A passive negative stiffness damper in series with a flexible support: Theoretical and experimental study

Dampers with negative stiffness behavior have been widely investigated for structural vibration control due to their superior performance. In practical applications, a support in series with these dampers might have some flexibility, that is, the stiffness is positive but finite. This paper investigates the effects of that flexibility on the performance of a passive negative stiffness damper (PNSD). First, a system consisting of a PNSD in series with a flexible support is presented, and the lower limit of the support stiffness needed to keep the system stable is derived. Second, a mechanical model for the proposed system is analyzed theoretically. An equivalent model of the damping force is established. The deformation of the flexible link is illustrated, followed by a demonstration of its effect on the hysteresis loops. Finally, an experimental investigation is performed to evaluate the performance of the PNSD support system. A device that contains an oil damper and two compressed springs is utilized to provide negative stiffness and Coulomb friction behavior. One of the set of springs is then incorporated to act as a positive but finite stiffness support in series with the device. Tests are conducted to assess the hysteretic behavior of the overall system. Theoretical and experimental results indicate that a range of equivalent negative stiffness and Coulomb friction level can be achieved simply, depending upon the positive stiffness of the flexible support in series with the PNSD.