As a size-dependent theory, flexoelectric effect is expected to be prominent at the small scale. In this paper, the band gap structure of elastic wave propagating in a periodically layered nanostructure is calculated by transfer matrix method when the effect of flexoelectricity is taken into account. Detailed calculations are performed for a BaTiO3-SrTiO3 two-layered periodic structure. It is shown that the effect of flexoelectricity can considerably flatten the dispersion curves, reduce the group velocities of the system, and decrease the midfrequency of the band gap. For periodic two-layered structures whose sublayers are of the same thickness, the width of the band gap can be decreased due to flexoelectric effect. It is also unveiled from our analysis that when the filling fraction is small, wider gaps at lower frequencies will be acquired compared with the results without considering flexoelectric effect. In addition, the band gap structures will approach the classical result as the total thickness of the unit cell increases. Our results indicate that the scaling law does not hold when the sizes of the periodic structures reach the nanoscale dimension. Therefore, the consideration of flexoelectric effect on the band structure of a nanosized periodic system is significant for precise manipulation of elastic wave propagation and its practical application.
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Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
e-mail: liuchenchen@stu.xjtu.edu.cn
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
e-mail: slhu@mail.xjtu.edu.cn
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
e-mail: sshen@mail.xjtu.edu.cn
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Research-Article
Effect of Flexoelectricity on Band Structures of One-Dimensional Phononic Crystals
Chenchen Liu,
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
e-mail: liuchenchen@stu.xjtu.edu.cn
Chenchen Liu
State Key Laboratory of Strength and
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049
, China
e-mail: liuchenchen@stu.xjtu.edu.cn
Search for other works by this author on:
Shuling Hu,
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
e-mail: slhu@mail.xjtu.edu.cn
Shuling Hu
State Key Laboratory of Strength and
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049
, China
e-mail: slhu@mail.xjtu.edu.cn
Search for other works by this author on:
Shengping Shen
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
e-mail: sshen@mail.xjtu.edu.cn
Shengping Shen
State Key Laboratory of Strength and
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049
, China
e-mail: sshen@mail.xjtu.edu.cn
Search for other works by this author on:
Chenchen Liu
State Key Laboratory of Strength and
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049
, China
e-mail: liuchenchen@stu.xjtu.edu.cn
Shuling Hu
State Key Laboratory of Strength and
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049
, China
e-mail: slhu@mail.xjtu.edu.cn
Shengping Shen
State Key Laboratory of Strength and
Vibration for Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049
, China
e-mail: sshen@mail.xjtu.edu.cn
Manuscript received September 30, 2013; final manuscript received November 4, 2013; accepted manuscript posted November 14, 2013; published online December 12, 2013. Assoc. Editor: Pradeep Sharma.
J. Appl. Mech. May 2014, 81(5): 051007 (6 pages)
Published Online: December 12, 2013
Article history
Received:
September 30, 2013
Revision Received:
November 4, 2013
Accepted:
November 4, 2013
Citation
Liu, C., Hu, S., and Shen, S. (December 12, 2013). "Effect of Flexoelectricity on Band Structures of One-Dimensional Phononic Crystals." ASME. J. Appl. Mech. May 2014; 81(5): 051007. https://doi.org/10.1115/1.4026017
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