Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
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Hao Dong
,
Rongchun Hu
Abstract
Dielectric elastomers are widely used in many fields due to their advantages of high deformability, light weight, biological compatibility, and high efficiency. In this study, the stochastic dynamic response and bifurcation of a dielectric elastomer balloon (DEB) with viscoelasticity are investigated. Firstly, the rheological model is adopted to describe the viscoelasticity of the DEB, and the dynamic model is deduced by using the free energy method. The effect of viscoelasticity on the state of equilibrium with static pressure and voltage is analysed. Then, the stochastic differential equation about the perturbation around the state of equilibrium is derived when the DEB is under random pressure and static voltage. The steady-state probability densities of the perturbation stretch ratio are determined by the generalized cell mapping method. The effects of parameter conditions on the mean value of the perturbation stretch ratio are calculated. Finally, sinusoidal voltage and random pressure are applied to the viscoelastic DEB, and the phenomenon of P-bifurcation is observed. Our results are compared with those obtained from Monte Carlo simulation to verify their accuracy. This work provides a potential theoretical reference for the design and application of DEs.
Funding source: National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809
Award Identifier / Grant number: 11972292
Award Identifier / Grant number: 11972293
Award Identifier / Grant number: 11902252
Funding source: National Key Laboratory of Science and Technology on Aerodynamic Design and Research
Award Identifier / Grant number: 614220119040101
Funding source: National Key Research and Development Program of China http://dx.doi.org/10.13039/501100012166
Award Identifier / Grant number: 2017YFB1102801
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos. 11972292, 11972293 and 11902252), the foundation of National Key Laboratory of Science and Technology on Aerodynamic Design and Research (No. 614220119040101), and the National Key Research and Development Program of China (No. 2017YFB1102801).
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: National Natural Science Foundation of China, National Key Laboratoryof Science and Technology on Aerodynamic Design and Research, National Key Research and Development Program of China.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] M. Wissler and E. Mazza, “Electromechanical coupling in dielectric elastomer actuators,” Sens. Actuators A: Phys., vol. 138, pp. 384–393, 2007. https://doi.org/10.1016/j.sna.2007.05.029.Suche in Google Scholar
[2] Z. G. Suo, “Theory of dielectric elastomers,” Acta Mech. Solida Sin., vol. 23, pp. 549–579, 2010. https://doi.org/10.1016/s0894-9166(11)60004-9.Suche in Google Scholar
[3] H. S. Lee, H. Phung, and D. H. Lee, “Design analysis and fabrication of arrayed tactile display based on dielectric elastomer actuator,” Sens. Actuators, A, vol. 205, pp. 191–198, 2014. https://doi.org/10.1016/j.sna.2013.11.009.Suche in Google Scholar
[4] Y. J. Liu, L. W. Liu, Z. Zhang, Y. Jiao, S. H. Sun, and J. S. Leng, “Analysis and manufacture of an energy harvester based on a Mooney-Rivlin–type dielectric elastomer,” EPL, vol. 90, pp. 1303–1324, 2010. https://doi.org/10.1209/0295-5075/90/36004.Suche in Google Scholar
[5] L. Liu, J. J. Sheng, and H. L. Chen, “Modelling of spring roll actuators based on viscoelastic dielectric elastomers,” Appl. Phys. A: Mater. Sci. Process., vol. 119, pp. 825–835, 2015.10.1007/s00339-015-9034-2Suche in Google Scholar
[6] R. Kaltseis, C. Keplinger, R. Baumgartner, M. Kaltenbrunner, T. Li, and M. Philipp, “Method for measuring energy generation and efficiency of dielectric elastomer generators,” Appl. Phys. Lett., vol. 99, pp. 162904.1–162904.3, 2011. https://doi.org/10.1063/1.3653239.Suche in Google Scholar
[7] I. A. Anderson, T. A. Gisby, T. G. Mckay, O. Brien, M. Benjamin, and E. P. Calius, “Multi-functional dielectric elastomer artificial muscles for soft and smart machines,” J. Appl. Phys., vol. 112, pp. 041101.1–041101.20, 2012. https://doi.org/10.1063/1.4740023.Suche in Google Scholar
[8] Z. Li, Y. Wang, C. C. Foo, H. Godaba, J. Zhu, and C. H. Yap, “The mechanism for large-volume fluid pumping via reversible snap-through of dielectric elastomer,” J. Appl. Phys., vol. 122, pp. 084503.1–084503.10, 2017. https://doi.org/10.1063/1.4985827.Suche in Google Scholar
[9] C. Jean-Mistral, M. Beaune, T. Vu-Cong, and A. Sylvestre, Energy Scavenging Strain Absorber: Application to Kinetic Dielectric Elastomer Generator, San Diego, Electroactive Polymer Actuators and Devices, 2014.10.1117/12.2044690Suche in Google Scholar
