空气耦合超声换能器的频域声场研究
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摘要
考虑介质的衰减及其引起的频散对频域声场的影响,提出幂函数衰减介质中圆形换能器声场的解析公式。基于该公式研究空气耦合超声换能器的轴向声压与径向声压分布特征。结果表明:空气中的衰减是引起声场变化的主要因素;相对于零衰减介质,空气中的声压幅度随着传播距离的增加而明显降低,近场长度明显减小,近场内轴向声压的零点、极大值点无偏移,径向声压分布和声束扩散角无变化。研究结果对于空气耦合换能器的设计、空气耦合声场的测量、校准具有重要参考价值,并可以作为ASTM E1065/E1065-14和IEC 62127标准的补充。
The influence of medium attenuation and the associated dispersion is considered of acoustic field in frequency domain.An analytical solution for the acoustic field radiated from circular ultrasonic transducer into lossy medium with power law attenuation is proposed. Based on the solution, a research on the axial-and radial-acoustic pressure distribution of air-coupled transducer is performed and it shows that: attenuation is the main factor causing acoustic field distortion in air; compared with non-attenuation case, in air, the amplitude of acoustic pressure drops down evidently as a function of propagation distance, the near-field length decreases, the zero-and maxima-points in near-field stay the same, the shape of directivity pattern and beam spread angle have no difference. The result is a good reference for the design of air-coupled transducer and the corresponding acoustic field measurement and calibration; as well it could be a compliment of transducer characterization standard ASTM E1065/E1065-14 and IEC 62127.
The influence of medium attenuation and the associated dispersion is considered of acoustic field in frequency domain.An analytical solution for the acoustic field radiated from circular ultrasonic transducer into lossy medium with power law attenuation is proposed. Based on the solution, a research on the axial-and radial-acoustic pressure distribution of air-coupled transducer is performed and it shows that: attenuation is the main factor causing acoustic field distortion in air; compared with non-attenuation case, in air, the amplitude of acoustic pressure drops down evidently as a function of propagation distance, the near-field length decreases, the zero-and maxima-points in near-field stay the same, the shape of directivity pattern and beam spread angle have no difference. The result is a good reference for the design of air-coupled transducer and the corresponding acoustic field measurement and calibration; as well it could be a compliment of transducer characterization standard ASTM E1065/E1065-14 and IEC 62127.
引文
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[2]REMILLIEUX M C,ANDERSON B E,ULRICH T J,et al.Review of air-coupled transduction for nondestructive testing and evaluation[J].Acoustics Today,2014,10(3):36-45.
[3]周正干,魏东.空气耦合超声波无损检测技术的发展[J].机械工程学报,2008,44(6):10-14.ZHOU Zhenggan,WEI Dong.Progress of air-coupled ultrasonic non-destructive testing technology[J].Chinese Journal of Mechanical Engineering,2008,44(6):10-14.
[4]周正干,孙广开.先进超声检测技术的研究应用进展[J].机械工程学报,2017,53(22):1-10.ZHOU Zhenggan,SUN Guangkai.New progress of the study and application of advanced ultrasonic testing technology[J].Journal of Mechanical Engineering,2017,53(22):1-10.
[5]American Society for Testing and Materials International,Standard Practice for Evaluating Characteristics of Ultrasonic Search Units.ASTM E1065/E1065M-14[S].West Conshohocken:ASTM International,2014.
[6]International Electrotechnical Commission.Ultrasonicshydrophones Part 1:Measurement and characterization of medical ultrasonic fields up to 40 MHz.IEC 62127-1[S].Geneva:IEC,2013.
[7]KRAUTKRAMER J,KRAUTKRAMER H.Ultrasonic testing of materials[M].New York:Springer-Verlag Berlin Heidelberg,1990.
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[9]GACHAGAN A,HAYWARD G,KELLY S P,et al.Characterization of air-coupled transducers[J].IEEETransactions on Ultrasonics,Ferroelectrics,and Frequency Control,1996,43(4):678-688.
