Nonlinear Dynamics

, Volume 97, Issue 4, pp 2499–2519 | Cite as

Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets

  • Bo YanEmail author
  • Hongye Ma
  • Bin Jian
  • Ke Wang
  • Chuanyu Wu
Original paper


This paper proposes a novel bi-state nonlinear vibration isolator (BS-NVI) consisting of a linear mass–spring–damper and several permanent magnets (PMs). The working state of the BS-NVI can be monostable or bistable depending on the relative position of the PMs. The theoretical model of the BS-NVI is established. The transmissibility of the BS-NVI is derived according to the harmonic balance method. Both the simulation and experimental efforts are performed to study the nonlinear dynamics and vibration isolation performance of the BS-NVI. The results demonstrate that the monostable isolator acts like a quasi-zero-stiffness isolator and exhibits the hardening-spring-liked characteristic. With the change in the relative position of the PMs, the transmissibility and the peak frequency are decreased. However, the bistable isolator undergoes the interwell and intrawell oscillations with the change in the excitation amplitude and frequency. The motion of the bistable isolator can be periodic or chaotic. Due to the snap-through action, the transmissibility of the bistable isolator could be smaller than 1 in part of the resonance region.


Bistable isolator Nonlinear isolator Monostable Nonlinear vibration Magnetic spring Negative stiffness 



Bi-state nonlinear vibration isolator


Harmonic balance method


High-static-low-dynamic stiffness


Permanent magnets

\(\hbox {PM}^{\mathrm{b}}\)

Base PM

\(\hbox {PM}^{\mathrm{M}}\)

Moving PM





This work was supported by the National Natural Science Foundation of China under Grant No. 11602223.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering and AutomationZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.China Manned Space AgencyBeijingChina
  3. 3.Key Laboratory of Space Utilization, Technology and Engineering Center for Space UtilizationChinese Academy of SciencesBeijingChina

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