Enhanced energy dissipation benefit of negative stiffness amplifying dampers

Negative-stiffness devices are of rapidly increasing interest for high-performance vibration control. With a tuning spring in series, the negative-stiffness device forms an enhancement mechanism for the dashpot, named the negative stiffness amplifying damper (NSAD), which is much more efficient in dissipating energy than the viscous damper alone. Based on the observed enhancement phenomenon, this study reveals the theoretical basis of the energy dissipation enhancement benefit by deriving the analytical enhanced energy dissipation formula. The basic concept and physical realization methods for the negative-stiffness device are introduced, based on which the mechanical models of NSAD and NSAD-equipped structures are established for dimensionless response analysis. Following a stochastic framework, the stochastic responses of the NSAD-equipped structure are solved in closed form. Correspondingly, simple and easy-to-understand equations are derived and denoted as the “enhanced energy dissipation formula” to quantify each component's contribution in the NSAD explicitly. Inspired by the formula, a design framework with two strategies is proposed for NSADs with a synthetic consideration of the energy dissipation enhancement mechanism and target control performance. Following the design principle, detailed design formulae are derived in a simple form. Finally, a design procedure is provided and applied to a series of design cases for illustration. The results show that the energy dissipation enhancement mechanism enables NSADs to offer improved energy dissipation efficiency over conventional dampers without sacrificing the vibration isolation effect or the excessive damping force. The analytical formula clearly explains the theoretical basis by quantifying the NSAD components’ contribution to the vibration control and energy dissipation enhancement effects. Based on this newly explained benefit, the design framework successively provides a high-efficiency energy dissipation device that fulfills its intended control performance. In addition, the easy-to-use design formulae are derived for the new design strategy to allow the direct design of NSADs.