1. From: Instability in Nonlinear Oscillation of Dielectric Elastomers
Date of download: 10/17/2017
Copyright © ASME. All rights reserved.
From: Instability in Nonlinear Oscillation of Dielectric Elastomers
J. Appl. Mech. 2015;82(6): doi: /
Figure Legend:
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.

2. From: Instability in Nonlinear Oscillation of Dielectric Elastomers
Date of download: 10/17/2017
Copyright © ASME. All rights reserved.
From: Instability in Nonlinear Oscillation of Dielectric Elastomers
J. Appl. Mech. 2015;82(6): doi: /
Figure Legend:
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.

3. From: Instability in Nonlinear Oscillation of Dielectric Elastomers
Date of download: 10/17/2017
Copyright © ASME. All rights reserved.
From: Instability in Nonlinear Oscillation of Dielectric Elastomers
J. Appl. Mech. 2015;82(6): doi: /
Figure Legend:
(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.

4. From: Instability in Nonlinear Oscillation of Dielectric Elastomers
Date of download: 10/17/2017
Copyright © ASME. All rights reserved.
From: Instability in Nonlinear Oscillation of Dielectric Elastomers
J. Appl. Mech. 2015;82(6): doi: /
Figure Legend:
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.

5. From: Instability in Nonlinear Oscillation of Dielectric Elastomers
Date of download: 10/17/2017
Copyright © ASME. All rights reserved.
From: Instability in Nonlinear Oscillation of Dielectric Elastomers
J. Appl. Mech. 2015;82(6): doi: /
Figure Legend:
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.

6. From: Instability in Nonlinear Oscillation of Dielectric Elastomers
Date of download: 10/17/2017
Copyright © ASME. All rights reserved.
From: Instability in Nonlinear Oscillation of Dielectric Elastomers
J. Appl. Mech. 2015;82(6): doi: /
Figure Legend:
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.