Skip to main content
SpringerLink
Log in

Analysis of quasi-periodic and chaotic motion of a dielectric elastomer shell under alternating voltage

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

The nonlinear dynamical behaviors are investigated for the dielectric elastomer (DE) spherical shell subjected to the internal pressure and alternating voltage, where the shell is composed of the incompressible hyperelastic material described by the third-order Ogden model. Considering the initial boundary conditions, the incompressible constraint and the Euler-Lagrange equation, the governing equations describing the radially symmetric motions for the dielectric elastic spherical shell are derived. Employing the qualitative analyses and numerical calculations, the dynamical response analyses of the nonlinear system are conducted. The effects of the direct current (DC) voltage and the uniformly distributed pressure on the quasi-periodic and chaotic motion for the DE spherical shell are discussed. The results indicate that the DC voltage and internal pressure have significant effects on the nonlinear oscillation of the shell. The critical values of the DC voltage and the internal pressure are presented for the shell undergoing the chaotic motions. The changes of the DC voltage and internal pressure, the corresponding critical values will increase or decrease. The present study may provide theoretical and practical significances for the design and applications of the DE structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

All the data in this paper are generated from the nonlinear differential equations studied and are real and reliable, and do not involve the use of data in other papers.

References

  1. Tan D, Wang K, Zhou J et al (2023) A brief review of nonlinear triboelectric nanogenerator. Int J Dyn Control. https://doi.org/10.1007/s40435-023-01292-5

    Article  Google Scholar 

  2. Lv XF, Liu LW, Leng JS et al (2018) Dynamic performance of dielectric elastomer balloon incorporating stiffening and damping effect. Smart Mater Struct 27(10):105036

    Article  Google Scholar 

  3. Touairi S, Mabrouki M (2022) Chaotic dynamics applied to piezoelectric harvester energy prediction with time delay. Int J Dyn Control 10:699–720

    Article  Google Scholar 

  4. Deng YF, Zhou HF, Li QL et al (2021) Research progress in actuator based on dielectric elastomer. China Plast 35(11):161–172

    Google Scholar 

  5. Wu W, Zhang S, Wu Z et al (2021) On the understanding of dielectric elastomer and its application for all-soft artificial heart. Sci Bull 66(10):981–990

    Article  Google Scholar 

  6. Suo ZG, Zhao XH, Greene WH (2008) A nonlinear field theory of deformable dielectrics. J Mech Phys Solids 56(2):467–486

    Article  MathSciNet  Google Scholar 

  7. Zhu J, Cai S, Suo Z (2010) Nonlinear oscillation of a dielectric elastomer balloon. Polym Int 59(3):378–383

    Article  Google Scholar 

  8. Fang K, Jin XL, Wang Y et al (2017) Dynamic stability of spherical delectric elastomer balloon. Chin J Solid Mech 38(2):146–156

    Google Scholar 

  9. Yin YD, Zhao DM, Liu JL et al (2022) Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction. Appl Math Mech-Engl 43:793–812

    Article  MathSciNet  Google Scholar 

  10. Shi HR, Xiang N, Li ZG (2021) Vibration characteristic analysis of opening spherical shell with local active constrained layer damping. J Harbin Inst Technol (Chin Ed) 53(7):154–163

    Google Scholar 

  11. Liang X, Cai S (2018) New electromechanical instability modes in dielectric elastomer balloons. Int J Solids Struct 132:96–104

    Article  Google Scholar 

  12. Bortot E (2017) Analysis of multilayer electro-active spherical balloons. J Mech Phys Solids 101:250–267

    Article  MathSciNet  Google Scholar 

  13. Alibakhshi A, Chen W, Destrade M (2023) Nonlinear vibration and stability of a dielectric elastomer balloon based on a strain-stiffening model. J Elasticity 153(4–5):533–548

    Article  MathSciNet  Google Scholar 

  14. Li T, Keplinger C, Baumgartner R et al (2013) Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. J Mech Phys Solids 61(2):611–628

