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.

References

1.
Dey
,
S.
,
Agra-Kooijman
,
D. M.
,
Ren
,
W.
,
McMullan
,
P. J.
,
Griffin
,
A. C.
, and
Kumar
,
S.
,
2013
, “
Soft Elasticity in Main Chain Liquid Crystal Elastomers
,”
Crystals
,
3
(
2
), pp.
363
390
.
2.
Biggins
,
J. S.
,
Warner
,
M.
, and
Bhattacharya
,
K.
,
2012
, “
Elasticity of Polydomain Liquid Crystal Elastomers
,”
J. Mech. Phys. Solids
,
60
(
4
), pp.
573
590
.
3.
Brown
,
A. W.
, and
Adams
,
J. M.
,
2012
, “
Negative Poisson’s Ratio and Semisoft Elasticity of Smectic-C Liquid-Crystal Elastomers
,”
Phys. Rev. E
,
85
(
1
), p.
011703
.
4.
Adams
,
J. M.
, and
Warner
,
M.
,
2005
, “
Soft Elasticity in Smectic Elastomers
,”
Phys. Rev. E
,
72
(
1
), p.
011703
.
5.
Corbett
,
D.
, and
Warner
,
M.
,
2009
, “
Changing Liquid Crystal Elastomer Ordering With Light—A Route to Opto-Mechanically Responsive Materials
,”
Liq. Cryst.
,
36
(
10–11
), pp.
1263
1280
.
6.
Dawson
,
N. J.
,
Kuzyk
,
M. G.
,
Neal
,
J.
,
Luchette
,
P.
, and
Palffy-Muhoray
,
P.
,
2011
, “
Modeling the Mechanisms of the Photomechanical Response of a Nematic Liquid Crystal Elastomer
,”
J. Opt. Soc. Am. B
,
28
(
9
), pp.
2134
2141
.
7.
Wermter
,
H.
, and
Finkelmann
,
H.
,
2001
, “
Liquid Crystalline Elastomers as Artificial Muscles
,”
e-Polymers
,
1
(
1
), pp.
111
123
.
8.
Petsch
,
S.
,
Rix
,
R.
,
Khatri
,
B.
,
Schuhladen
,
S.
,
Müller
,
P.
,
Zentel
,
R.
, and
Zappe
,
H.
,
2015
, “
Smart Artificial Muscle Actuators: Liquid Crystal Elastomers With Integrated Temperature Feedback
,”
Sensor. Actuat. A
,
231
, pp.
44
51
.
9.
Xing
,
H. H.
,
Li
,
J.
,
Guo
,
J. B.
, and
Wei
,
J.
,
2015
, “
Bio-Inspired Thermal-Responsive Inverse Opal Films With Dual Structural Colors Based on Liquid Crystal Elastomer
,”
J. Mater. Chem. C
,
3
(
17
), pp.
4424
4430
.
10.
Li
,
M. H.
, and
Keller
,
P.
,
2006
, “
Artificial Muscles Based on Liquid Crystal Elastomers
,”
Philos. Trans. R. Soc., A
,
364
(
1847
), pp.
2763
2777
.
11.
Schmidtke
,
J.
,
Kniesel
,
S.
, and
Finkelmann
,
H.
,
2005
, “
Probing the Photonic Properties of a Cholesteric Elastomer Under Biaxial Stress
,”
Macromolecules
,
38
(
4
), pp.
1357
1363
.
12.
Schmidtke
,
J.
,
Stille
,
W.
,
Finkelmann
,
H.
, and
Kim
,
S. T.
,
2002
, “
Laser Emission in a Dye Doped Cholesteric Polymer Network
,”
Adv. Mater.
,
14
(
10
), pp.
746
749
.
13.
Dawson
,
N. J.
,
Kuzyk
,
M. G.
,
Neal
,
J.
,
Luchette
,
P.
, and
Palffy-Muhoray
,
P.
,
2011
, “
Cascading of Liquid Crystal Elastomer Photomechanical Optical Devices
,”
Opt. Commun.
,
284
(
4
), pp.
991
993
.
14.
Shilov
,
S. V.
,
Skupin
,
H.
,
Kremer
,
F.
,
Skarp
,
K.
,
Stein
,
P.
, and
Finkelmann
,
H.
,
1998
, “
Segmental Motion of Ferroelectric Liquid Crystal Polymer and Elastomer During Electro-Optical Switching
,”
Proc. SPIE
,
3318
, pp.
62
67
.
15.
Krishnan
,
D.
, and
Johnson
,
H. T.
,
2014
, “
Light-Induced Deformation in a Liquid Crystal Elastomer Photonic Crystal
,”
J. Mech. Phys. Solids
,
62
, pp.
48
56
.
16.
Li
,
M. E.
,
Lv
,
S.
, and
Zhou
,
J. X.
,
2014
, “
Photo-Thermo-Mechanically Actuated Bending and Snapping Kinetics of Liquid Crystal Elastomer Cantilever
,”
Smart Mater. Struct.
,
23
(
12
), p.
125012
.
17.
Dunn
,
M. L.
, and
Maute
,
K.
,
2009
, “
Photomechanics of Blanket and Patterned Liquid Crystal Elastomer Films
,”
Mech. Mater.
,
41
(
10
), pp.
1083
1089
.
18.
Dunn
,
M. L.
,
2007
, “
Photomechanics of Mono- and Polydomain Liquid Crystal Elastomer Films
,”
J. Appl. Phys.
,
102
(
1
), p.
013506
.
19.
Hauser
,
A. W.
,
Evans
,
A. A.
,
Na
,
J. H.
, and
Hayward
,
R. C.
,
2015
, “
Photothermally Reprogrammable Buckling of Nanocomposite Gel Sheets
,”
Angew. Chem., Int. Ed.
