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Revisited chaotic vibrations in dielectric elastomer systems with stiffening

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Abstract

Dielectric elastomer is a type of soft materials which can deform under applied voltage. Here, irregular vibrations in a circular dielectric elastomer membrane with stiffening under periodic forcing are studied. The stiffening phenomenon can induce fast increases in the potential energies near the limiting stretches, which induces challenges to the numerical simulations. By comparing different numerical strategies, the adaptive step size method with allowable very small step sizes is used to simulate the system. For the system with or without damping, the existence of chaos is then verified through the positive maximum Lyapunov exponent and the fractal structures in the phase plane simultaneously. The local dynamic analysis shows the strong contribution of regions near the limiting stretches to the occurrence of chaos, revealing the important role of the stiffening. For the system with damping, the rich dynamical behaviors accompanying chaos such as the period-doubling route to chaos and the long chaotic transients also provide further consistent supports for the existence of chaos. For the system without damping, chaos region in a parameter plane is located by using different initial conditions, revealing the transitional behaviors from periodic states to chaos. Besides, the chaos is more easily to occur in the system without damping. Thus, the study here is useful to avoid or further handle such complex irregular dynamics.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (11972290), as well as the Natural Science Foundation of Shaanxi Province of China (2020JM-105).

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710072, China

    Hai-Lin Zou & Zi-Chen Deng

  2. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, China

    Hai-Lin Zou & Zi-Chen Deng

  3. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, 100124, China

    Hongyuan Zhou

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  1. Hai-Lin Zou
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  2. Zi-Chen Deng
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Correspondence to Hai-Lin Zou.

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Zou, HL., Deng, ZC. & Zhou, H. Revisited chaotic vibrations in dielectric elastomer systems with stiffening. Nonlinear Dyn 110, 55–67 (2022). https://doi.org/10.1007/s11071-022-07617-x

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