Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

doi:10.1007/s10483-020-2590-7

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (3): 459-470.doi: https://doi.org/10.1007/s10483-020-2590-7

Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

Yin WANG^1,2, Ling ZHANG², Jinxiong ZHOU^1,2

1. State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China;
2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Laboratory for Vibration Control of Aerospace Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2019-10-05 修回日期:2019-12-25 出版日期:2020-03-01 发布日期:2020-02-17
通讯作者: Jinxiong ZHOU E-mail:jxzhouxx@mail.xjtu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11702215 and 11972277) and the Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2017JQ5062 and 2018JQ1029)

Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

Yin WANG^1,2, Ling ZHANG², Jinxiong ZHOU^1,2

1. State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China;
2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Laboratory for Vibration Control of Aerospace Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China

Received:2019-10-05 Revised:2019-12-25 Online:2020-03-01 Published:2020-02-17
Contact: Jinxiong ZHOU E-mail:jxzhouxx@mail.xjtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11702215 and 11972277) and the Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2017JQ5062 and 2018JQ1029)

摘要/Abstract

摘要： Dielectric elastomer (DE) is suitable in soft transducers for broad applications, among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices call for an efficient and reliable method to analyze the dynamic response of DE. This remains to be a challenge since the resultant vibration equation of DE, for example, the vibration of a DE balloon considered here is highly nonlinear with higher-order power terms and time-dependent coefficients. Previous efforts toward this goal use largely the numerical integration method with the simple harmonic balance method as a supplement. The numerical integration and the simple harmonic balance method are inefficient for large parametric analysis or with difficulty in improving the solution accuracy. To overcome the weakness of these two methods, we describe formulations of the incremental harmonic balance (IHB) method for periodic forced solutions of such a unique system. Combined with an arc-length continuation technique, the proposed strategy can capture the whole solution branches, both stable and unstable, automatically with any desired accuracy.

关键词: dielectric elastomer, nonlinear oscillation, incremental harmonic method, arc-length continuation

Abstract: Dielectric elastomer (DE) is suitable in soft transducers for broad applications, among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices call for an efficient and reliable method to analyze the dynamic response of DE. This remains to be a challenge since the resultant vibration equation of DE, for example, the vibration of a DE balloon considered here is highly nonlinear with higher-order power terms and time-dependent coefficients. Previous efforts toward this goal use largely the numerical integration method with the simple harmonic balance method as a supplement. The numerical integration and the simple harmonic balance method are inefficient for large parametric analysis or with difficulty in improving the solution accuracy. To overcome the weakness of these two methods, we describe formulations of the incremental harmonic balance (IHB) method for periodic forced solutions of such a unique system. Combined with an arc-length continuation technique, the proposed strategy can capture the whole solution branches, both stable and unstable, automatically with any desired accuracy.

Key words: dielectric elastomer, nonlinear oscillation, incremental harmonic method, arc-length continuation

中图分类号:

74H45

Yin WANG, Ling ZHANG, Jinxiong ZHOU. Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 459-470.

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Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

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