Compact Analytical Model for Electromagnetic Disk-Shaped Underwater Transducer

Author details

I.A. Popov
Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russian Federation
A.V. Lukin
Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russian Federation
N.V. Piskun
Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russian Federation

https://doi.org/10.15593/perm.mech/2024.1.08

This paper proposes a mathematical model for a disk-type pulsed electrodynamic transducer operating in the low-frequency range. A well-known architecture of an electromagnetic acoustic radiator with a helical coil and a conducting disk is studied. In the work, the equations of the electromechanical system in the form of the Lagrange-Maxwell equations are built with the use of the Green's functions of a plane axisymmetric acoustic problem to estimate the reaction force of the fluid. A comparison is made between the results of a numerical solution of the obtained equations and direct numerical calculation in the COMSOL finite element analysis software. The resulting model shows good qualitative agreement with the results of finite element calculations while allowing calculations with a variation for all main model parameters required to design the transducer.

Keywords

low-frequency transduceracoustic mediumelectromechanical systemLagrange-Maxwell equationsGreen's functionelectrodynamic transducereddy currents.

КОМПАКТНАЯ АНАЛИТИЧЕСКАЯ МОДЕЛЬ ИМПУЛЬСНОГО ЭЛЕКТРОДИНАМИЧЕСКОГО ДИСКОВОГО ИЗЛУЧАТЕЛЯ

Предложена математическая модель импульсного электродинамического излучателя дискового типа, работающего в области низких частот. Объектом исследования выступает известная архитектура электромагнитного акустического излучателя со спиралевидной катушкой и проводящим диском. В настоящей работе выполнено построение уравнений электромеханической системы в форме Лагранжа – Максвелла. С применением функций Грина плоской осесимметричной акустической задачи получена оценка силы реакции жидкости. Проводится сравнение результатов численного решения полученных уравнений и прямого численного расчета в комплексе конечно-элементного анализа COMSOL. Полученная модель показывает хорошее качественное соответствие с результатами конечно-элементного анализа, при этом позволяет производить расчеты с вариацией всех основных параметров модели для проектирования излучателя.

Ключевые слова

низкочастотный излучательакустическая средаэлектромеханическая системауравнения Лагранжа – Максвеллафункция Гринаэлектродинамический излучательиндукционные токи.

