Power flow behaviour and dynamic performance of a nonlinear vibration absorber coupled to a nonlinear oscillator

The vibrational power flow characteristics of a two-degree-of-freedom system are investigated to examine the performance of nonlinear absorbers in vibration attenuation of nonlinear primary oscillators. The nonlinearities in the oscillator and those in the absorber are both characterised by cubic restoring and damping forces. Both analytical approximations and numerical integrations are used to obtain time-averaged power flow variables, as well as kinetic energies of the system. Power absorption ratio and the kinetic energy of the nonlinear oscillator are proposed to quantitatively evaluate the effectiveness of nonlinear absorbers with respect to the existing nonlinearities in the oscillator. Comparing with linear absorbers, it is found that softening (hardening) stiffness absorber provides benefits for vibration mitigation of a hardening (softening) stiffness primary oscillator by enhancing power absorption efficiency and reducing the kinetic energy of the oscillator so that the functioning frequency range of the absorber can be enlarged. Nonlinear cubic damping in the absorber is shown beneficial for vibration suppression as the power absorption ratio becomes large at resonance frequencies so that the peak power flow and kinetic energy levels are reduced. The developed model can be conveniently extended to study other types of nonlinearities in the absorber/oscillator. Conclusions and suggestions are provided for applications.