Coupling between two kinds of band gaps of a shunted tube piezoelectric phononic crystal

Abstract

A tube-type piezoelectric phononic crystal model is proposed to study interaction between locally resonant and Bragg band gaps, which is arrayed periodically by metal and piezoelectric segments. Each piezoelectric segment consists of a shell with series-connected and opposite directions polarized double layers and a resonant shunting circuit. According to the interaction between Bragg scattering and local electromagnetic oscillation, three regions corresponding to the inductance can be divided as follows: quasi-short circuits region, coupling region, and quasi-open circuits region. Some interesting phenomena are found from the coupling between Bragg scattering and locally resonant of electromagnetic oscillation. (1) In the coupling region, a pass band splits a Bragg band gap into two band gaps. But the cut-off frequency of the second band gap does not change with the inductance. (2) In the quasi-open circuits region, Bragg and locally resonant band gaps exist independently. (3) The first band gap transits from Bragg scattering to local resonance when the inductance increases from quasi-short circuits region to quasi-open circuits region. (4) The cut-off frequency of the first band gap is always less than the estimated resonant frequency of inductor-capacitor oscillators. Finally, the theoretical result is validated by two kinds of finite element models based on ANSYS.

Keywords

periodic tube piezoelectric phononic crystal resonant shunting circuit locally resonant band gap

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References

Baz

(2001) Active control of periodic structures. Journal of Vibration and Acoustics 123: 472–479.

Cao

Schmidt

Zhang

et al . (2004) Elastic, piezoelectric, and dielectric properties of 0.58Pb (Mg_1/3 Nb_2/3) O₃-0.42PbTiO₃ single crystal. Journal of Applied Physics 96: 549–554.

Casadei

Beck

Cunefare

et al . (2012) Vibration control of plates through hybrid configurations of periodic piezoelectric shunts. Journal of Intelligent Material Systems and Structures 23: 1169–1177.

Casadei

Ruzzene

Dozio

et al . (2010) Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates. Smart Materials and Structures 19: 015002.

Chen

Wang

Wen

et al . (2013) Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches. Journal of Sound and Vibration 332: 1520–1532.

Chen

Wen

Wang

et al . (2011) Locally resonant gaps of phononic beams induced by periodic arrays of resonant shunts. Chinese Physics Letters 28: 094301.

Chen

Wen

Wang

et al . (2012) Improved modeling of rods with periodic arrays of shunted piezoelectric patches. Journal of Intelligent Material Systems and Structures 23: 1613–1621.

Chen

Huang

(2015) A design of active elastic metamaterials for control of flexural waves using the transformation method. Journal of Intelligent Material Systems and Structures. Epub ahead of print 29 June. DOI: 10.1177/1045389X15590273.

Chen

Huang

Sun

(2014) Band gap control in an active elastic metamaterial with negative capacitance piezoelectric shunting. Journal of Vibration and Acoustics 136: 061008.

10.

Dai

Jiang

Lian

et al . (2015) Locally resonant band gaps achieved by equal frequency shunting circuits of piezoelectric rings in a periodic circular plate. Journal of Sound and Vibration 337: 150–160.

11.

Yang

(2009) On the inaccuracy of using Mindlin’s first-order plate theory for calculating the motional capacitance of a thickness-shear resonator. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 56: 7–8.

12.

Kraus

(1967) Thin Elastic Shells. New York: John Wiley & Sons.

13.

Liu

Hussein

(2012) Wave motion in periodic flexural beams and characterization of the transition between Bragg scattering and local resonance. Journal of Applied Mechanics 79: 011003.

14.

Liu

Zhang

Mao

et al . (2000) Locally resonant sonic materials. Science 289: 1734–1736.

15.

Ruzzene

Baz

(2001) Active control of wave propagation in periodic fluid-loaded shells. Smart Materials and Structures 10: 893–906.

16.

Sadd

(2005) Elasticity Theory, Applications, and Numerics. Burlington, MA: Elsevier.

17.

Singh

Pines

Baz

(2004) Active/passive reduction of vibration of periodic one-dimensional structures using piezoelectric actuators. Smart Materials and Structures 13: 698–711.

18.

Sorokin

Ershova

(2004) Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading. Journal of Sound and Vibration 278: 501–526.

19.

Spadoni

Ruzzene

Cunefare

(2009) Vibration and wave propagation control of plates with periodic arrays of shunted piezoelectric patches. Journal of Intelligent Material Systems and Structures 20: 979–990.

20.

Thorp

Ruzzene

Baz

(2001) Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches. Smart Materials and Structures 10: 979–989.

21.

Thorp

Ruzzene

Baz

(2005) Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings. Smart Materials and Structures 14: 594–604.

22.

Tzou

(1993) Piezoelectric Shells: Distributed Sensing and Control of Continua. London: Kluwer Academic Publishers.

23.

Wang

Chen

Wen

(2011a) Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou’s circuit: experimental investigation on beams. Smart Materials and Structures 20: 015026.

24.

Wang

Chen

et al . (2011b) Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits. Smart Materials and Structures 20: 125019.

25.

Wang

Lian

Wang

et al . (2013) Analysis of a piezoelectric power harvester with adjustable frequency by precise electric field method. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 60: 2154–2161.

26.

Xiao

Wen

et al . (2013) Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms. Journal of Sound and Vibration 332: 867–893.

27.

Yang

(2005) An Introduction to the Theory of Piezoelectricity. Boston, MA: Springer.

28.

Wen

Shen

et al . (2012) Propagation of flexural wave in periodic beam on elastic foundations. Physics Letters A 376: 626–630.

29.

Zhou

Zuo

(2015) Vibration and wave propagation attenuation for metamaterials by periodic piezoelectric arrays with high-order resonant circuit shunts. Smart Materials and Structures 24: 065021.