Analytical Solution and Energy Flow Analysis of a Vertical Vibration-Controlled System Using the Nonlinear Energy Sink

The nonlinear energy sink (NES) has drawn increasing research attention in recent years. In this study, we investigated a novel disc spring-based vertical NES device capable of counterbalancing payload gravity and providing a combination of linear and cubic restoring forces. The vertical NES device is used to mitigate vibration responses in vertically flexible structures caused by human or machinery-induced actions. To simplify the NES controlled system, a two-degree-of-freedom model was used to account for harmonic forces acting on the primary structure. Using the complexification-averaging (CX-A) method, we obtained the frequency-amplitude solution and subsequently derived the force transmissibility (T_f). Parametric comparisons between the NES and traditional tuned mass damper (TMD)-controlled systems were performed by comparing the T_f curves and numerically verifying the theoretical solutions. Results confirmed the accuracy of the theoretical force transmissibility solutions and affirmed the advantage of the NES system by overcoming the limited operating frequency bandwidth of the traditional TMD system. The inclusion of a linear stiffness term in an NES system has been shown to enhance the vibration control performance within the resonant frequency bandwidth. In addition, the time history energy analysis for the NES and TMD systems was conducted. The energy flow analysis elucidated the broad operating bandwidth of the NES system. This finding suggests that the vibration energy flow to the attachment in the NES system is irreversible, thereby preventing amplification of the response in the primary structure, even when the system is mistuned.