[10] G. Moretti, G. P. Rosati Papini, M. Right, D. Forehand, D. Ingram, and R. Vertechy, “Resonant wave energy harvester based on dielectric elastomer generator,” Smart Mater. Struct., vol. 27, p. 035015, 2018. https://doi.org/10.1088/1361-665x/aaab1e.Suche in Google Scholar
[11] T. F. Li, G. R. Li, Y. M. Liang, T. Dai, and X. Yang, “Fast-moving soft electronic fish,” Sci. Adv., vol. 3, p. e1602045, 2017. https://doi.org/10.1126/sciadv.1602045.Suche in Google Scholar PubMed PubMed Central
[12] S. Q. An, H. L. Zou, and Z. C. Deng, “Control instability and enhance performance of a dielectric elastomer balloon with a passive layer,” J. Phys. D Appl. Phys., vol. 52, p. 195301, 2019. https://doi.org/10.1088/1361-6463/ab0795.Suche in Google Scholar
[13] L. Du, Y. P. Zhao, Y. M. Lei, J. Hu, and X. L. Yue, “Suppression of chaos in a generalized Duffing oscillator with fractional-order deflection,” Nonlinear Dynam., vol. 92, pp. 1921–1933, 2018. https://doi.org/10.1007/s11071-018-4171-8.Suche in Google Scholar
[14] J. J. Sheng, H. L. Chen, B. Li, and Y. Wang, “Nonlinear dynamic characteristics of a dielectric elastomer membrane undergoing in-plane deformation,” Smart Mater. Struct., vol. 23, p. 045010, 2014. https://doi.org/10.1088/0964-1726/23/4/045010.Suche in Google Scholar
[15] S. Son and N. C. Goulbourne, “Finite deformations of tubular dielectric elastomer sensors,” J. Intell. Mater. Syst. Struct., vol. 20, pp. 2187–2199, 2009. https://doi.org/10.1177/1045389x09350718.Suche in Google Scholar
[16] S. Son and N. C. Goulbourne, “Dynamic response of tubular dielectric elastomer transducers,” Int. J. Solids Struct., vol. 47, pp. 2672–2679, 2010. https://doi.org/10.1016/j.ijsolstr.2010.05.019.Suche in Google Scholar
[17] J. Zhu, “Nonlinear oscillation of a dielectric elastomer balloon,” Polym. Int., vol. 59, pp. 378–383, 2010. https://doi.org/10.1002/pi.2767.Suche in Google Scholar
[18] Z. Wang and H. E. Tianhu, “Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion,” Appl. Math. Mech. (Engl. Ed.), vol. 39, pp. 547–560, 2018. https://doi.org/10.1007/s10483-018-2318-8.Suche in Google Scholar
[19] W. Hong, “Modeling viscoelastic dielectrics,” J. Mech. Phys. Solids, vol. 59, pp. 637–650, 2011. https://doi.org/10.1016/j.jmps.2010.12.003.Suche in Google Scholar
[20] C. C. Foo, S. Q. Cai, S. J. A. Koh, S. Bauer, and Z. G. Suo, “Model of dissipative dielectric elastomers,” J. Appl. Phys., vol. 111, p. 034102, 2012.10.1063/1.3680878Suche in Google Scholar
[21] J. Zhang, H. L. Chen, J. J. Sheng, and L. Liu, “Dynamic performance of dissipative dielectric elastomers under alternating mechanical load,” Appl. Phys. A, vol. 116, pp. 59–67, 2014. https://doi.org/10.1007/s00339-013-8092-6.Suche in Google Scholar
[22] F. Liu and J. X. Zhou, “Shooting and arc-length continuation method for periodic solution and bifurcation of nonlinear oscillation of viscoelastic dielectric elastomers,” J. Appl. Mech-T. Asme., vol. 85, p. 011005, 2018. https://doi.org/10.1115/1.4038327.Suche in Google Scholar
[23] X. L. Jin and Z. L. Huang, “Random response of dielectric elastomer balloon to electrical or mechanical perturbation,” J. Intell. Mater. Syst. Struct., vol. 28, pp. 195–203, 2017. https://doi.org/10.1177/1045389x16649446.Suche in Google Scholar
[24] X. L. Jin, Y. Wang, and Z. L. Huang, “On the ratio of expectation crossings of random-excited dielectric elastomer balloon,” Theor. Appl. Mech. Lett., vol. 7, pp. 100–104, 2017. https://doi.org/10.1016/j.taml.2017.03.005.Suche in Google Scholar
[25] J. Q. Sun and C. S. Hsu, “First-passage time probability of non-linear stochastic systems by generalized cell mapping method,” J. Sound Vib., vol. 134, pp. 181–185, 1989.10.1016/S0022-460X(88)80185-8Suche in Google Scholar
[26] X. L. Yue, W. Xu, L. Wang, and B. Zhou, “Transient and steady-state responses in a self-sustained oscillator with harmonic and bounded noise excitations,” Probabilist. Eng. Mech., vol. 30, pp. 70–76, 2012. https://doi.org/10.1016/j.probengmech.2012.06.001.Suche in Google Scholar
[27] Q. Han, W. Xu, and X. L. Yue, “Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method,” Appl. Math. Mech., vol. 36, pp. 329–336, 2015. https://doi.org/10.1007/s10483-015-1918-6.Suche in Google Scholar
[28] C. C. Foo, J. A. K. Soo, C. Keplinger, R. Kaltseis, S. Bauer, and Z. G. Suo, “Performance of dissipative dielectric elastomer generators,” J. Appl. Phys., vol. 111, p. 094107, 2012.10.1063/1.4714557Suche in Google Scholar
[29] B. Li, H. L. Chen, J. H. Qiang, J. J. Sheng, and J. X. Zhou, “Effect of viscoelastic relaxation on the electromechanical coupling of dielectric elastomer,” in International Conference on Electroactive Polymer Actuators and Devices, San Diego, 2013.10.1117/12.2009322Suche in Google Scholar