[10]BASHFORD A G,SCHINDEL D W,HUTCHINS D A,et al.Field characterization of an air-coupled micromachined ultrasonic capacitance transducer[J].Journal of Acoustic Society of America,1997,101(1):315-322.
[11]NEILD A,HUTCHINS D A,ROBERTSON T J,et al.The radiated fields of focusing air-coupled ultrasonic phased arrays[J].Ultrasonics,2005,43(3):183-195.
[12]NEILD A,HUTCHINS D A.A theoretical model for a finite-size acoustic receiver[J].Journal of Acoustic Society of America,2003,115(4):1546-1556.
[13]HUTCHINS D A,MCLNTOSH J S,NEILD A,et al.Radiated fields of capacitive micromachined ultrasonic transducers in air[J].Journal of Acoustic Society of America,2003,114(3):1435-1449.
[14]LI J,PIWAKOWSKI B.A time-domain model and experimental validation of the acoustic field radiated by air-coupled transducers[J].Ultrasonics,2018,82(1):114-129.
[15]SZABO T L.Time domain wave equations for lossy media obeying a frequency power law[J].Journal of Acoustic Society of America,1994,96(1):491-500.
[16]PINKERTON J M M.The absorption of ultrasonic waves in liquids and its relation to molecular constitution[J].Proceeding of the Physical Society,1949,62(2):129-141.
[17]BASS H E,SUTHERLAND L C,ZUCKERWAR A J.Atmospheric absorption of sound:Update[J].Journal of Acoustic Society of America,1990,88(4):2019-2021.
[18]LEE C C,LAHHAM M,MARTIN B G.Experimental verification of the Kramers-Kronig relationship for acoustic waves[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,1990,37(4):286-294.
[19]WATERS K R,MOBLEY J,MILLER J G.Causality-imposed(Kramers-Kronig)relationships between attenuation and dispersion[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2005,52(5):822-833.
[20]KELLY J F,MCGOUGH R J.Analytical time-domain Green's functions for power-law media[J].Journal of Acoustic Society of America,2008,124(5):2861-2872.
[21]WATERS K R,HUGHES M S,MOBLEY J,et al.Differential forms of the Kramers-Kronig dispersion relations[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2003,50(1):68-76.
[22]KINSLER L E,FREY A R,COPPENS A B,et al.Fundamentals of acoustics[M].London:John Wiley&Sons,Inc.,1999.
[23]WATSON G N,S.S D F R.A treatise on the theory of bessel functions[M].London:Cambridge University Press,1992.
[24]YOUSIF H A,MELKA R.Bessel function of the first kind with complex argument[J].Computer Physics Communications,1997,106(3):199-206.
[25]TOIT C F D.Bessel functions Jn(z)and Yn(z)of integer order and complex argument[J].Computer Physics Communications,1993,78(1-2):181-189.
[26]ABRAHAM O,PIWAKOWSKI B,VILLAIN G,et al.Non-contact,automated surface wave measurements for the mechanical characterization of concrete[J].Construction and Building Materials,2012,34:904-915.
[2]REMILLIEUX M C,ANDERSON B E,ULRICH T J,et al.Review of air-coupled transduction for nondestructive testing and evaluation[J].Acoustics Today,2014,10(3):36-45.
[3]周正干,魏东.空气耦合超声波无损检测技术的发展[J].机械工程学报,2008,44(6):10-14.ZHOU Zhenggan,WEI Dong.Progress of air-coupled ultrasonic non-destructive testing technology[J].Chinese Journal of Mechanical Engineering,2008,44(6):10-14.
[4]周正干,孙广开.先进超声检测技术的研究应用进展[J].机械工程学报,2017,53(22):1-10.ZHOU Zhenggan,SUN Guangkai.New progress of the study and application of advanced ultrasonic testing technology[J].Journal of Mechanical Engineering,2017,53(22):1-10.
[5]American Society for Testing and Materials International,Standard Practice for Evaluating Characteristics of Ultrasonic Search Units.ASTM E1065/E1065M-14[S].West Conshohocken:ASTM International,2014.
