压电材料在声子晶体中的应用探索
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摘要
本文对压电材料在可调带隙声子晶体中的应用进行了有益的探索。将振动控制中的压电分流阻尼技术引入到声子晶体中,设计了贴片式压电声子晶体梁结构。研究了电路参数对梁带隙的调控,并分析了带隙形成和带隙调控的机理。进一步对二组元嵌入式压电声子晶体梁、轴和板结构的带隙特性进行了探索,从电极状态、压电常数和极化方向等方面研究了压电效应对带隙的影响。
主要研究结论包括:
(1)对贴片式和嵌入式压电声子晶体带隙特性的理论仿真研究表明,在声子晶体结构中引入压电材料可以设计带隙特性可调的声子晶体,而且调节简便。
(2)类似于局域共振带隙,在压电声子晶体中存在电磁振荡带隙,该带隙频率与压电片外接分流电路的固有电磁振荡频率强相关,且比该电磁振荡频率稍高。
(3)压电材料调节声子晶体带隙特性的途径是:利用外接分流电路的电磁特性来改变压电材料的等效弹性模量,进而改变声子晶体内部材料组分之间的弹性模量对比,最终改变声子晶体的带隙性能。
(4)具有电磁振荡特性的外接分流电路对声子晶体带隙性能的调节效果更加显著,而且压电材料为各向异性材料,不同的极化方向对声子晶体带隙性能的调节会有差别。
本文研究工作对带隙可调的声子晶体设计具有指导意义。
In the thesis, some favorable explorations are conducted in the application of piezoelectric materials in phononic crystals (PCs). By introducing piezoelectric shunting techniques into PCs, a type of phononic beam on which piezoelectric patches are periodically mounted is designed. The active control of the beam’s band gaps by properly adjusting parameters of shunting circuits has been investigated. Furthermore, the gaps’formation and control mechanisms are also researched. The band gaps properties of phononic beams, shafts and plates with piezoelectric materials embedded in are also investigated, then the influences of piezoelectric effect to band gaps are analyzed from the perspectives of electrodes’status and piezoelectric constant and polarized direction.
The conclusions are drawn as follows:
(1) By the theoretical analysis and numerical simulation of PCs with piezoelectric materials in mounted type or embedded type, the approach that introducing piezoelectric materials in PCs to design PCs whose band gaps can be actively tuned is proved reasonable, moreover, the process is simple and convenient.
(2) Similar to the locally resonant PCs owning locally resonant band gaps, the PCs with electromagnetic-oscillation circuits also have electromagnetic-oscillation band gap. The frequencies of the gap are related to the eigenfrequency of piezoelectric shunting circuits, but a little higher than it.
(3) The approach to tuning PCs’band gaps using piezoelectric materials is using the shunting circuits’electromagnetic properties to adjust equivalent elastic modulus of the piezoelectric materials, and actively tune the discrepancy of elastic modulus between different components in the PCs, which finally lead to the changes of band gaps’properties.
(4) The band gap’s tuning effects are more remarkable when its shunting circuits own electromagnetic loops. Because piezoelectric materials are elastic and electromagnetic anisotropy, the tuning abilities of PCs with different polarized directions will differ.
The work in the thesis can be used to guide the design of PCs whose band gaps can be actively tuned.
主要研究结论包括:
(1)对贴片式和嵌入式压电声子晶体带隙特性的理论仿真研究表明,在声子晶体结构中引入压电材料可以设计带隙特性可调的声子晶体,而且调节简便。
(2)类似于局域共振带隙,在压电声子晶体中存在电磁振荡带隙,该带隙频率与压电片外接分流电路的固有电磁振荡频率强相关,且比该电磁振荡频率稍高。
(3)压电材料调节声子晶体带隙特性的途径是:利用外接分流电路的电磁特性来改变压电材料的等效弹性模量,进而改变声子晶体内部材料组分之间的弹性模量对比,最终改变声子晶体的带隙性能。
(4)具有电磁振荡特性的外接分流电路对声子晶体带隙性能的调节效果更加显著,而且压电材料为各向异性材料,不同的极化方向对声子晶体带隙性能的调节会有差别。
本文研究工作对带隙可调的声子晶体设计具有指导意义。
In the thesis, some favorable explorations are conducted in the application of piezoelectric materials in phononic crystals (PCs). By introducing piezoelectric shunting techniques into PCs, a type of phononic beam on which piezoelectric patches are periodically mounted is designed. The active control of the beam’s band gaps by properly adjusting parameters of shunting circuits has been investigated. Furthermore, the gaps’formation and control mechanisms are also researched. The band gaps properties of phononic beams, shafts and plates with piezoelectric materials embedded in are also investigated, then the influences of piezoelectric effect to band gaps are analyzed from the perspectives of electrodes’status and piezoelectric constant and polarized direction.
