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Global dynamics for a class of tristable system with negative stiffness

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  • Zhou, Biliu
  • Jin, Yanfei
  • Xu, Huidong

Abstract

Tristable system with negative stiffness has attracted extensive attention in the low frequency vibration isolation and vibration energy harvester. As a low frequency vibration isolator, it can achieve high static stiffness and low dynamic stiffness. As a vibration energy harvester, it had a wider bandwidth for resonance than the bistable one. The introduction of negative stiffness may induce subharmonic resonance and chaos in the tristable system. Chaos usually brings disorder to mechanical vibration system. Subharmonic resonance plays the negative effect on low frequency vibration isolation because they will transfer the high frequency energy of the system to the low frequency, but it is beneficial to broaden the working frequency band of vibration energy harvester. In this paper, the subharmonic bifurcation and chaos of a class of tristable system with negative stiffness are studied. The piecewise linearized systems are established to approximate the system with tristable potential. In order to conduct Melnikov analysis, the homoclinic-heteroclinic orbits and periodic orbits for the unperturbed piecewise linearized system are obtained respectively. The subharmonic Melnikov method for nonsmooth systems with four switched manifolds is developed. The thresholds for homoclinic-heteroclinic chaos and subharmonic resonance are derived by using non-smooth Melnikov method. It provides a theoretical support not only for design of the vibration energy harvester to obtain wider working frequency band, but also for design of the vibration isolation system to avoid high frequency energy transfer to low frequency. Moreover, the phenomena for infinite subharmonic bifurcations to chaos from odd order subharmonic orbit and the coexistence for chaotic and subharmonic attractors are revealed. The subharmonic Melnikov method with four switching manifolds developed in this paper lays a foundation for the subharmonic resonance analysis of other nonsmooth tristable systems.

Suggested Citation

  • Zhou, Biliu & Jin, Yanfei & Xu, Huidong, 2022. "Global dynamics for a class of tristable system with negative stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007123
    DOI: 10.1016/j.chaos.2022.112509
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    References listed on IDEAS

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    1. Chen, Enli & Xing, Wuce & Wang, Meiqi & Ma, Wenli & Chang, Yujian, 2021. "Study on chaos of nonlinear suspension system with fractional-order derivative under random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Castro, Jose & Alvarez, Joaquin & Verduzco, Fernando & Palomares-Ruiz, Juan E., 2017. "Chaotic behavior of driven, second-order, piecewise linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 8-13.
    3. Yang, Tao & Liu, Jiye & Cao, Qingjie, 2018. "Response analysis of the archetypal smooth and discontinuous oscillator for vibration energy harvesting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 358-373.
    4. Zhou, Liangqiang & Ji, Peng & Chen, Fangqi, 2021. "Chaos and subharmonic bifurcation of a composite laminated buckled beam with a lumped mass," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    5. Li, Yi & Zhou, Shengxi & Yang, Zhichun & Guo, Tong & Mei, Xutao, 2019. "High-performance low-frequency bistable vibration energy harvesting plate with tip mass blocks," Energy, Elsevier, vol. 180(C), pages 737-750.
    6. Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2006. "Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 705-714.
    7. Deng, Shuning & Ji, Jinchen & Wen, Guilin & Xu, Huidong, 2021. "A comparative study of the dynamics of a three-disk dynamo system with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    8. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz, 2019. "Evolution of the geometric structure of strange attractors of a quasi-zero stiffness vibration isolator," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 47-57.
    9. Lou, Jing-Jun & Zhu, Shi-Jian & He, Lin & He, Qi-Wei, 2009. "Experimental chaos in nonlinear vibration isolation system," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1367-1375.
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    Cited by:

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    3. Peng, Ruyue & Li, Qunhong & Zhang, Wei, 2024. "Homoclinic bifurcation analysis of a class of conveyor belt systems with dry friction and impact," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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