Dynamics of a novel 2-DOF coupled oscillators with geometry nonlinearity.

This paper focuses on the investigation of the dynamics of novel 2-DOF coupled oscillators. The system consists of a linear oscillator (main structure) and an attached lightweight nonlinear oscillator, called a nonlinear energy sink (NES), under harmonic forcing in the regime of 1:1:1 resonance. The studied NES has geometrically nonlinear stiffness and damping. Due to the degeneracies that the NES brings to the system, diverse bifurcation structures and rich dynamical phenomena such as nonlinear beating and strongly modulated response occur. The latter two phenomena represent different patterns of energy transfer. To capture the bifurcation structure, the slow flow of the system can be acquired with the use of the complex-averaging method. Furthermore, by applying the bifurcation analysis technique, we get curve boundaries of several bifurcation points in the parameter space. These boundaries will induce different types of folding structures, which can lead to complicated patterns of strongly modulated responses, in which intense energy transfer from the main structure to NES occurs. To study the necessary parameter conditions of strongly modulated responses, we analyzed the dynamics of different time scales of the slow flow in detail and determined the corresponding parameter ranges finally. It is worth noting that the small parameter ε may have a qualitative impact on the dynamics of the system. [ABSTRACT FROM AUTHOR]