[30] M. N. Silberstein and M. C. Boyce, “Constitutive modeling of the rate, temperature, and hydration dependent deformation response of Nafion to monotonic and cyclic loading,” J. Power Sources, vol. 195, pp. 5692–5706, 2010. https://doi.org/10.1016/j.jpowsour.2010.03.047.Suche in Google Scholar
[31] X. Zhao, S. J. A. Koh, and Z. Suo, “Nonequilibrium thermodynamics of dielectric elastomers,” Int. J. Appl. Mech., vol. 3, pp. 203–217, 2011. https://doi.org/10.1142/s1758825111000944.Suche in Google Scholar
[32] X. L. Yue, W. Xu, W. T. Jia, and L. Wang, “Stochastic response of a 6 oscillator subjected to combined harmonic and Poisson white noise excitations,” Physica A, vol. 392, pp. 2988–2998, 2013. https://doi.org/10.1016/j.physa.2013.03.023.Suche in Google Scholar
[33] M. Su, W. Xu, and G. D. Yang, “Response analysis of van der pol vibro-impact system with Coulomb friction under Gaussian white noise,” Int. J. Bifurc. Chaos, vol. 28, p. 1830043, 2018. https://doi.org/10.1142/s0218127418300434.Suche in Google Scholar
[34] L. Du, Q. Guo, and Z. Sun, “Influence of non-Gaussian noise on a tumor growth system under immune surveillance,” Eur. Phys. J. Spec. Top., vol. 227, pp. 895–905, 2018. https://doi.org/10.1140/epjst/e2018-700136-8.Suche in Google Scholar
[35] Y. Zheng and J. H. Huang, “Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise,” Appl. Math. Mech. (Engl. Ed.), vol. 32, pp. 11–22, 2011. https://doi.org/10.1007/s10483-011-1389-7.Suche in Google Scholar
[36] X. Zhao and Z. Suo, “Method to analyze electromechanical stability of dielectric elastomers,” Appl. Phys. Lett., vol. 91, p. 061921, 2007. https://doi.org/10.1063/1.2768641.Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
- Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
- Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
- Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
- Battery discharging model on fractal time sets
- Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
- Optimal control for dengue eradication program under the media awareness effect
- Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
- Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
- Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
- Anti-sway method for reducing vibrations on a tower crane structure
-
Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized
- Convergence analysis of online learning algorithm with two-stage step size
- An estimative (warning) model for recognition of pandemic nature of virus infections
- Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
- Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
- An efficient class of fourth-order derivative-free method for multiple-roots
- Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
- Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
- Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
- Construction of complexiton-type solutions using bilinear form of Hirota-type
- Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
- Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
- Lump solutions to a generalized nonlinear PDE with four fourth-order terms
- Quantum motion control for packaging machines
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
- Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
- Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
- Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
- Battery discharging model on fractal time sets
- Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
- Optimal control for dengue eradication program under the media awareness effect
- Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
- Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
- Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
- Anti-sway method for reducing vibrations on a tower crane structure
-
Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized
- Convergence analysis of online learning algorithm with two-stage step size
- An estimative (warning) model for recognition of pandemic nature of virus infections
- Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
- Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
- An efficient class of fourth-order derivative-free method for multiple-roots
- Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
- Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
- Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
- Construction of complexiton-type solutions using bilinear form of Hirota-type
- Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
- Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
- Lump solutions to a generalized nonlinear PDE with four fourth-order terms
- Quantum motion control for packaging machines