[6]International Electrotechnical Commission.Ultrasonicshydrophones Part 1:Measurement and characterization of medical ultrasonic fields up to 40 MHz.IEC 62127-1[S].Geneva:IEC,2013.
[7]KRAUTKRAMER J,KRAUTKRAMER H.Ultrasonic testing of materials[M].New York:Springer-Verlag Berlin Heidelberg,1990.
[8]孔涛,徐春广,张运涛,等.空气耦合超声换能器声场计算与测量研究[J].机械工程学报,2011,47(22):19-24.KONG Tao,XU Chunguang,ZHANG Yuntao,et al.Investigation of acoustic field calculation and measurement method for air-coupled ultrasonic transducer[J].Journal of Mechanical Engineering,2011,47(22):19-24.
[9]GACHAGAN A,HAYWARD G,KELLY S P,et al.Characterization of air-coupled transducers[J].IEEETransactions on Ultrasonics,Ferroelectrics,and Frequency Control,1996,43(4):678-688.
[10]BASHFORD A G,SCHINDEL D W,HUTCHINS D A,et al.Field characterization of an air-coupled micromachined ultrasonic capacitance transducer[J].Journal of Acoustic Society of America,1997,101(1):315-322.
[11]NEILD A,HUTCHINS D A,ROBERTSON T J,et al.The radiated fields of focusing air-coupled ultrasonic phased arrays[J].Ultrasonics,2005,43(3):183-195.
[12]NEILD A,HUTCHINS D A.A theoretical model for a finite-size acoustic receiver[J].Journal of Acoustic Society of America,2003,115(4):1546-1556.
[13]HUTCHINS D A,MCLNTOSH J S,NEILD A,et al.Radiated fields of capacitive micromachined ultrasonic transducers in air[J].Journal of Acoustic Society of America,2003,114(3):1435-1449.
[14]LI J,PIWAKOWSKI B.A time-domain model and experimental validation of the acoustic field radiated by air-coupled transducers[J].Ultrasonics,2018,82(1):114-129.
[15]SZABO T L.Time domain wave equations for lossy media obeying a frequency power law[J].Journal of Acoustic Society of America,1994,96(1):491-500.
[16]PINKERTON J M M.The absorption of ultrasonic waves in liquids and its relation to molecular constitution[J].Proceeding of the Physical Society,1949,62(2):129-141.
[17]BASS H E,SUTHERLAND L C,ZUCKERWAR A J.Atmospheric absorption of sound:Update[J].Journal of Acoustic Society of America,1990,88(4):2019-2021.
[18]LEE C C,LAHHAM M,MARTIN B G.Experimental verification of the Kramers-Kronig relationship for acoustic waves[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,1990,37(4):286-294.
[19]WATERS K R,MOBLEY J,MILLER J G.Causality-imposed(Kramers-Kronig)relationships between attenuation and dispersion[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2005,52(5):822-833.
[20]KELLY J F,MCGOUGH R J.Analytical time-domain Green's functions for power-law media[J].Journal of Acoustic Society of America,2008,124(5):2861-2872.
[21]WATERS K R,HUGHES M S,MOBLEY J,et al.Differential forms of the Kramers-Kronig dispersion relations[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2003,50(1):68-76.
[22]KINSLER L E,FREY A R,COPPENS A B,et al.Fundamentals of acoustics[M].London:John Wiley&Sons,Inc.,1999.
[23]WATSON G N,S.S D F R.A treatise on the theory of bessel functions[M].London:Cambridge University Press,1992.
[24]YOUSIF H A,MELKA R.Bessel function of the first kind with complex argument[J].Computer Physics Communications,1997,106(3):199-206.
[25]TOIT C F D.Bessel functions Jn(z)and Yn(z)of integer order and complex argument[J].Computer Physics Communications,1993,78(1-2):181-189.
[26]ABRAHAM O,PIWAKOWSKI B,VILLAIN G,et al.Non-contact,automated surface wave measurements for the mechanical characterization of concrete[J].Construction and Building Materials,2012,34:904-915.
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