纵向换能器的频率方程
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摘要
目前应用的纵向换能器频率方程是通过1个未知节点分成2个部分分别描述的,该方程必须借助数学迭代方法计算整体换能器的谐振频率。针对其应用的不便性和对不同截面形状的适应性问题,本文基于一维振动理论和能量法,给出纵向换能器的简化机电等效模型,考虑部件截面参数,通过动能和位能等效关系得出等效元件参数表达式,根据谐振条件经过严格数学推导,给出关于整体换能器频率方程的参数化数学表达式。可应用于部件不等截面以及多种截面形状尺寸的纵向换能器谐振频率和振动节点计算,具有更广泛的适用性,计算结果与有限元方法符合很好。
Currently used frequency equations for a longitudinal transducer are described as two segments from an unknown node,which must employ the mathematical iterative method to calculate the resonant frequency of the entire transducer. Therefore,frequency equations are inconvenient and have adaptability problems on transducers with different cross-sectional shapes. In this study,we obtained the simplified electromechanical equivalent model on the basis of the one-dimensional vibration theory and energy method and deduced the parametric expression of equivalent elements through the equivalent relationship between kinetic and potential energies,considering the parameters of cross sections. Finally,on the basis of the mechanical resonance condition,we derived the parameterized mathematical expression of frequency equations for the entire transducer,which is precisely deduced through the mathematical method. This parameterized mathematical expression can be widely used to calculate the resonant frequency and vibrational node of longitudinal transducers with unequal cross-sectional parts or different cross-sectional shapes and sizes. The calculated results are consistent with those of the finite element method.
Currently used frequency equations for a longitudinal transducer are described as two segments from an unknown node,which must employ the mathematical iterative method to calculate the resonant frequency of the entire transducer. Therefore,frequency equations are inconvenient and have adaptability problems on transducers with different cross-sectional shapes. In this study,we obtained the simplified electromechanical equivalent model on the basis of the one-dimensional vibration theory and energy method and deduced the parametric expression of equivalent elements through the equivalent relationship between kinetic and potential energies,considering the parameters of cross sections. Finally,on the basis of the mechanical resonance condition,we derived the parameterized mathematical expression of frequency equations for the entire transducer,which is precisely deduced through the mathematical method. This parameterized mathematical expression can be widely used to calculate the resonant frequency and vibrational node of longitudinal transducers with unequal cross-sectional parts or different cross-sectional shapes and sizes. The calculated results are consistent with those of the finite element method.
引文
[1]周福洪.水声换能器及基阵[M].北京:国防工业出版社,1984:62-84.
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[3]林书玉.夹心式压电陶瓷功率超声换能器的优化设计[J].压电与声光,2003,25(3):199-202.LIN Shuyu.Optimization design of the sandwich piezoelectric ceramic ultrasonic transducer[J].Piezoelectrics&acoustooptics,2003,25(3):199-202.
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[10]周天放,蓝宇,桑永杰.空腔式前盖板宽带纵向换能器研究[J].哈尔滨工程大学学报,2016,37(9):1215-1219.ZHOU Tianfang,LAN Yu,SANG Yongjie.Research on longitudinal broadband transducer with cavity-type front cover[J].Journal of Harbin Engineering University,2016,37(9):1215-1219.
[11]HAWKINS D W,GOUGH P T.Multiresonance design of a Tonpilz transducer using the Finite Element Method[J].IEEE transactions on ultrasonics,ferroelectrics,and frequency control,1996,43(5):782-790.
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[13]ZHANG Kai.The study of 33 mode single crystal longitudinal transducer[C]//2015 Symposium on Piezoelectricity,Acoustic waves,and device applications,Jinan,China,282-284.
[14]莫喜平,刘永平,崔政,等.宽带宽波束纵向水声换能器研究[J].应用声学,2006,25(5):270-272.MO Xiping,LIU Yongping,CUI Zhen,et al.A broadband and wide-beam longitudinal underwater transducer[J].Journal of applied acoustics,2006,25(5):270-272.
[15]GOU Yue,DAI Yuyu.Simulation study on wideband transducer with longitudinal-flexural coupling vibration[C]//2019 Symposium on Piezoelectrcity,Acoustic Waves and Device Applications(SPAWDA),2019:1-4.
