Analytical asymptotic approximations for large amplitude nonlinear free vibration of a dielectric elastomer balloon

Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period and periodic solution for a spherical dielectric elastomer balloon subjected to static pressure and voltage are derived thro...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-05, Vol.88 (3), p.2255-2264
Main Authors: Tang, Dafeng, Lim, C. W., Hong, Ling, Jiang, Jun, Lai, S. K.
Format: Article
Language:English
Subjects:
Amplitudes
Automotive Engineering
Balloons
Classical Mechanics
Control
Dielectrics
Dynamical Systems
Elastomers
Engineering
Free vibration
Harmonic balance method
Mechanical Engineering
Nonlinear differential equations
Nonlinear programming
Nonlinear systems
Nonlinearity
Numerical integration
Original Paper
Runge-Kutta method
Static pressure
System effectiveness
Vibration
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Summary:Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period and periodic solution for a spherical dielectric elastomer balloon subjected to static pressure and voltage are derived through an analytical method, called the Newton–harmonic balance (NHB) method. The elastomeric spherical balloon is modeled as an autonomous nonlinear differential equation with general and negatively powered nonlinearities. The NHB method enables to linearize the governing equation prior to applying the harmonic balance method. Even for such a nonlinear system with negatively powered variable and non-classical non-odd nonlinearity, the NHB method is capable of deriving highly accurate approximate solutions. Several practical examples with different initial stretch ratios are solved to illustrate the dynamic inflation of elastomeric spherical balloons. When the initial amplitude is sufficiently large, the system will lose its stability. Comparison with Runge–Kutta numerical integration solutions is also presented and excellent agreement has been observed.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3374-8