0
Research Papers

Instability in Nonlinear Oscillation of Dielectric Elastomers

[+] Author and Article Information
Jian Zhu

Department of Mechanical Engineering,
National University of Singapore,
9 Engineering Drive 1,
117575, Singapore
e-mail: mpezhuj@nus.edu.sg

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 30, 2014; final manuscript received March 17, 2015; published online April 30, 2015. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 82(6), 061001 (Jun 01, 2015) (6 pages) Paper No: JAM-14-1616; doi: 10.1115/1.4030075 History: Received December 30, 2014; Revised March 17, 2015; Online April 30, 2015

A membrane of a dielectric elastomer oscillates when subject to AC voltage. Its oscillation is nonlinear due to large deformation and nonlinear electromechanical coupling. Dynamic instability in dielectric elastomers—the oscillation with an unbounded amplitude—is investigated in this paper. The critical amplitude of AC voltage for dynamic instability varies with the frequency of AC voltage and reaches a valley when the superharmonic, harmonic, or subharmonic resonance is excited. Prestretches can improve dielectric elastomer actuators' capabilities to resist dynamic instability. The critical deformation at the onset of dynamic instability can be much larger than that at the onset of static instability. Oscillation of dielectric elastomers can be used for applications, such as vibration shakers for haptic feedback, soft loudspeakers, soft motors, and soft pumps. We hope that the current analyses can improve the understanding of dynamic behavior of dielectric elastomers and enhance their stability and reliability.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

A schematic of a membrane of a dielectric elastomer, sandwiched between two compliant electrodes. (a) In the reference state, a membrane of a dielectric elastomer is subject to no force and voltage. (b) In the prestretched state, the membrane has stretches λp when subject to equal-biaxial forces P. (c) In a current state, the membrane has stretches λ and gains charges ±Q on the two electrodes when subject to both the forces P and the voltage Φ.

Grahic Jump Location
Fig. 2

The stretch of the membrane as a function of time at different levels of Vac when λp = 2 and (ω·lp)ρ/μ = 2. The membrane of a dielectric elastomer suffers dynamic instability when Vac reaches a critical value. (a) The amplitude of oscillation is small when Vac is small. (b) The amplitude of oscillation increases as Vac increases. (c) The amplitude of oscillation becomes unbounded when Vac reaches a critical value.

Grahic Jump Location
Fig. 3

(a) The critical amplitude of AC voltage for dynamic instability as a function of the frequency of AC voltage when λp = 2. Above the curve (the gray area), the membrane of a dielectric elastomer suffers dynamic instability. Below the curve (the green area), the oscillator is stable. There are three valleys in the curve. (b) The amplitude of oscillation as a function of the frequency of AC voltage when λp = 2 and ɛ/μ(Vac/2hp) = 0.4. There are three peaks in the curve, which correspond to the three valleys in (a). For interpretation of the references to color in this figure, the reader is referred to the web version of this article.

Grahic Jump Location
Fig. 4

The critical amplitude of AC voltage for dynamic instability as a function of the frequency of AC voltage at several levels of prestretches. Above the curve (the gray area), the membrane suffers dynamic instability. Below the curve (the green area), the oscillator is stable. The curve reaches the minimum as represented by VHResonance, when the harmonic resonance is excited at ω = ω0. For interpretation of the references to color in this figure, the reader is referred to the web version of this article.

Grahic Jump Location
Fig. 5

The voltage as a function of the voltage-induced deformation. The blue curve represents the amplitude of AC voltage ((ɛ/μ)(Vac/2hp)) at the harmonic resonance as a function of the amplitude of oscillation ((λmax-λmin)/λp). At the peak, the membrane suffers dynamic instability induced by AC voltage. The black curve represents the step voltage ((ɛ/μ)(Φ/2hp)) as a function of the amplitude of oscillation ((λmax-λmin)/λp). At the peak, the membrane suffers dynamic instability induced by step voltage. The green curve represents the ramp voltage ((ɛ/μ)(Φ/2hp)) as a function of the actuation strain ((λ-λp)/λp). At the peak, the membrane suffers static instability. For interpretation of the references to color in this figure, the reader is referred to the web version of this article.

Grahic Jump Location
Fig. 6

The critical value of voltage for instability as a function of the prestretches. The blue curve represents the critical amplitude of AC voltage for dynamic instability at the harmonic resonance. The black curve represents the critical value of step voltage for dynamic instability. The green curve represents the critical value of ramp voltage for static instability. For all these three cases, the critical voltage for instability increases as the prestretches increase, which suggests that prestretches can improve dielectric elastomer actuators' capabilities to resist not only static instability but also dynamic instability. For interpretation of the references to color in this figure, the reader is referred to the web version of this article.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In