Homoclinic Bifurcations and Chaos Thresholds of Tristable Piezoelectric Vibration Energy Harvesting Systems

LI Haitao; DING Hu; CHEN Liqun; QIN Weiyang

doi:10.21656/1000-0887.410164

Volume 41 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(12): 1311-1322

LI Haitao, DING Hu, CHEN Liqun, QIN Weiyang. Homoclinic Bifurcations and Chaos Thresholds of Tristable Piezoelectric Vibration Energy Harvesting Systems[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1311-1322. doi: 10.21656/1000-0887.410164

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Homoclinic Bifurcations and Chaos Thresholds of Tristable Piezoelectric Vibration Energy Harvesting Systems

doi: 10.21656/1000-0887.410164

¹Department of Engineering Mechanics, School of Science, North University of China, Taiyuan 030051, P.R.China;²Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China;³Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Science Fund for Young Scholars of China(11902294)；China Postdoctoral Science Foundation(2018M640373)

Received Date: 2020-06-08
Publish Date: 2020-12-01

Abstract

Abstract

Nonlinear dynamic performances such as homoclinic bifurcation and chaos were investigated for tristable vibration energy harvesting systems. The analytical expression of the symmetric and asymmetric homoclinic solution was obtained through the Padé approximation, which was consistent with the numerical solution. According to the Melnikov theory, the qualitative method of studying the homoclinic bifurcation of the energy harvesting system with a triple well was developed, and the necessary condition for the occurrence of homoclinic bifurcation was obtained. Numerical simulations yielded bifurcation diagrams and maximum Lyapunov exponents that demonstrated the inter-well responses predicted with the Melnikov method. Compared with the system with symmetric potential energy, the system with asymmetric potential energy has a lower threshold of homoclinic bifurcation. For a low excitation level, the system with asymmetric potential energy witnesses inter-well chaos, while the response of the system with symmetric potential energy still keeps trapped in a single well. The change of symmetry of the system potential energy function improves the output voltage due to the increase in the probability of generating a large periodical inter-well oscillation response. The research on the homoclinic bifurcation of nonlinear energy harvesting systems with symmetric and asymmetric triple potential wells provides an effective tool for the parametric design of high-performance energy harvesters.
- tristability,
- energy harvesting,
- Melnikov function,
- homoclinic bifurcation

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References(21)

References

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