Stability evaluation and design of negative stiffness amplifying damper-incorporated nonlinear structures

Negative stiffness-incorporated dampers have been widely accepted as effective vibration mitigation systems for flexible structural stiffness adjustment and enhanced energy dissipation. However, current investigations and optimal designs of negative stiffness-incorporated structures are limited to the linear elastic assumption of primary structures, potentially causing stability issues and unsatisfactory control performance. In this case, this study derives the stability criterion for negative stiffness amplifying damper (NSAD)-incorporated nonlinear structures and establishes stability-oriented design as well as modification formulae. The theoretical foundation of NSADs and nonlinear primary structures are initially introduced, based on which the stability criterion is derived according to the Routh–Hurwitz stability criterion. Following the existing design of linear elastic assumption, an endurance time acceleration series is generated subsequently to examine the proposed stability criterion for NSAD-equipped nonlinear structures. Consequently, the stability-oriented design method and corresponding modification formulae are proposed for near-field and far-field earthquakes, of which the effectiveness is validated through design cases. The results underscore the importance of considering structural nonlinearity for ensuring stability and designing NSAD-equipped nonlinear structures, demonstrating the feasibility of using the proposed correction factors to guarantee the stability of NSAD-equipped nonlinear structures subjected to multi-type earthquakes with various intensities. Additionally, the established design framework successively provides a high-efficiency energy dissipation device for seismic control of nonlinear structures, simultaneously generating easy-to-use design formulae for NSADs by combining the linear structure-based design and modification factors, facilitating direct design of nonlinear structures.