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Smart Structures and Systems
  Volume 26, Number 4, October 2020, pages 481-493
DOI: http://dx.doi.org/10.12989/sss.2020.26.4.481
 


A negative stiffness inerter system (NSIS) for earthquake protection purposes
Zhipeng Zhao, Qingjun Chen, Ruifu Zhang, Yiyao Jiang and Chao Pan

 
Abstract
    The negative stiffness spring and inerter are both characterized by the negative stiffness effect in the force-displacement relationship, potentially yielding an amplifying mechanism for dashpot deformation by being incorporated with a series tuning spring. However, resisting forces of the two mechanical elements are dominant in different frequency domains, thus leading to necessary complementarity in terms of vibration control and the amplifying benefit. Inspired by this, this study proposes a Negative Stiffness Inerter System (NSIS) as an earthquake protection system and developed analytical design formulae by fully utilizing its advantageous features. The NSIS is composed of a sub-configuration of a negative stiffness spring and an inerter in parallel, connected to a tuning spring in series. First, closed-form displacement responses are derived for the NSIS structure, and a stability analysis is conducted to limit the feasible domains of NSIS parameters. Then, the dual advantageous features of displacement reduction and the dashpot deformation amplification effect are revealed and clarified in a parametric analysis, stimulating the establishment of a displacement-based optimal design framework, correspondingly yielding the design formulae in analytical form. Finally, a series of examples are illustrated to validate the derived formulae. In this study, it is confirmed that the synergistic incorporation of the negative stiffness spring and the inerter has significant energy dissipation efficiency in a wide frequency band and an enhanced control effect in terms of the displacement and shear force responses. The developed displacement-based design strategy is suitable to utilize the dual benefits of the NSIS, which can be accurately implemented by the analytical design formulae to satisfy the target vibration control with increased energy dissipation efficiency.
 
Key Words
    inerter; negative stiffness; energy dissipation efficiency; deformation amplification; optimal design
 
Address
(1) Zhipeng Zhao, Qingjun Chen, Ruifu Zhang:
State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
(2) Zhipeng Zhao, Qingjun Chen, Ruifu Zhang, Yiyao Jiang:
Department of Disaster Mitigation for Structures, Tongji University, Shanghai 200092, China
(3) Chao Pan:
College of Civil Engineering, Yantai University, Yantai 264005, China
 

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