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

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Abstract

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.

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Abbreviations

BS-NVI:

Bi-state nonlinear vibration isolator

HBM:

Harmonic balance method

HSLDS:

High-static-low-dynamic stiffness

PM:

Permanent magnets

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

Base PM

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

Moving PM

QZS:

Quasi-zero-stiffness

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Acknowledgements

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

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Authors and Affiliations

  1. Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Bo Yan, Hongye Ma & Chuanyu Wu

  2. China Manned Space Agency, Beijing, 100071, China

    Bin Jian

  3. Key Laboratory of Space Utilization, Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing, 100094, China

    Bo Yan & Ke Wang

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Appendix A: Effect of higher-order terms of nonlinear restoring force on the response of the isolator

Appendix A: Effect of higher-order terms of nonlinear restoring force on the response of the isolator

Figure 28a shows the comparison of the nonlinear restoring force between the ninth-order and cubic polynomial fits, where \(D=28.6\,\hbox {mm}\), \(H=13\,\hbox {mm}\). The corresponding nonlinear stiffness coefficients are listed in Table 4. It demonstrates that the accuracy of the ninth-order polynomial is better than that of the cubic polynomial fit. Based on these two kinds of polynomial fit shown in Fig. 28a and Table 4, the displacement bifurcation diagram is plotted when the excitation frequency is 5Hz and the result is presented in Fig. 28b. One can clearly see that these two nonlinear dynamic responses are totally different with each other. The results imply that the ninth-order polynomial fit could more exactly describe the nonlinear restoring force and nonlinear dynamic responses.

Table 4 Nonlinear stiffness coefficients of the ninth-order and cubic polynomial fits
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Yan, B., Ma, H., Jian, B. et al. Nonlinear dynamics analysis of a bi-state nonlinear vibration isolator with symmetric permanent magnets. Nonlinear Dyn 97, 2499–2519 (2019). https://doi.org/10.1007/s11071-019-05144-w

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