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Research Papers

Effect of Flexoelectricity on Band Structures of One-Dimensional Phononic Crystals

[+] Author and Article Information
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 81(5), 051007 (Dec 12, 2013) (6 pages) Paper No: JAM-13-1413; doi: 10.1115/1.4026017 History: Received September 30, 2013; Accepted November 04, 2013; Revised November 04, 2013

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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Figures

Grahic Jump Location
Fig. 1

Schematic diagram of one-dimensional layered phononic crystal

Grahic Jump Location
Fig. 3

Variation of the upper and lower edges of the first band gap with the thickness of the subcell for a BaTiO3-SrTiO3 two-layered periodic structure (dBaTiO3 = dSrTiO3)

Grahic Jump Location
Fig. 4

Variation of the bandwidth of the first band gap with the thickness of the subcell for a BaTiO3-SrTiO3 two-layered periodic structure (dBaTiO3 = dSrTiO3)

Grahic Jump Location
Fig. 5

Variation of the midfrequency of the first band gap with the thickness of BaTiO3 layer for a BaTiO3-SrTiO3 two-layered periodic structure (dBaTiO3/dSrTiO3 = 1/5)

Grahic Jump Location
Fig. 6

Variation of the bandwidth of the first band gap with the thickness of BaTiO3 layer for a BaTiO3-SrTiO3 two-layered periodic structure (dBaTiO3/dSrTiO3 = 1/5)

Grahic Jump Location
Fig. 2

The phononic band structure of a BaTiO3-SrTiO3 two-layered periodic structure. The black triangular symbols are for neglecting the flexoelectric effect; the red circular symbols are for taking into account of the flexoelectric effect. The open and solid symbols correspond to the upper and lower edges, respectively.

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