The conclusions are drawn as follows:
(1) By the theoretical analysis and numerical simulation of PCs with piezoelectric materials in mounted type or embedded type, the approach that introducing piezoelectric materials in PCs to design PCs whose band gaps can be actively tuned is proved reasonable, moreover, the process is simple and convenient.
(2) Similar to the locally resonant PCs owning locally resonant band gaps, the PCs with electromagnetic-oscillation circuits also have electromagnetic-oscillation band gap. The frequencies of the gap are related to the eigenfrequency of piezoelectric shunting circuits, but a little higher than it.
(3) The approach to tuning PCs’band gaps using piezoelectric materials is using the shunting circuits’electromagnetic properties to adjust equivalent elastic modulus of the piezoelectric materials, and actively tune the discrepancy of elastic modulus between different components in the PCs, which finally lead to the changes of band gaps’properties.
(4) The band gap’s tuning effects are more remarkable when its shunting circuits own electromagnetic loops. Because piezoelectric materials are elastic and electromagnetic anisotropy, the tuning abilities of PCs with different polarized directions will differ.
The work in the thesis can be used to guide the design of PCs whose band gaps can be actively tuned.
引文
[1]丁文镜.减振理论.北京:清华大学出版社,1988
[2]温熙森.光子/声子晶体理论与技术.北京:科学出版社,2006
[3]温熙森,温激鸿等.声子晶体.北京:科学出版社,1979
[4]陈永富,刘俊卿.压电智能结构振动控制研究[硕士学位论文].西安:西安建筑科技大学,2004
[5]王加春,李旦等.机械振动主动控制技术的研究现状和发展综述.机械强度,2001,23(2):156-160
[6] Hussein M I. Dynamics of Banded Materials and Structures: Analysis, Design and Computation in Multiple Scales [PhD thesis]. The University of Michigan, 2004
[7] Brillouin L. Wave Propagation in Periodic Structures, 2nd edition. New York: Dover Publications, 1953
[8] Cremer L, Hekl M and Petersson B A T. Structure-Borne Sound, 3rd edition. Berlin: Springer, 2005
[9] Mead D J. Free wave propagation in periodically-supported, infinite beams. J. Sound Vib., 1970, 11: 181-197
[10] Mead D J, Parthan S. Free wave propagation in two-dimensional periodic plates. J. Sound Vib., 1979, 64(3): 325-346
[11] Mead D J and Markus S. Coupled flexural-longitudinal wave motion in a periodic beam. J. Sound Vib., 1983, 90(1): 1-24
[12] Heckl M A. Coupled waves on a periodically supported Timoshenko beam. J. Sound Vib., 2002, 252(5): 849-882
[13] Mangaraju V, Sonti V R. Wave attenuation in periodic three-layered beams: analytical and FEM study. J. Sound Vib., 2004, 276: 541-570
[14] Mei C. Vibration suppression through tunable periodic structures. Twelfth International Congress on Sound and vibration, 2005
[15] Diaz-de-Anda A, Pimentel A, Flores J, Morales A, Gutierrez L and Mendez-sanchez RA. Locally periodic Timoshenko rod: experiment and theory. J. Acoust. Soc. Am., 2005, 117(5): 2814-2819
[16] A.S. Phani, J. Woodhouse, and N.A. Fleck. Wave propagation in two-dimensional periodic lattices. J. Acoustic Soc. Am., 2006, 119: 1995-2005
[17]张小铭,张维衡.周期简支梁的振动功率流.振动与冲击,1990,35:28-34
[18]温激鸿.声子晶体振动带隙及减振特性研究[博士学位论文].长沙:国防科技大学,2005
[19]郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[博士论文].长沙:国防科技大学,2006
[20] Kushwaha M. S. , Halevi P. , Dobrzynski L. et al. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. , 1993, 71(13): 2022-2025
[21] Martínez-Sala R. , Sancho J. , Sánchez J. V. et al. Sound attenuation by sculpture. Nature, 1995, 378: 241
[22] Liu Z Y, Zhang X, Mao Y et al. Locally resonant sonic materials. Science, 2000, 289: 1734-1736
[23] A. Preumont et al. The damping of a truss structure with a piezoelectric transducer. Computers and Structures, 2008, 86: 227-239
[24] W. Chen, S. Yan, and F. Chu. Immune genetic algorithm used to integrated optimal design of active vibration control system for piezoelectric intelligent truss structures. Chinese Journal of Mechanical Engineering, 2008, 44: 196-200
