FrequencyEnergy Analysis of Coupled Linear Oscillator With Unsymmetrical Nonlinear Energy Sink

Abstract

The underlying nonlinear dynamical behavior of a linear oscillator (LO) attached with nonlinear energy sink (NES) is usually revealed by studying the LONES system on the frequencyenergy plot (FEP). Accordingly, different kinds of periodic motions on the backbone curves of the nonlinear normal modes (NNMs) and their associated subharmonic branches are analyzed. Here, the considered unsymmetrical nonlinear energy sink (UNES) incorporates a cubic stiffness element in one direction of the motion and a weak linear restoring coupling stiffness in both directions of the motion. This UNES is attached with the LO in the LOUNES system which is studied here on the FEP. Therefore, the obtained FEP of the LOUNES system is generated and analyzed. Accordingly, several unsymmetrical backbone curves of periodic oscillations between the UNES mass and the LO mass at 1:1 resonance have been obtained for broad range of nonlinear frequency levels.