[16]LIU Yingxiang,CHEN Weishan,LU Di,et al.Study on the vibration coupling of ultrasonic motor using longitudinal transducers[C]//2012 Symposium on Piezoelectricity,Acoustic Waves,and Device,Shanghai,China,2012.
[2]栾桂冬,张金铎,金欢阳.传感器及其应用[M].西安:西安电子科技大学出版社,2002:161-165.
[3]林书玉.夹心式压电陶瓷功率超声换能器的优化设计[J].压电与声光,2003,25(3):199-202.LIN Shuyu.Optimization design of the sandwich piezoelectric ceramic ultrasonic transducer[J].Piezoelectrics&acoustooptics,2003,25(3):199-202.
[4]林书玉.双激励源压电陶瓷超声换能器的共振频率特性分析[J].电子学报,2009,37(11):2504-2509.LIN Shuyu.Analysis on the resonance frequency of sandwich ultrasonic transducers with two sets of piezoelectric ceramic elements[J].Acta electronica sinica,2009,37(11):2504-2509.
[5]贺西平,胡静.穿单孔型宽频带换能器[J].声学学报,2007,32(3):221-225.HE Xiping,HU Jing.Study on the wide-band sandwich transducer with single hole[J].Acta acustica,2007,32(3):221-225.
[6]秦雷,王丽坤,唐会彦,等.夹心式复合变幅杆换能器频率方程的推导[J].振动与冲击,2011,30(7):188-191.QIN Lei,WANG Likun,TANG Huiyan,et al.Frequency equation of a sandwich transducer with complex transformer[J].Journal of vibration and shock,2011,30(7):188-191.
[7]BUTLER S C.Triple-resonant transducers[J].IEEE transactions on ultrasonics,ferroelectrics,and frequency control,2012,59(6):1292-1300.
[8]莫喜平.ANSYS软件在模拟分析声学换能器中的应用[J].声学技术,2007,26(6):1279-1290.MO Xiping.Simulation and analysis of acoustics transducers using the ANSYS software[J].Technical acoustics,2007,26(6):1279-1290.
[9]李英明,莫喜平,潘耀宗,等.铁镓驱动弯曲圆盘换能器设计及振动特性研究[J].应用声学,2016,35(6):471-479.LI Yingming,MO Xiping,PAN Yaozong,et al.Flexural vibration of bender disk transducer driven by Galfenol[J].Journal of applied acoustics,2016,35(6):471-479.
[10]周天放,蓝宇,桑永杰.空腔式前盖板宽带纵向换能器研究[J].哈尔滨工程大学学报,2016,37(9):1215-1219.ZHOU Tianfang,LAN Yu,SANG Yongjie.Research on longitudinal broadband transducer with cavity-type front cover[J].Journal of Harbin Engineering University,2016,37(9):1215-1219.
[11]HAWKINS D W,GOUGH P T.Multiresonance design of a Tonpilz transducer using the Finite Element Method[J].IEEE transactions on ultrasonics,ferroelectrics,and frequency control,1996,43(5):782-790.
[12]CHARLES D,GREG W,LISA N,et al.Analyses and measurements of acoustically matched,air-coupled tonpilz transducers[C]//1999 IEEE ultrasonics symposium,1045-1048.
[13]ZHANG Kai.The study of 33 mode single crystal longitudinal transducer[C]//2015 Symposium on Piezoelectricity,Acoustic waves,and device applications,Jinan,China,282-284.
[14]莫喜平,刘永平,崔政,等.宽带宽波束纵向水声换能器研究[J].应用声学,2006,25(5):270-272.MO Xiping,LIU Yongping,CUI Zhen,et al.A broadband and wide-beam longitudinal underwater transducer[J].Journal of applied acoustics,2006,25(5):270-272.
[15]GOU Yue,DAI Yuyu.Simulation study on wideband transducer with longitudinal-flexural coupling vibration[C]//2019 Symposium on Piezoelectrcity,Acoustic Waves and Device Applications(SPAWDA),2019:1-4.
[16]LIU Yingxiang,CHEN Weishan,LU Di,et al.Study on the vibration coupling of ultrasonic motor using longitudinal transducers[C]//2012 Symposium on Piezoelectricity,Acoustic Waves,and Device,Shanghai,China,2012.