Dynamic characteristics of a quasi-zero stiffness vibration isolator with nonlinear stiffness and damping

  • Yanqi LiuEmail author
  • Longlong Xu
  • Chunfang SongEmail author
  • Huangsen Gu
  • Wen Ji


A quasi-zero stiffness (QZS) isolator is devised to acquire the feature of high-static-low-dynamic stiffness. Cam–roller–nonlinear spring mechanisms, where two horizontal dampers are installed symmetrically, are employed as a negative stiffness provider to connect in parallel with a vertical spring. From the static analysis, the piecewise restoring force in the vertical direction of the system is inferred considering possible separation between the cam and roller. The stiffness characteristics and parameters for offering zero stiffness at the equilibrium position are then determined. The dynamic equation is established and used for the deduction of the amplitude–frequency equation by means of the Harmonic Balance Method. The definitions of force and displacement transmissibility are introduced, and their expressions are derived for subsequent investigations of the effects of horizontal spring’s nonlinearity, excitation amplitude, horizontal damping, and vertical damping on the transmissibility performance. The comparative study is implemented on the isolation performance afforded by the QZS isolator and an equivalent linear counterpart, whose static bearing stiffness is same as the QZS isolator. Results indicate that the system with softening nonlinear horizontal spring can exhibit better performance than that with opposite stiffness spring. With the increase in horizontal damping ratio, the force transmissibility is further suppressed in resonance frequency range but increased in a small segment of higher frequencies and tends to unite in high frequency range. However, the horizontal damper deteriorates the ability to isolate the displacement excitation to a certain extent. Besides, the isolation capability of the QZS system depends on the magnitude of excitation amplitude. The quasi-zero stiffness system possesses lower initial isolation frequency and better isolation ability around resonance frequency compared with the linear system. Therefore, the quasi-zero stiffness isolator has superior low-frequency ability in isolating vibration over its linear counterpart.


Quasi-zero stiffness Nonlinear damping Low-frequency vibration isolation Force and displacement transmissibility 



The authors acknowledge the financial support from the Beijing Natural Science Foundation (1182010), Innovation Team Foundation of Beijing Academy of Science and Technology (IG201403C2) and Open Topic Funding Project of Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology (FM-201802).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Environment Noise and VibrationBeijing Municipal Institute of Labor ProtectionBeijingChina
  2. 2.Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical EngineeringJiangnan UniversityWuxiChina

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