Bibliography

1.Roi N.A. Impul'snye elektrodinamicheskie izluchateli // Akusticheskii zhurnal - 1970. - Vol XVI Issue 1. - p.121-128. Scholar
2.Xiping Mo, Houqing Zhu. Thirty years' progress of under- water sound projectors in China// AIP Conference Proceedings 1495, 94. - 2012. - pp. 94-104. doi: 10.1063/1.4765910. Scholar
3.Bertrand Dubus. Ultra-low frequency underwater acoustic projectors: Present status and future trends// The Journal of the Acoustical Society of America. Proceedings of Meetings on Acous- tics - 2013. - Vol. 19. - pp.1-6. - doi: 10.1121/1.4800545 Scholar
4.John L. Butler, Charles H. Sherman. Transducers and Ar- rays for Underwater Sound. Ed.2// Springer. - 2016. - doi: 10.1007/978-3-319-39044-4. Scholar
5.COMSOL Multiphysics. www.comsol.com Scholar
6.Neimark Iu.I., Fufaev N.A. Dinamika negolonomnykh sis- tem. - M.: Nauka, 1967. - 520p. Scholar
7.Martynenko Iu.G. Dinamika tverdogo tela v elektricheskikh i magnitnykh poliakh. - M.: Nauka, 1988. - 368p. Scholar
8.Kalantarov P.L., Tseitlin L.A. Raschet induktivnostei. Spra- vochnaia kniga. - Leningrad: ENERGOATOMIZDAT, 1986. - 447 s. Scholar
9.Nayfeh Ali H., Pai Frank P. Linear and Nonlinear Structural Mechanics//Wiley. - 2004. - 746p. Scholar
10.Gorshkov A.G., Medvedskii A.L., Rabinskii L.N., Tarla- kovskii D.V. Volny v splosnykh sredakh. - M.: FIZMATLIT, 2004. - 472p. Scholar
11.Slepian L.I., Iakovlev Iu.S. Integral'nye preobrazovaniia v nestatsionarnykh zadachakh mekhaniki. - Leningrad.: izd. «Su- dostroenie», 1980. - 344p. Scholar
12.J.L. Butler, S.J. Ciosek, Rare earth iron octagonal trans- ducer. J. Acoust. Soc. Am. 67, p.1809-1811 (1980). Scholar
13.S.C. Butler, F.A. Tito, A broadband hybrid magnetostic- tive/piezoelectric transducer array. Oceans 2000 MTS/IEEE Conference Proceedings, Providence, RI, vol 3, September (2000), pp. 1469-1475 Scholar
14.J. Mudiyala, H. Shim, D. Kim, Y. Roh - Development of a Dual-Layer Structure for Cymbal Transducer Arrays to Achieve a Wider Bandwidth. Sensors #22, 6614 (2022). Scholar
15.C.H. Sherman, Underwater sound transducers—a review. IEEE Trans. Sonics Ultrason. Su-22, 281-290 (1975). Scholar
16.D. Stansfield, Underwater Electroacoustic Transducers (Bath University Press, Bath, UK, 1991). Scholar
17.Y. Zhang, L. Wang, L. Qin , C. Zhong, S. Hao - Spheri- cal-Omnidirectional Piezoelectric Composite Transducer for High Frequency Underwater Acoustics. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 68, NO. 5, MAY 2021. Scholar
18.G.W. Benthien, S.L. Hobbs, Modeling of Sonar Transduc- ers and Arrays. Tech Doc. 3181, April, 2004, available on CD, Spawar Systems Center, San Diego, CA Scholar
19.Z. Abdulla, S. Naz, M.A.Z. Raja, A. Zameer - Design of Wideband Tonpilz Transducers for Underwater SONAR Applica- tions with Finite Element Model. Appl. Acoust. 2021, 183, 108293. Scholar
20.B. Aronov, The energy method for analyzing the piezoe- lectric electroacoustic transducers. J. Acoust. Soc. Am. 117, 210-220 (2005). Scholar
21.Design and Construction of Magnetostrictive Transduc- ers. Summary Technical Report of Division 6, vol 13 (National De- fense Research Committee, 1946). Scholar
22.D. Teng, X. Liu, F. Gao - Effect of Concave Stave on Class I Barrel-Stave Flexetensional Transducer. Micromachines #12, 1258 (2021). Scholar
23.J.Y. Pyun, Y.H. Kim, K.K. Park - Design of Piezoelectric Acoustic Transducers for Underwater Applications. MDPI Sensors #23(4), 1821 (2023). Scholar
24.H. Robinson, in High Pressure Characterization of Single Crystal Cylinder Transducers. 2007 U.S. Navy Workshop on Acoustic Transduction Materials and Devices, State College, PA. Scholar
25.J. Tang,Y. Bai, L. Yan, W. Wang - GMA Phased Array for Active Echo Control of Underwater Target. Appl. Acoust. 2022, 190, 108646. Scholar
26.J.L. Butler, Transducer figure of merit. J. Acoust. Soc. Am. 132, 2158-2160 (2012). Scholar
27.J.L. Butler, A.L. Butler, J.A. Rice, A tri-modal directional transducer, J. Acoust. Soc. Am. 115, 658-665 (2004). Scholar
28.J.L. Butler, A.L. Butler, Multimode Synthesized Beam Transducer Apparatus, U.S. Patent 6,734,604 B2, (11 May, 2004) Scholar
29.O.C. Zienkiewicz, The Finite Element Method (McGraw- Hill Book Company, Maidenhead, 1986). Scholar
30.K.J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice-Hall, Englewood Cliffs, 1982). Scholar