[25] S. Yan, K. Zheng, and Y. Li, Vibration suppression of adaptive truss structure using fuzzy neural network, Lecture Notes in Computer Science, Chongqing, China, 2005
[26] A. Dominguez, R. Sedaghati, and I. Stiharu. Modeling and application of MR dampers in semi-adaptive structures. Computers and Structures, 2008, 86: 407-415
[27]高伟,陈建军,马洪波等.随机参数智能桁架结构振动控制中主动杆的优化配置.振动工程学报.2003,16: 89-94
[28] W. Gao, J.J. Chen, H.B. Ma et al. Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters. Computers and Structures, 2003, 81:53-60
[29]李东旭.大型挠性空间桁架结构动力学分析与模糊振动控制.长沙:科学出版社, 2008
[30] M. Ruzzene and A. Baz. Attenuation and localization of wave propagation in periodic rods using shape memory inserts. Smart Materials and Structures, 2000, 9: 805-816
[31] A. Baz. Active control of periodic structures. Journal of Vibration and Acoustics, 2001, 123:472-479
[32] O. Thorp, M. Ruzzene, and A. Baz. Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches. Smart Materials and Structures, 2001, 10: 979-989
[33] A. Singh, D.J. Pines, and A. Baz. Active/passive reduction of vibration of periodic one-dimensional structures using piezoelectric actuators. Smart Materials and Structures, 2004, 13: 698-711
[34] R.A. M. Active control of wave propagation in periodic fluid-loaded shells. Smart Materials and Structures, 2001, 10: 893-906
[35] M. Ruzzene, Z. Gu, and A.M. Baz, Wavelet analysis of wave propagation in shells with periodic stiffeners, Smart Structures and Materials 2001: Smart Structures and Integrated Systems, Newport Beach, CA, USA, 2001
[36] O. Thorp, M. Ruzzene, and A. Baz. Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings. Smart Materials and Structures, 2005, 14: 594-604
[37] Y. Kim and A.M. Baz, Active control of a two-dimensional periodic structure, Smart Structures and Materials 2004: Damping and Isolation. Proceedings of the SPIE, 2004, 5386: 329-339
[38] J. Tang and K.W. Wang. Vibration control of rotationally periodic structures using passive piezoelectric shunt networks and active compensation. Journal of Vibration and Acoustics, 1999,121:379-390
[39] J. Tang and K.W. Wang. Vibration delocalization of nearly periodic structures using coupled piezoelectric networks. Journal of Vibration and Acoustics, 2003, 125:95-108
[40] A. Singh and D.J. Pines, Active/passive vibration reduction of periodic 1-D structures using piezoelectric actuators, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con, Denver, Colorado, 2002
[41]任建亭,林磊等.简单周期结构波传播主动控制研究.应用力学学报, 2004, 21: 85-88
[42]李凤明,汪越胜.压电周期结构振动主动控制研究.振动工程学报, 2004, 17: 828-830
[43] M.M.A. El-Din and M. Tawfik, Vibration attenuation in rotating beams with periodically distributedpiezoelectric controllers, The thirteenth international congress on sound and vibration, Vienna, Austria,2006
[44] Y.Z. Wang, F.M. Li, W.H. Huang et al. Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals. Int. J. Solids Struct. , 2008, 45: 4203-4210
[45] Y.Z. Wang, F.M. Li, K. Kishimoto et al. ok_Elastic wave band gaps in magnetoelectroelastic phononic crystals. Wave Motion, 2009, 46: 47-56
[46] S. Gonella, A.C. To, and W.K. Liu. Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting, Journal of the Mechanics and Physics of Solids, 2009, 57:621-633
[47]周云,谭平.磁流变阻尼控制理论与技术.北京:科学出版社,2007
[48]张景绘,李宁等.一体化振动控制:若干理论、技术问题引论.北京:科学出版社,2005
[49]栾桂冬,张金铎等.压电换能器和换能器阵.北京:北京大学出版社,2005
[50]单辉祖.材料力学.北京:高等教育出版社,2004
[51]诸德超,邢誉峰等.工程振动基础.北京:北京航空航天大学出版社,2004
[52]周长城,胡仁喜等.ANSYS 11.0基础与典型范例.北京:电子工业出版社,2007
[53] H Karagülle, L Malgaca and H F ?ktem. Analysis of active vibration control in smart structures by ANSYS. Smart materials and Structures, 2004, 13: 661-667
[54]吴翊,李超等.应用数学基础.北京:高等教育出版社,2006
[55]《数学手册》编写组.数学手册.北京:人民教育出版社,1979
[56]孙慷,张福学.压电学.北京:国防工业出版社,1984
[57] Landau L. D. , Lifshitz E. M. . Theory of Elasticity (3rd edition). New York: Pergamon Press, 1986.
