Enhancements of Vibration Absorption of Nonlinear Energy Sink by Additional Degree of Freedom Oscillator

The vibration absorption performance of two kinds of two-degree-of-freedom (TDOF) nonlinear energy sinks (NESs) is studied and compared to that of a single-degree-of-freedom (SDOF) NES. The two TDOF NESs have different stiffness characteristics in their second degree of freedom. One has a purely cubic, and the other one has a bi-stable stiffness characteristic. Complexification-averaging and Runge–Kutta methods are used to investigate the performance of the NESs. The results show that the vibration absorption performance of both TDOF NESs is significantly higher than that of the SDOF NES after the excitation amplitude increases to a certain value, under both harmonic and shock excitations. The performance of all three NESs is similar below this critical value. In addition, the unstable response induced by the SDOF NES is found to precede higher response branches. However, the additional oscillators in the two TDOF NESs cause the unstable responses to revert to stable responses, and the unstable responses reappear and further transformed into higher branches until the excitation amplitude reaches a relatively high value. Moreover, the results demonstrate that the two TDOF NESs have advantages over each other in different excitation ranges. The NES with a bi-stable component is superior to the NES with only purely cubic components in a relatively wide excitation range of harmonic and shock excitations.