,
54
(
18
), pp.
5434
5437
.
20.
Camacho-Lopez
,
M.
,
Finkelmann
,
H.
,
Palffy-Muhoray
,
P.
, and
Shelley
,
M.
,
2004
, “
Fast Liquid Crystal Elastomer Swims Into the Dark
,”
Nat. Mater.
,
3
(
5
), pp.
307
310
.
21.
Nagele
,
T.
,
Hoche
,
R.
,
Zinth
,
W.
, and
Wachtveitl
,
J.
,
1997
, “
Femtosecond Photoisomerization of Cis-Azobenzene
,”
Chem. Phys. Lett.
,
272
(
5–6
), pp.
489
495
.
22.
Garcia-Amoros
,
J.
,
Nonell
,
S.
, and
Velasco
,
D.
,
2011
, “
Photo-Driven Optical Oscillators in the kHz Range Based on Push–Pull Hydroxyazopyridines
,”
Chem. Commun.
,
47
(
13
), pp.
4022
4024
.
23.
Hiscock
,
T.
,
Warner
,
M.
, and
Palffy-Muhoray
,
P.
,
2011
, “
Solar to Electrical Conversion Via Liquid Crystal Elastomers
,”
J. Appl. Phys.
,
109
(
10
), p.
104506
.
24.
Torras
,
N.
,
Zinoviev
,
K. E.
,
Marshall
,
J. E.
,
Terentjev
,
E. M.
, and
Esteve
,
J.
,
2011
, “
Bending Kinetics of a Photo-Actuating Nematic Elastomer Cantilever
,”
Appl. Phys. Lett.
,
99
(
25
), p.
254102
.
25.
Serak
,
S.
,
Tabiryan
,
N.
,
Vergara
,
R.
,
White
,
T. J.
,
Vaia
,
R. A.
, and
Bunning
,
T. J.
,
2010
, “
Liquid Crystalline Polymer Cantilever Oscillators Fueled by Light
,”
Soft Matter
,
6
(
4
), pp.
779
783
.
26.
Shankar
,
M. R.
,
Smith
,
M. L.
,
Tondiglia
,
V. P.
,
Lee
,
K. M.
,
McConney
,
M. E.
,
Wang
,
D. H.
,
Tan
,
L.
, and
White
,
T. J.
,
2013
, “
Contactless, Photoinitiated Snap-Through in Azobenzene-Functionalized Polymers
,”
Proc. Natl. Acad. Sci. U.S.A.
,
110
(
47
), pp.
18792
18797
.
27.
White
,
T. J.
,
Tabiryan
,
N. V.
,
Serak
,
S. V.
,
Hrozhyk
,
U. A.
,
Tondiqlia
,
V. P.
,
Koerner
,
H.
,
Vaia
,
R. A.
, and
Bunning
,
T. J.
,
2008
, “
A High Frequency Photodriven Polymer Oscillator
,”
Soft Matter
,
4
(
9
), pp.
1796
1798
.
28.
Lee
,
K. M.
,
Smith
,
M. L.
,
Koerner
,
H.
,
Tabiryan
,
N.
,
Vaia
,
R. A.
,
Bunning
,
T. J.
, and
White
,
T. J.
,
2011
, “
Photodriven, Flexural–Torsional Oscillation of Glassy Azobenzene Liquid Crystal Polymer Networks
,”
Adv. Funct. Mater.
,
21
(
15
), pp.
2913
2918
.
29.
Shimamura
,
A.
,
Priimagi
,
A.
,
Mamiya
,
J. I.
,
Kinoshita
,
M.
,
Ikeda
,
T.
, and
Shishido
,
A.
,
2011
, “
Photoinduced Bending Upon Pulsed Irradiation in Azobenzene-Containing Crosslinked Liquid-Crystalline Polymers
,”
J. Nonlinear Opt. Phys.
,
20
(
4
), pp.
405
413
.
30.
Corbett
,
D.
, and
Warner
,
M.
,
2007
, “
Linear and Nonlinear Photoinduced Deformations of Cantilevers
,”
Phys. Rev. Lett.
,
99
(
17
), p.
174302
.
31.
Marshall
,
J. E.
, and
Terentjev
,
E. M.
,
2013
, “
Photo-Sensitivity of Dye-Doped Liquid Crystal Elastomers
,”
Soft Matter
,
9
(
35
), pp.
8547
8551
.
32.
Finkelmann
,
H.
,
Nishikawa
,
E.
,
Pereira
,
G. G.
, and
Warner
,
M.
,
2001
, “
A New Opto-Mechanical Effect in Solids
,”
Phys. Rev. Lett.
,
87
(
1
), p.
015501
.
33.
Hogan
,
P. M.
,
Tajbakhsh
,
A. R.
, and
Terentjev
,
E. M.
,
2002
, “
UV Manipulation of Order and Macroscopic Shape in Nematic Elastomers
,”
Phys. Rev. E
,
65
(
4
), p.
041720
.
34.
Jin
,
L. H.
,
Lin
,
Y.
, and
Huo
,
Y. Z.
,
2011
, “
A Large Deflection Light-Induced Bending Model for Liquid Crystal Elastomers Under Uniform or Non-Uniform Illumination
,”
Int. J. Solids Struct.
,
48
(
22–23
), pp.
3232
3242
.
35.
Thomson
,
W. T.
, and
Dahleh
,
M. D.
,
1998
,
Theory of Vibration With Applications
, 5th ed.,
Prentice Hall
,
Upper Saddle River, NJ
.
You do not currently have access to this content.