[58]清华大学工程力学系固体力学教研组.机械振动(上).北京:机械工业出版社,1980
[2]温熙森.光子/声子晶体理论与技术.北京:科学出版社,2006
[3]温熙森,温激鸿等.声子晶体.北京:科学出版社,1979
[4]陈永富,刘俊卿.压电智能结构振动控制研究[硕士学位论文].西安:西安建筑科技大学,2004
[5]王加春,李旦等.机械振动主动控制技术的研究现状和发展综述.机械强度,2001,23(2):156-160
[6] Hussein M I. Dynamics of Banded Materials and Structures: Analysis, Design and Computation in Multiple Scales [PhD thesis]. The University of Michigan, 2004
[7] Brillouin L. Wave Propagation in Periodic Structures, 2nd edition. New York: Dover Publications, 1953
[8] Cremer L, Hekl M and Petersson B A T. Structure-Borne Sound, 3rd edition. Berlin: Springer, 2005
[9] Mead D J. Free wave propagation in periodically-supported, infinite beams. J. Sound Vib., 1970, 11: 181-197
[10] Mead D J, Parthan S. Free wave propagation in two-dimensional periodic plates. J. Sound Vib., 1979, 64(3): 325-346
[11] Mead D J and Markus S. Coupled flexural-longitudinal wave motion in a periodic beam. J. Sound Vib., 1983, 90(1): 1-24
[12] Heckl M A. Coupled waves on a periodically supported Timoshenko beam. J. Sound Vib., 2002, 252(5): 849-882
[13] Mangaraju V, Sonti V R. Wave attenuation in periodic three-layered beams: analytical and FEM study. J. Sound Vib., 2004, 276: 541-570
[14] Mei C. Vibration suppression through tunable periodic structures. Twelfth International Congress on Sound and vibration, 2005
[15] Diaz-de-Anda A, Pimentel A, Flores J, Morales A, Gutierrez L and Mendez-sanchez RA. Locally periodic Timoshenko rod: experiment and theory. J. Acoust. Soc. Am., 2005, 117(5): 2814-2819
[16] A.S. Phani, J. Woodhouse, and N.A. Fleck. Wave propagation in two-dimensional periodic lattices. J. Acoustic Soc. Am., 2006, 119: 1995-2005
[17]张小铭,张维衡.周期简支梁的振动功率流.振动与冲击,1990,35:28-34
[18]温激鸿.声子晶体振动带隙及减振特性研究[博士学位论文].长沙:国防科技大学,2005
[19]郁殿龙.基于声子晶体理论的梁板类周期结构振动带隙特性研究[博士论文].长沙:国防科技大学,2006
[20] Kushwaha M. S. , Halevi P. , Dobrzynski L. et al. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. , 1993, 71(13): 2022-2025
[21] Martínez-Sala R. , Sancho J. , Sánchez J. V. et al. Sound attenuation by sculpture. Nature, 1995, 378: 241
[22] Liu Z Y, Zhang X, Mao Y et al. Locally resonant sonic materials. Science, 2000, 289: 1734-1736
[23] A. Preumont et al. The damping of a truss structure with a piezoelectric transducer. Computers and Structures, 2008, 86: 227-239
[24] W. Chen, S. Yan, and F. Chu. Immune genetic algorithm used to integrated optimal design of active vibration control system for piezoelectric intelligent truss structures. Chinese Journal of Mechanical Engineering, 2008, 44: 196-200
[25] S. Yan, K. Zheng, and Y. Li, Vibration suppression of adaptive truss structure using fuzzy neural network, Lecture Notes in Computer Science, Chongqing, China, 2005
[26] A. Dominguez, R. Sedaghati, and I. Stiharu. Modeling and application of MR dampers in semi-adaptive structures. Computers and Structures, 2008, 86: 407-415
[27]高伟,陈建军,马洪波等.随机参数智能桁架结构振动控制中主动杆的优化配置.振动工程学报.2003,16: 89-94
[28] W. Gao, J.J. Chen, H.B. Ma et al. Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters. Computers and Structures, 2003, 81:53-60
[29]李东旭.大型挠性空间桁架结构动力学分析与模糊振动控制.长沙:科学出版社, 2008
[30] M. Ruzzene and A. Baz. Attenuation and localization of wave propagation in periodic rods using shape memory inserts. Smart Materials and Structures, 2000, 9: 805-816
