A majority of dielectric elastomers (DE) developed so far have more or less viscoelastic properties. Understanding the dynamic behaviors of DE is crucial for devices where inertial effects cannot be neglected. Through construction of a dissipation function, we applied the Lagrange's method and theory of nonequilibrium thermodynamics of DE and formulated a physics-based approach for dynamics of viscoelastic DE. We revisited the nonlinear oscillation of DE balloons and proposed a combined shooting and arc-length continuation method to solve the highly nonlinear equations. Both stable and unstable periodic solutions, along with bifurcation and jump phenomenon, were captured successfully when the excitation frequency was tuned over a wide range of variation. The calculated frequency–amplitude curve indicates existence of both harmonic and superharmonic resonances, soft-spring behavior, and hysteresis. The underlying physics and nonlinear dynamics of viscoelastic DE would aid the design and control of DE enabled soft machines.
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January 2018
Research-Article
Shooting and Arc-Length Continuation Method for Periodic Solution and Bifurcation of Nonlinear Oscillation of Viscoelastic Dielectric Elastomers
Fan Liu,
Fan Liu
Xi'an Institute of Space Radio Technology,
Xi'an 710100, China
Xi'an 710100, China
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Jinxiong Zhou
Jinxiong Zhou
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
Shaanxi Engineering Laboratory for Vibration
Control of Aerospace Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
Vibration of Mechanical Structures,
Shaanxi Engineering Laboratory for Vibration
Control of Aerospace Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
Search for other works by this author on:
Fan Liu
Xi'an Institute of Space Radio Technology,
Xi'an 710100, China
Xi'an 710100, China
Jinxiong Zhou
State Key Laboratory for Strength and
Vibration of Mechanical Structures,
Shaanxi Engineering Laboratory for Vibration
Control of Aerospace Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
Vibration of Mechanical Structures,
Shaanxi Engineering Laboratory for Vibration
Control of Aerospace Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 28, 2017; final manuscript received October 29, 2017; published online November 16, 2017. Assoc. Editor: Kyung-Suk Kim.
J. Appl. Mech. Jan 2018, 85(1): 011005 (7 pages)
Published Online: November 16, 2017
Article history
Received:
September 28, 2017
Revised:
October 29, 2017
Citation
Liu, F., and Zhou, J. (November 16, 2017). "Shooting and Arc-Length Continuation Method for Periodic Solution and Bifurcation of Nonlinear Oscillation of Viscoelastic Dielectric Elastomers." ASME. J. Appl. Mech. January 2018; 85(1): 011005. https://doi.org/10.1115/1.4038327
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