Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

doi:10.1007/s10483-022-2853-9

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (6): 793-812.doi: https://doi.org/10.1007/s10483-022-2853-9

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

Yaode YIN, Demin ZHAO, Jianlin LIU, Zengyao XU

College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, Shandong Province, China

收稿日期:2021-12-27 修回日期:2022-04-08 出版日期:2022-06-01 发布日期:2022-06-11
通讯作者: Demin ZHAO, E-mail:zhaodemin@upc.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 11672334 and 11972375), the Natural Science Foundation of Shandong Province of China (No. ZR202011050038), and the Key R&D Program in Shandong Province of China (No. 2019GHZ001)

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

Yaode YIN, Demin ZHAO, Jianlin LIU, Zengyao XU

College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, Shandong Province, China

Received:2021-12-27 Revised:2022-04-08 Online:2022-06-01 Published:2022-06-11
Contact: Demin ZHAO, E-mail:zhaodemin@upc.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 11672334 and 11972375), the Natural Science Foundation of Shandong Province of China (No. ZR202011050038), and the Key R&D Program in Shandong Province of China (No. 2019GHZ001)

摘要/Abstract

摘要： The dielectric elastomer (DE) is an important intelligent soft material widely used in soft actuators, and the dynamic response of the DE is highly nonlinear due to the material properties. In the DE, electrostriction denotes the deformation-dependent permittivity. In the present study, we formulate the nonlinear dynamic governing equations of the DE membrane considering the electrostriction effect. The free vibration and parametric excitation of the DE membrane with different geometric sizes are calculated. The free vibration bifurcations induced by the initial location and the voltage are both discussed according to an energy-based approach. The amplitude-frequency characteristics and bifurcation diagrams of parametric excitation are also given. The results show that electrostriction decreases the free vibration amplitude and increases the frequency, but it has less influence on the parametric excitation oscillation frequency and decreases the parametric excitation amplitude except when the membrane resonates. The initial location and the applied voltage can induce the snap-through instability of the free vibration. A large geometric size will lead to a much lower resonance frequency. The resonance amplitudes increase while the resonance frequencies decrease with the increase in the applied voltage. The critical voltage of snap-through instability for the parametric excitation is larger than that for the free vibration one.

关键词: dielectric elastomer (DE), nonlinear dynamics, electrostriction, bifurcation, electroelasticity

Abstract: The dielectric elastomer (DE) is an important intelligent soft material widely used in soft actuators, and the dynamic response of the DE is highly nonlinear due to the material properties. In the DE, electrostriction denotes the deformation-dependent permittivity. In the present study, we formulate the nonlinear dynamic governing equations of the DE membrane considering the electrostriction effect. The free vibration and parametric excitation of the DE membrane with different geometric sizes are calculated. The free vibration bifurcations induced by the initial location and the voltage are both discussed according to an energy-based approach. The amplitude-frequency characteristics and bifurcation diagrams of parametric excitation are also given. The results show that electrostriction decreases the free vibration amplitude and increases the frequency, but it has less influence on the parametric excitation oscillation frequency and decreases the parametric excitation amplitude except when the membrane resonates. The initial location and the applied voltage can induce the snap-through instability of the free vibration. A large geometric size will lead to a much lower resonance frequency. The resonance amplitudes increase while the resonance frequencies decrease with the increase in the applied voltage. The critical voltage of snap-through instability for the parametric excitation is larger than that for the free vibration one.

Key words: dielectric elastomer (DE), nonlinear dynamics, electrostriction, bifurcation, electroelasticity

中图分类号:

74H45
65P40

Yaode YIN, Demin ZHAO, Jianlin LIU, Zengyao XU. Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 793-812.

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Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

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