 internal resonance for which a saturation phenomenon exists. The authors of this interesting and very well written paper study the saturation phenomenon in systems where the coupling is done with cubic terms instead of quadratic ones. Using the method of multiple scales, the authors construct approximate solutions to nonlinear equations of motion. A bifurcation analysis of solutions is performed, and a small domain of existence of saturation phenomenon is calculated. Additionally, the authors prove the existence of more complicated dynamic behavior.