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Research Papers

Modeling of Light-Driven Bending Vibration of a Liquid Crystal Elastomer Beam

[+] Author and Article Information
Kai Li

Department of Civil Engineering,
Anhui Jianzhu University,
Hefei, Anhui 230601, China
e-mail: kli@ahjzu.edu.cn

Shengqiang Cai

Department of Mechanical and
Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: s3cai@ucsd.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 8, 2015; final manuscript received November 18, 2015; published online December 14, 2015. Editor: Yonggang Huang.

J. Appl. Mech 83(3), 031009 (Dec 14, 2015) (6 pages) Paper No: JAM-15-1488; doi: 10.1115/1.4032073 History: Received September 08, 2015; Revised November 18, 2015

In this paper, we study light-driven bending vibration of a liquid crystal elastomer (LCE) beam. Inhomogeneous and time-dependent number fraction of photochromic liquid crystal molecules in cis state in an LCE beam is considered in our model. Using mode superposition method, we obtain semi-analytic form of light-driven bending vibration of the LCE beam. Our results show that periodic vibration or a statically deformed state can be induced by a static light source in the LCE beam, which depends on the light intensity and position of the light source. We also demonstrate that the amplitude of the bending vibration of the LCE beam can be regulated by tuning light intensity, damping factor of the beam, and thermal relaxation time from cis to trans state, while the frequency of the vibration in the beam mainly depends on the thermal relaxation time. The method developed in the paper can be important for designing light-driven motion structures and photomechanical energy conversion systems.

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Figures

Grahic Jump Location
Fig. 1

Schematic model of an LCE cantilever beam with length l and thickness h exposed to a static light source. The bending stiffness of the beam is B=Eh3/12(1−ν2) with modulus E and Poisson’s ratio ν, and the mass density of the beam is ρ. The damping factor is α. In the model, the light source is assumed to be far away from the LCE beam.

Grahic Jump Location
Fig. 2

Two states of the LCE beam can be induced by light, depending on the light intensity I¯0: (a) a statically deformed state (I¯0=0.025) and (b) periodic vibration state (I¯0=0.05). (c) The amplitude of light-driven vibration increases with increasing light intensity (I¯0=0.075). In the calculation, we fix the parameters: thermal relaxation time of the cis to trans state T¯0=1, damping factor α¯=1, and light source position w¯0=0.02.

Grahic Jump Location
Fig. 3

Influence of light source position on the light-driven vibration of the LCE beam. The positions of the light source are: (a) w¯0=0.1, (b) w¯0=0.01, and (c) w¯0=0.001. Light source position can also determine whether the light can induce the beam vibration. In the calculation, we fix the parameters: thermal relaxation time of the cis to trans state T¯0=0.2, damping factor α¯=1, and light intensity I¯0=0.25.

Grahic Jump Location
Fig. 4

Influence of damping factor α¯ on the light-driven vibration of the LCE beam. In the calculation, we choose (a) α¯=0.2 and (b) α¯=1. The amplitude decreases with increasing damping factor. In the calculation, we fix the parameters: light intensity I¯0=0.1, thermal relaxation time of the cis to trans state T¯0=0.2, and light source position w¯0=0.0001.

Grahic Jump Location
Fig. 5

Influence of thermal relaxation time of the cis to trans state T¯0 on the light-driven vibration in the LCE beam. (a) We set thermal relaxation time T¯0=0.3, first-order vibration mode is induced in the LCE beam. (b) We set thermal relaxation time T¯0=0.1, second-order vibration mode is induced in the beam with smaller amplitude. The other parameters used in the calculations are light intensity I¯0=0.2, damping factor α¯=1, and light source position w¯0=0.0001.

Grahic Jump Location
Fig. 6

Snapshots of light-induced bending vibration of the LCE beam, for Figs. 5(a) and 5(b). (a) For thermal relaxation time of the cis to trans state T¯0=0.3, first-order vibration mode in the beam is driven by the light. (b) For thermal relaxation time of the cis to trans state T¯0=0.1, second-order vibration mode in the beam is driven by the light.

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