    Article  Google Scholar 

  15. Xie YX, Liu JC, Fu YB (2016) Bifurcation of a dielectric elastomer balloon under pressurized inflation and electric actuation. Int J Solids Struct 78:182–188

    Article  Google Scholar 

  16. Zhang H, Dai M, Zhang ZS et al (2019) Analytical models for circular and spherical dielectric elastomers. J Southeast Univ Engl Ed 35(3):288–291

    Google Scholar 

  17. Huo YJ, Zhao J, Liu SN (2021) Research and application of curved cylindrical dielectric elastomer drive unit. Sm Spl ELEC Mach 49(3):21–25

    Google Scholar 

  18. Jin XL, Wang Y, Huang ZL (2017) Random history curve of dielectric elastomer balloon subjected to disturbed uniformly distributed pressure. J Dyn Control 15(03):250–255

    Google Scholar 

  19. Jin X, Wang Y, Huang Z (2017) On the ratio of expectation crossings of random-excited dielectric elastomer balloon. Theor Appl Mech Lett 7(2):100–104

    Article  Google Scholar 

  20. Jin X, Tian Y, Wang Y et al (2018) Optimal bounded parametric control for random vibration of dielectric elastomer balloon. Nonlinear Dynam 94:1081–1093

    Article  Google Scholar 

  21. Tian Y, Jin X, Huang Z et al (2020) Reliability evaluation of dielectric elastomer balloon subjected to harmonic voltage and random uniformly distributed pressure. Mech Res Commun 103:103459–103459

    Article  Google Scholar 

  22. Liu F, Zhou J (2018) Shooting and arc-length continuation method for periodic solution and bifurcation of nonlinear oscillation of viscoelastic dielectric elastomers. J Appl Mech 85(1):011005

    Article  MathSciNet  Google Scholar 

  23. Zhao XH, Suo ZG (2007) Method to analyze electromechanical stability of dielectric Elastomers. Appl Phys Lett 10(1063/1):2768641

    Google Scholar 

  24. Liu YJ, Liu LW, Sun SH et al (2009) Stability analysis of dielectric elastomer film actuator. Sci China Ser E 52(9):2715–2723

    Article  Google Scholar 

  25. Ogden RW, Saccomandi G, Sgura I (2004) Fitting hyperelastic models to experimental data. Comput Mech 34:484–502

    Article  Google Scholar 

  26. Ogden RW (1972) Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc A Math Phys Eng Sci 326:565–584

    Google Scholar 

  27. Zhou JX, Wei ZG, Mao H et al (2022) Numerical calculation for isotropic hyperelasticity of constitutive model and verification. Chin J Comput Mech 39(4):523–530

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 12172086) and the Doctoral Start-up Foundation of Liaoning Province (No. 2023-BS-080).

Funding

This work was supported by the National Natural Science Foundation of China and the Doctoral Start-up Foundation of Liaoning Province.

Author information

Authors and Affiliations

  1. School of Science, Dalian Minzu University, Dalian, 116600, China

    Yuping Tang & Xuegang Yuan

  2. College of Mechanical and Electronic Engineering, Dalian Minzu University, Dalian, 116600, China

    Zhentao Zhao

Authors
  1. Yuping Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhentao Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuegang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. In this manuscript, authorship contribution as follows: YP contributed to writing—original draft, calculation, investigation and formal analysis. XG contributed to writing—review and editing, supervision, project administration and funding acquisition. ZT contributed to writing—review and editing, supervision, resources, project administration, methodology, funding acquisition and conceptualization.

Corresponding author

Correspondence to Xuegang Yuan.

Ethics declarations

Conflict of interest

This manuscript has no financial interest in the work submitted for publication. The authors have no financial or proprietary interests in any material discussed in this article.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, Y., Zhao, Z. & Yuan, X. Analysis of quasi-periodic and chaotic motion of a dielectric elastomer shell under alternating voltage. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01436-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40435-024-01436-1

Keywords

Search

Navigation