The Non-Linear Energy Sink Applied to Vertical Floor Vibration Mitigation

This thesis investigates the non-linear energy sink (NES) and its application to floor vibration mitigation. The NES is a passive type mass damper comprised of an essentially non-linear stiffness component. This non-linear stiffness property allows the NES to interact with a wide variety of frequency regimes that can vary both widely and randomly throughout flooring systems. Flooring systems are regularly subjected to these changing inputs from general use and occupancy, as well as, human and mechanical induced loading. It is known that the NES has been successfully implemented for vibration mitigation in the horizontal direction. However, to achieve this non-linearity in the vertical direction, the offset produced by gravitational force needs to be considered. This thesis proposes an NES device that compensates for this gravitational force and investigates its interaction and application to vertical floor vibration mitigation. The device’s geometric mechanism and its derivation are presented, as well as, the limitations and extent of its physical properties. In addition, a simplified floor model is derived using structural dynamic analysis techniques and is studied under three cases which include: a control, a traditional tuned mass damper, and the new proposed device. The results support the assumption that the device’s non-linear restoring force can be approximately modeled as a cubic function. This approximation allows for simplification in both the model’s analysis and optimization stages. Also, the results show that the device can be affective at mitigating vertical vibration modes. This supports the theory that a frequency independent non-linear mechanism can be produced for the vertical vibration mitigation needed in flooring systems.