压电周期结构阻尼特性分析方法
|
摘要
周期结构是按照一定的规则和周期设计并制造的,由若干相同的子结构通过一定的方式连接形成。通过调整子结构的形状、各组成成分的排布和体积分数,可以改变周期结构的宏观性能。周期结构具有“禁频”特性,对频率处于“禁频”范围内的弹性波或振动,在周期结构中传播时,能量和幅值会产生衰减。
本文基于压电被动阻尼技术,提出了一种新型的周期结构单胞,即子结构。以压电杆的形式,将包含外部电路的压电单元加入到单胞中,从而将压电材料用于提高周期结构的阻尼。对于无限周期结构,根据Bloch定理,将问题转换为对单胞的求解。采用有限元法建立压电周期结构的单胞模型,通过施加周期边界条件,将独立单胞转换为无限周期结构中的任意单胞。根据损耗因子与材料阻尼系数之间的等效关系,将单胞的动力平衡方程转化为包含阻尼项的复系数特征值方程,实现对压电周期结构阻尼特性的分析。
根据上述理论,编写了分析压电周期结构阻尼特性的算法程序,通过对具体算例进行迭代求解,得到了压电周期结构的频散关系和阻尼特性,对于周期结构减振的研究和应用,有一定理论指导意义。
Periodic structures, which consist of several identical substructures arranged in a definite way, are designed and manufactured in accordance with certain principles. The macroscopic properties of periodic structures could be changed by adjusting the shape, distribution and volume fraction of the composition of the substructure. Meanwhile, periodic structures have a band-gap. The energy and amplitude of the elastic wave or vibration with the frequency in the band-gap will reduce while propagating in periodic structures.
In this thesis, a new type of unit cell of periodic structures is proposed, i.e., the substructure. In order to improve the damping of periodic structures using the piezoelectric material, piezoelectric elements shunted with electric circuits are added to the cell. For infinite periodic structures, the problem is reduced to one cell by Bloch's theorem. An independent unit cell is converted to anyone of periodic structures by applying the periodic boundary conditions to the model established by the finite element method. Based on the equivalent relation between the loss factor and the structural damping, the dynamic equilibrium equations of the unit cell are reduced to complex coefficient eigenvalue equations.
In view of the above observations, the program for analyzing the damping property of piezoelectric periodic structures is written, and a specific example is given. The dispersion relation and damping property of piezoelectric periodic structures are obtained by iteration computation. Our research will provide a theoretical basis for further study.
本文基于压电被动阻尼技术,提出了一种新型的周期结构单胞,即子结构。以压电杆的形式,将包含外部电路的压电单元加入到单胞中,从而将压电材料用于提高周期结构的阻尼。对于无限周期结构,根据Bloch定理,将问题转换为对单胞的求解。采用有限元法建立压电周期结构的单胞模型,通过施加周期边界条件,将独立单胞转换为无限周期结构中的任意单胞。根据损耗因子与材料阻尼系数之间的等效关系,将单胞的动力平衡方程转化为包含阻尼项的复系数特征值方程,实现对压电周期结构阻尼特性的分析。
根据上述理论,编写了分析压电周期结构阻尼特性的算法程序,通过对具体算例进行迭代求解,得到了压电周期结构的频散关系和阻尼特性,对于周期结构减振的研究和应用,有一定理论指导意义。
Periodic structures, which consist of several identical substructures arranged in a definite way, are designed and manufactured in accordance with certain principles. The macroscopic properties of periodic structures could be changed by adjusting the shape, distribution and volume fraction of the composition of the substructure. Meanwhile, periodic structures have a band-gap. The energy and amplitude of the elastic wave or vibration with the frequency in the band-gap will reduce while propagating in periodic structures.
In this thesis, a new type of unit cell of periodic structures is proposed, i.e., the substructure. In order to improve the damping of periodic structures using the piezoelectric material, piezoelectric elements shunted with electric circuits are added to the cell. For infinite periodic structures, the problem is reduced to one cell by Bloch's theorem. An independent unit cell is converted to anyone of periodic structures by applying the periodic boundary conditions to the model established by the finite element method. Based on the equivalent relation between the loss factor and the structural damping, the dynamic equilibrium equations of the unit cell are reduced to complex coefficient eigenvalue equations.
In view of the above observations, the program for analyzing the damping property of piezoelectric periodic structures is written, and a specific example is given. The dispersion relation and damping property of piezoelectric periodic structures are obtained by iteration computation. Our research will provide a theoretical basis for further study.
引文
[1]王春雷,李吉超,赵明磊.压电铁电物理[M].北京：科学出版社,2009.
