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The band structure and transmission characteristics of a new two-dimensional (2D) piezoelectric phononic crystal plate consisting of four epoxy short plates periodically connected with a square lattice of a prismatic piezoelectric material coated with plexiglass are investigated by supercell method and finite element method. By changing the electric boundary conditions imposed on the upper and lower surfaces of piezoelectric scatterers, a point defect waveguide with adjustable paths is formed, which overcomes the limitation of immutability in the direction of the vibration waveguide, with material and structural parameters fixed. Then the controlling of the piezoelectric effect can change the material parameters of piezoelectric components in phononic crystals, showing that the piezoelectric constants have a great influence on the complete bandgap, which is beneficial to the formation of defect states; when the frequency of the defect state appears in the band gap, the frequency-responding range of the defect state expands. The analysis of the displacement vector field indicates that the strain energy in the resonance of the new structure is almost completely limited to the upper and lower surfaces of the central piezoelectric scatterer. We use the recycling circuit to connect the electrodes on the upper and lower surfaces of the piezoelectric sheet. At this time, the output electrical energy can supply the power to the DC load, and the mechanical energy of vibration can be converted into electrical energy. The results of this work provide a reference for the self-powered technology of waveguide and wireless sensor device with adjustable path.
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Keywords:
- phononic crystal /
- finite element method /
- point defect /
- vibration energy recovery
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图 1 1 × 5超元胞二维压电声子晶体板及其初基原胞示意图 (a) 1 × 5超胞; (b)原胞立体图; (c)原胞平面图; (d)第一布里渊区(阴影部分为不可约布里渊区)
Figure 1. 1 × 5 supercell two-dimensional piezoelectric phonon crystal plate and its primary cells: (a) The supercell plan; (b) the protocell stereogram; (c) the protocell floor plan; (d) the first Brillouin zone (the shadow part is the irreducible brillouin zone).
表 1 压电材料0.27PIN-0.4PMN-0.33PT的参数
Table 1. Piezoelectric material parameters of 0.27PIN-0.4PMN-0.33PT.
密度ρ/kg·m–3 弹性常数Cij/1010 N·m–2 压电常数e/C·m–2 介电常数ε/10–11 F·m–1 C11 C12 C13 C33 C44 C66 e15 e31 e33 ε11 ε33 8189 12.2 11.3 10.8 11.2 6.9 6.2 16.0 –2.7 18.6 4193 585 表 2 弹性材料参数
Table 2. Material parameters of elastic materials.
密度ρ/kg·m–3 杨氏模量E/1010 Pa 剪切模量μ/1010 Pa 有机玻璃 1142 0.200 0.072 环氧树脂 1180 0.435 0.159 -
[1] Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022
Google Scholar
[2] Caballero D, Sánchez-Dehesa J, Rubio C, Mártinez-Sala R, Sánchez-Pérez J V, Meseguer F, Llinares J 1999 Phys. Rev. E 60 R6316
Google Scholar
[3] Wu F G, Liu Z Y, Liu Y Y 2004 Phys. Rev. E 69 066609
Google Scholar
[4] Lv H Y, Tian X Y, Wang M Y, Li D C 2013 Appl. Phys. Lett. 102 034103
Google Scholar
[5] Fox L, Zhang X 2011 Phys. Rev. B 83 214304
Google Scholar
[6] Khelif A, Djafari-Rouhani B, Vasseur J O, Deymier P A 2003 Phys. Rev. B 68 024302
[7] Zhao J F, Marchal R, Bonello B, Boyko O 2012 Appl. Phys. Lett. 101 261905
Google Scholar
[8] Jin Y B, Torrent D, Pennec Y, Pan Y D, Djafari-Rouhani B 2015 J. Appl. Phys. 117 244904
Google Scholar
[9] Kim M, Hong S, Miller D J, Dugundji J, Wardle B L 2011 Appl. Phys. Lett. 99 24
[10] Wu L Y, Chen L W, Liu C M 2009 Phys. Lett. A 373 1189
Google Scholar
[11] Sodano H A, Inman D J, Park G 2004 Shock Vib. Dig. 36 197
Google Scholar
[12] Anton S R, Sodano H A 2007 Smart Mater. Struct. 16 204
[13] Taylor G W, Burns J R, Kammann S M, Powers W B, Welsh T R 2001 IEEE J. Ocean. Eng. 26 539
Google Scholar
[14] Priya S, Chen C T, Fye D, Zahnd J 2005 J. Appl. Phys. 2 44
[15] Priya S 2005 Appl. Phys. Lett. 87 184101
Google Scholar
[16] Yu K P, Chen T N, Wang X P 2013 J. Appl. Phys. 416 12
[17] Hsu J C 2012 Jpn. J. Appl. Phys. 51 07GA04
Google Scholar
[18] Khelif A, Aoubiza B, Mohammadi S, Adibi A, Laude V 2006 Phys. Rev. E 74 046610
Google Scholar
[19] Wang W C, Chen L W, Liu C M 2010 Smart Mater. Struct. 19 045016
Google Scholar
[20] Lee K Y, Gupta M K, Kim S W 2015 Nano Energy 14 139
Google Scholar
[21] Poulin G, Sarraute E, Costa F 2004 Sens. Actuators 116 461
Google Scholar
[22] Roundy S, Leland E 2005 IEEE Pervasive Comput. 4 28
[23] Lu F, Lee H P, Lim S P 2004 Smart Mater. Struct. 13 57
Google Scholar
[24] Horowitz S B, Sheplak M, Cattafesta III L N, Nishida T 2006 J. Micromech. Microeng. 16 174
Google Scholar
[25] Liu F, Phipps A, Horowitz S, Ngo K, Cattafesta L, Nishida T, Sheplak M 2008 J. Acoust. Soc. Am. 123 1983
Google Scholar
[26] Wu L Y, Chen L W, Liu C M 2009 Appl. Phys. Lett. 95 013506
Google Scholar
[27] Qi S B, Oudich M, Li Y, Assouar B 2016 Appl. Phys. Lett. 108 263501
Google Scholar
[28] Gao W T, Xia J P, Sun H X, Yuan S Q, Ge Y, Liu X J 2019 Appl. Phys. Express 12 044002
Google Scholar
[29] Park C S, Shin Y C, Jo S H, Yoon H J, Choi W, Younb B D, Kim M 2019 Nano Energy 57 327
Google Scholar
[30] 廖涛, 孙小伟, 宋婷, 田俊红, 康太凤, 孙伟彬 2018 物理学报 67 214208
Google Scholar
Liao T, Sun X W, Song T, Tian J H, Kang T F, Sun W B 2018 Acta Phys. Sin. 67 214208
Google Scholar
[31] COMSOL Multiphysics®v.5.3.cn.comsol.com. COMSOL AB, Stockholm, Sweden. http://cn.comsol.com/support/knowledge base/1223/[2018-1-1]
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