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.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- 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
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- 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
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- 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
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Articles in the same Issue
- 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