[2]Baz A, Tempia A. Active piezoelectric damping composites [J]. Sensors and Actuators,2004, A112:340-350.
[3]Edward Crawley F, Javier de Luis. Use of piezoelectric actuators as elements of intelligent structures [J].AIAA Journal,1987,25:1373-1385.
[4]Fuller C R, Elliott S J, Nelson P A. Active control of vibration [M]. London:Academic Press,1996.
[5]Benjeddou A, Qhayon R. Piezoeletric active vibration control of damped sandwich beams [J].Journal of Sound and Vibration,2001,264(4):653-677.
[6]Benjeddou A. Advances in hybrid active-passive vibration and noise control via piezoelectric and viscoelastic constrained layer treatments [J].Journal of Vibration and Control,2001,7(4):565-602.
[7]Forward R L. Electronic damping of vibration in optical structures [J]. Applied Optics,1979,18(5):690-697.
[8]Hagood N W, von Flotow A. Damping of structure vibrations with piezoelectric materials and passive electrical networks [J]. Journal of Sound and Vibration 1991,146(2):243-268.
[9]Lesieutre G A. Vibration damping and control using shunted piezoelectric materials [J]. The Shock and Vibration Digest,1998,30(3):187-195.
[10]Davis C, Lesieutre G A. A modal strain energy approach to the prediction of resistively shunted piezoelectric damping [J]. Journal of Sound and Vibration,1995,184(1):129-139.
[11]Law H H, Rossiter P L, Simon G P, Koss L L. Characterization of mechanical vibration damping by piezoelectric materials [J]. Journal of Sound and Vibration,1996,197(4):489-513.
[12]Moheimani S O R. A survey of recent innovations in vibration damping and control using shunted piezoelectric transducers [J].IEEE Control Systems Technology,2003,11 (4):482-494.
[13]常道庆,刘碧龙,李晓东,田静.智能吸声控制中压电片位置的选取[J].声学技术,2007,26(5)：978-979.
[14]李宁,程礼.压电分流阻尼的虚拟实现[J].空军工程大学学报,2008,9(4)：59-63.
[15]卜雄洙,刘莹,庞俊恒.基于压电元件的同步开关减震技术的实验研究[J].压电与声光,2007,29(5)：606-608.
[16]赵永春,季宏丽,裘进浩,朱孔军.基于压电元件的悬臂梁半主动振动控制研究[J].振动、测试与诊断,2009,29(4)：424-429.
[17]孙浩,杨春智,李凯翔,解江,李斌,张玲凌.压电分流阻尼控制精密机械结构振动的研究[J].振动与冲击,2008,27(6)：86-91.
[18]杨春智,孙浩,李凯翔,武丹,王臻.精密机械结构的自适应分流阻尼抑振[J].压电与声光,2009,31(3)：428-432.
[19]Evans A G, Hutchinson J W, Fleck N A, Ashby M F, Wadley H N G. The topological design of multifunctional cellular metals [J]. Journal of Progress in Materials Science,2001,46:309-327.
[20]Wadley H N G, Cellular Metals Manufacturing [J]. Advanced engineering materials,2002,4:726-733.
[21]Wadley H N G, Fleck N A, Evans A G. Fabrication and structural performance of periodic cellular metal sandwich structures [J]. Journal of Composites Science and Technology,2003,63:2331-2343.
[22]El-Raheb M. Frequency response of a two dimensional truss-like periodic panel [J]. Journal of the Acoustical Society of America,1997,101:3457-3465.
[23]El-Raheb M, Wagner P. Transmission of sound across a truss-like periodic panel:2d analysis [J]. Journal of the Acoustical Society of America,1997,102:2176-2183.
[24]El-Raheb M, Wagner P. Effects of cap and aspect ratio on transmission of sound across a truss-like periodic double panel [J].Journal of Sound and Vibration,2002,250:299-322.
[25]Torsten Kohrs, Bjorn, Petersson A T. Wave propagation in light weight profiles with truss-like cores:Wavenumber content, forced response and influence of periodicity perturbations [J]. Journal of Sound and Vibration,2007,304:691-721.
[26]Torsten Kohrs, Bjorn, Petersson A T. Forced response of light weight plates with truss-like cores [J]. Journal of Sound and Vibration,2009,325:252-265.
[27]Querin O M, Victoria M, Marti P. Topology optimization of truss-like continua with different material properties in tension and compression [J]. Structural and Multidisciplinary Optimization,2010,42:25-32.
[28]Yan J, Liu L, Cheng G D. Concurrent material and structure optimization of hollow plate with truss-like material[J]. Structural and Multidisciplinary Optimization,2008,35:153-163.