[31] A. Baz. Active control of periodic structures. Journal of Vibration and Acoustics, 2001, 123:472-479
[32] O. Thorp, M. Ruzzene, and A. Baz. Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches. Smart Materials and Structures, 2001, 10: 979-989
[33] A. Singh, D.J. Pines, and A. Baz. Active/passive reduction of vibration of periodic one-dimensional structures using piezoelectric actuators. Smart Materials and Structures, 2004, 13: 698-711
[34] R.A. M. Active control of wave propagation in periodic fluid-loaded shells. Smart Materials and Structures, 2001, 10: 893-906
[35] M. Ruzzene, Z. Gu, and A.M. Baz, Wavelet analysis of wave propagation in shells with periodic stiffeners, Smart Structures and Materials 2001: Smart Structures and Integrated Systems, Newport Beach, CA, USA, 2001
[36] O. Thorp, M. Ruzzene, and A. Baz. Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings. Smart Materials and Structures, 2005, 14: 594-604
[37] Y. Kim and A.M. Baz, Active control of a two-dimensional periodic structure, Smart Structures and Materials 2004: Damping and Isolation. Proceedings of the SPIE, 2004, 5386: 329-339
[38] J. Tang and K.W. Wang. Vibration control of rotationally periodic structures using passive piezoelectric shunt networks and active compensation. Journal of Vibration and Acoustics, 1999,121:379-390
[39] J. Tang and K.W. Wang. Vibration delocalization of nearly periodic structures using coupled piezoelectric networks. Journal of Vibration and Acoustics, 2003, 125:95-108
[40] A. Singh and D.J. Pines, Active/passive vibration reduction of periodic 1-D structures using piezoelectric actuators, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con, Denver, Colorado, 2002
[41]任建亭,林磊等.简单周期结构波传播主动控制研究.应用力学学报, 2004, 21: 85-88
[42]李凤明,汪越胜.压电周期结构振动主动控制研究.振动工程学报, 2004, 17: 828-830
[43] M.M.A. El-Din and M. Tawfik, Vibration attenuation in rotating beams with periodically distributedpiezoelectric controllers, The thirteenth international congress on sound and vibration, Vienna, Austria,2006
[44] Y.Z. Wang, F.M. Li, W.H. Huang et al. Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals. Int. J. Solids Struct. , 2008, 45: 4203-4210
[45] Y.Z. Wang, F.M. Li, K. Kishimoto et al. ok_Elastic wave band gaps in magnetoelectroelastic phononic crystals. Wave Motion, 2009, 46: 47-56
[46] S. Gonella, A.C. To, and W.K. Liu. Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting, Journal of the Mechanics and Physics of Solids, 2009, 57:621-633
[47]周云,谭平.磁流变阻尼控制理论与技术.北京:科学出版社,2007
[48]张景绘,李宁等.一体化振动控制:若干理论、技术问题引论.北京:科学出版社,2005
[49]栾桂冬,张金铎等.压电换能器和换能器阵.北京:北京大学出版社,2005
[50]单辉祖.材料力学.北京:高等教育出版社,2004
[51]诸德超,邢誉峰等.工程振动基础.北京:北京航空航天大学出版社,2004
[52]周长城,胡仁喜等.ANSYS 11.0基础与典型范例.北京:电子工业出版社,2007
[53] H Karagülle, L Malgaca and H F ?ktem. Analysis of active vibration control in smart structures by ANSYS. Smart materials and Structures, 2004, 13: 661-667
[54]吴翊,李超等.应用数学基础.北京:高等教育出版社,2006
[55]《数学手册》编写组.数学手册.北京:人民教育出版社,1979
[56]孙慷,张福学.压电学.北京:国防工业出版社,1984
[57] Landau L. D. , Lifshitz E. M. . Theory of Elasticity (3rd edition). New York: Pergamon Press, 1986.
[58]清华大学工程力学系固体力学教研组.机械振动(上).北京:机械工业出版社,1980