[29]Liu L, Yan J, Cheng G D. Optimum structure with homogeneous optimum truss-like material[J]. Computers and Structures,2008,86:1417-1425.
[30]郑华勇,吴林志,马力,王新筑Kagome点阵夹芯板的抗冲击性能研究[J].工程力学,24(8)：86-92.
[31]刘敬礼,刘华,杨嘉陵.点阵材料夹芯悬臂梁在端部承受撞击的动力响应分析[J].应用力学学报,2008,25(2)：235-238.
[32]徐庆红,刘华,杨嘉陵.基于最小加速度原理分析点阵材料夹芯梁的弹塑性动力响应[J].固体力学学报,2009,20(4)：389-394.
[33]贾成厂,郭宏.复合材料教程[M].北京：高等教育出版社,2010.
[34]张少辉,陈花玲.国外纤维增强树脂基复合材料阻尼研究综述[N].航空材料学报,22：58-62.
[35]温熙森,温激鸿,郁殿龙,王刚,刘耀宗,韩小云.声子晶体[M].北京：国防工业出版社,2009.
[36]Bondaryk J E. Vibration of truss structures [J]. Acoustical Society of America,1997,102(4):2167-2175.
[37]Langley R S, Smith J R D, Fahy F J. Statistical energy analysis of periodically stiffened damped plate structures [J]. Journal of Sound and Vibration,1997,208(3):407-426.
[38]Richards D, Pines D J. Passive reduction of gear mesh vibration using a periodic drive shaft [J]. Journal of Sound and Vibration,2003,264(2):317-342.
[39]Diaz-de-Anda A, Pimentel A, Flores J, Morales A. Locally periodic Timoshenko rod Experiment and theory [J]. Acoustical Society of America,2005,117(5):2814-2819.
[40]方俊鑫,陆栋.固体物理学[M].上海：上海科学技术出版社,1980.
[41]温熙森.光子/声子晶体理论与技术.北京：科学出版社,2006.
[42]章维益.固体物理学[M].北京：高等教育出版社,2010.
[43]Liu Z. Y., Zhang X.,Mao Y. et al. Locally resonant sonic materials [J]. Science,2000,289:1734-1736.
[44]张亚辉,林家浩.结构动力学基础[M].辽宁：大连理工大学出版社,2007.
[2]Baz A, Tempia A. Active piezoelectric damping composites [J]. Sensors and Actuators,2004, A112:340-350.
[3]Edward Crawley F, Javier de Luis. Use of piezoelectric actuators as elements of intelligent structures [J].AIAA Journal,1987,25:1373-1385.
[4]Fuller C R, Elliott S J, Nelson P A. Active control of vibration [M]. London:Academic Press,1996.
[5]Benjeddou A, Qhayon R. Piezoeletric active vibration control of damped sandwich beams [J].Journal of Sound and Vibration,2001,264(4):653-677.
[6]Benjeddou A. Advances in hybrid active-passive vibration and noise control via piezoelectric and viscoelastic constrained layer treatments [J].Journal of Vibration and Control,2001,7(4):565-602.
[7]Forward R L. Electronic damping of vibration in optical structures [J]. Applied Optics,1979,18(5):690-697.
[8]Hagood N W, von Flotow A. Damping of structure vibrations with piezoelectric materials and passive electrical networks [J]. Journal of Sound and Vibration 1991,146(2):243-268.
[9]Lesieutre G A. Vibration damping and control using shunted piezoelectric materials [J]. The Shock and Vibration Digest,1998,30(3):187-195.
[10]Davis C, Lesieutre G A. A modal strain energy approach to the prediction of resistively shunted piezoelectric damping [J]. Journal of Sound and Vibration,1995,184(1):129-139.
[11]Law H H, Rossiter P L, Simon G P, Koss L L. Characterization of mechanical vibration damping by piezoelectric materials [J]. Journal of Sound and Vibration,1996,197(4):489-513.
[12]Moheimani S O R. A survey of recent innovations in vibration damping and control using shunted piezoelectric transducers [J].IEEE Control Systems Technology,2003,11 (4):482-494.
[13]常道庆,刘碧龙,李晓东,田静.智能吸声控制中压电片位置的选取[J].声学技术,2007,26(5)：978-979.
[14]李宁,程礼.压电分流阻尼的虚拟实现[J].空军工程大学学报,2008,9(4)：59-63.
[15]卜雄洙,刘莹,庞俊恒.基于压电元件的同步开关减震技术的实验研究[J].压电与声光,2007,29(5)：606-608.
[16]赵永春,季宏丽,裘进浩,朱孔军.基于压电元件的悬臂梁半主动振动控制研究[J].振动、测试与诊断,2009,29(4)：424-429.
[17]孙浩,杨春智,李凯翔,解江,李斌,张玲凌.压电分流阻尼控制精密机械结构振动的研究[J].振动与冲击,2008,27(6)：86-91.
[18]杨春智,孙浩,李凯翔,武丹,王臻.精密机械结构的自适应分流阻尼抑振[J].压电与声光,2009,31(3)：428-432.
[19]Evans A G, Hutchinson J W, Fleck N A, Ashby M F, Wadley H N G. The topological design of multifunctional cellular metals [J]. Journal of Progress in Materials Science,2001,46:309-327.
[20]Wadley H N G, Cellular Metals Manufacturing [J]. Advanced engineering materials,2002,4:726-733.
[21]Wadley H N G, Fleck N A, Evans A G. Fabrication and structural performance of periodic cellular metal sandwich structures [J]. Journal of Composites Science and Technology,2003,63:2331-2343.
[22]El-Raheb M. Frequency response of a two dimensional truss-like periodic panel [J]. Journal of the Acoustical Society of America,1997,101:3457-3465.
[23]El-Raheb M, Wagner P. Transmission of sound across a truss-like periodic panel:2d analysis [J]. Journal of the Acoustical Society of America,1997,102:2176-2183.
[24]El-Raheb M, Wagner P. Effects of cap and aspect ratio on transmission of sound across a truss-like periodic double panel [J].Journal of Sound and Vibration,2002,250:299-322.
[25]Torsten Kohrs, Bjorn, Petersson A T. Wave propagation in light weight profiles with truss-like cores:Wavenumber content, forced response and influence of periodicity perturbations [J]. Journal of Sound and Vibration,2007,304:691-721.
[26]Torsten Kohrs, Bjorn, Petersson A T. Forced response of light weight plates with truss-like cores [J]. Journal of Sound and Vibration,2009,325:252-265.
[27]Querin O M, Victoria M, Marti P. Topology optimization of truss-like continua with different material properties in tension and compression [J]. Structural and Multidisciplinary Optimization,2010,42:25-32.
[28]Yan J, Liu L, Cheng G D. Concurrent material and structure optimization of hollow plate with truss-like material[J]. Structural and Multidisciplinary Optimization,2008,35:153-163.
[29]Liu L, Yan J, Cheng G D. Optimum structure with homogeneous optimum truss-like material[J]. Computers and Structures,2008,86:1417-1425.
[30]郑华勇,吴林志,马力,王新筑Kagome点阵夹芯板的抗冲击性能研究[J].工程力学,24(8)：86-92.
[31]刘敬礼,刘华,杨嘉陵.点阵材料夹芯悬臂梁在端部承受撞击的动力响应分析[J].应用力学学报,2008,25(2)：235-238.
[32]徐庆红,刘华,杨嘉陵.基于最小加速度原理分析点阵材料夹芯梁的弹塑性动力响应[J].固体力学学报,2009,20(4)：389-394.
[33]贾成厂,郭宏.复合材料教程[M].北京：高等教育出版社,2010.
[34]张少辉,陈花玲.国外纤维增强树脂基复合材料阻尼研究综述[N].航空材料学报,22：58-62.
[35]温熙森,温激鸿,郁殿龙,王刚,刘耀宗,韩小云.声子晶体[M].北京：国防工业出版社,2009.
[36]Bondaryk J E. Vibration of truss structures [J]. Acoustical Society of America,1997,102(4):2167-2175.
[37]Langley R S, Smith J R D, Fahy F J. Statistical energy analysis of periodically stiffened damped plate structures [J]. Journal of Sound and Vibration,1997,208(3):407-426.
[38]Richards D, Pines D J. Passive reduction of gear mesh vibration using a periodic drive shaft [J]. Journal of Sound and Vibration,2003,264(2):317-342.
[39]Diaz-de-Anda A, Pimentel A, Flores J, Morales A. Locally periodic Timoshenko rod Experiment and theory [J]. Acoustical Society of America,2005,117(5):2814-2819.
[40]方俊鑫,陆栋.固体物理学[M].上海：上海科学技术出版社,1980.
[41]温熙森.光子/声子晶体理论与技术.北京：科学出版社,2006.
[42]章维益.固体物理学[M].北京：高等教育出版社,2010.
[43]Liu Z. Y., Zhang X.,Mao Y. et al. Locally resonant sonic materials [J]. Science,2000,289:1734-1736.
[44]张亚辉,林家浩.结构动力学基础[M].辽宁：大连理工大学出版社,2007.