1.Рой, Н.А. Импульсные электродинамические излуча- тели / Н.А. Рой // Акустический журнал – 1970. – Т. XVI, вып. 1. – С. 121–128. Scholar
2.Xiping, Mo Thirty years' progress of underwater sound pro- jectors in China / Mo Xiping, Zhu Houqing // AIP Conference Pro- ceedings 1495, 94. – 2012. – P. 94–104. DOI: 10.1063/1.4765910 Scholar
3.Bertrand, Dubus. Ultra-low frequency underwater acoustic projectors: Present status and future trends / Dubus Bertrand // The Journal of the Acoustical Society of America. Proceedings of Meet- ings on Acoustics – 2013. – Vol. 19. – P. 1–6. DOI: 10.1121/1.4800545 Scholar
4.Butler, J.L. Transducers and Arrays for Underwater Sound. Ed.2 / J.L. Butler, Ch.H. Sherman // Springer. – 2016. DOI: 10.1007/978-3-319-39044-4 Scholar
5.COMSOL Multiphysics [Электронный ресурс]. – URL: www.comsol.com Scholar
6.Неймарк, Ю.И. Динамика неголономных систем / Ю.И. Неймарк, Н.А. Фуфаев. – М.: Наука, 1967. – 520 с. Scholar
7.Мартыненко, Ю.Г. Динамика твердого тела в электри- ческих и магнитных полях / Ю.Г. Мартыненко. – М.: Наука, 1988. – 368 с. Scholar
8.Калантаров, П.Л. Расчет индуктивностей: справочная книга / П.Л. Калантаров, Л.А. Цейтлин. – Ленинград: ЭНЕРГО- АТОМИЗДАТ, 1986. – 447 с. Scholar
9.Nayfeh, Ali H. Linear and nonlinear structural mechanics / Ali H. Nayfeh, Frank P. Pai // Wiley. – 2004. – 746 p. Scholar
10.Волны в сплошных средах / А.Г. Горшков, А.Л. Мед- ведский, Л.Н. Рабинский, Д.В. Тарлаковский. – М.: ФИЗМАТ- ЛИТ, 2004. – 472 с. Scholar
11.Слепян, Л.И. Интегральные преобразования в неста- ционарных задачах механики / Л.И. Слепян, Ю.С. Яковлев. – Л.: Судостроение, 1980. – 344 с. Scholar
12.Butler, J.L. Rare earth iron octagonal transducer / J.L. Butler, S.J. Ciosek // J. Acoust. Soc. Am. – 1980. – Vol. 67. – P. 1809–1811. Scholar
13.Butler, S.C. A broadband hybrid magnetostrictive/piezo- electric transducer array / S.C. Butler, F.A. Tito // Oceans 2000 MTS/IEEE Conference Proceedings, Providence, RI. – 2000. – Vol 3, September (2000). – P. 1469–1475. Scholar
14.Development of a dual-layer structure for cymbal trans- ducer arrays to achieve a wider Bandwidth / J. Mudiayla, H. Shim, D. Kim, Y. Roh // Sensors. – 2022. – Vol. 22. – P. 6614. Scholar
15.C.H. Sherman, Underwater sound transducers – a review. IEEE Trans. Sonics Ultrason. Su-22, 281–290 (1975). Scholar
16.Stansfield D. Underwater electroacoustic transducers / D. Stansfield. – Bath University Press, Bath, UK, 1991. Scholar
17.Spherical-Omnidirectional Piezoelectric Composite Transducer for High Frequency Underwater Acoustics / Y. Zhang, L. Wang, L. Qin, C. Zhong, S. Hao // IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL. – 2021. – Vol. 68, no. 5. Scholar
18.Benthien, G.W. Modeling of sonar transducers and ar- rays / G.W. Benthien, S.L. Hobbs // Tech Doc. 3181, April, San Di- ego, CA, 2004. Scholar
19.Abdulla, Z. Design of Wideband tonpilz transducers for underwater SONAR applications with finite element model / Z. Ab- dulla, S. Naz, M.A.Z. Raja, A. Zameer // Appl. Acoust. – 2021. – Vol. 183. – P. 108293. Scholar
20.Aronov, B. The energy method for analyzing the piezoe- lectric electroacoustic transducers / B. Aronov // J. Acoust. Soc. Am. – 2005. – Vol. 117. – P. 210–220. Scholar
21.Design and construction of magnetostrictive transduc- ers // Summary Technical Report of Division 6. – 1946. – Vol. 13. Scholar
22.Teng, D. Effect of concave stave on class i Barrel-Stave flextensional transducer / D. Teng, X. Liu, F. Gao // Microm- achines. – 2021. – Vol. 12. – P. 1258. Scholar
23.Pyun, J.Y. Design of piezoelectric acoustic transducers for underwater applications / J.Y. Pyun, Y.H. Kim, K.K. Park // MDPI Sensors. – 2023. – Vol. 23(4). – P. 1821. Scholar
24.Robinson, H. In high pressure characterization of single crys- tal cylinder transducers / H. Robinson // U.S. Navy Workshop on Acoustic Transduction Materials and Devices, State College, PA 2007. Scholar
25.GMA phased array for active echo control of underwater target / J. Tang, Y. Bai, L. Yan, W. Wang // Appl. Acoust. – 2022. – Vol. 190. – P. 108646. Scholar
26.Butler, J.L. Transducer figure of merit / J.L. Butler // J. Acoust. Soc. Am. – 2012. – Vol. 132. – P. 2158–2160. Scholar
27.Butler, J.L. A tri-modal directional transducer / J.L. But- ler, A.L. Butler, J.A. Rice // J. Acoust. Soc. Am. – 2004. – Vol. 115. – P. 658–665. Scholar
28.Butler, J.L. Multimode synthesized beam transducer ap- paratus / J.L. Butler, A.L. Butler. – U.S. Patent 6,734,604 B2, (11 May, 2004). Scholar
29.Zienkiewicz, O.C. The finite element method / O.C. Zien- kiewicz. – McGraw-Hill Book Company, Maidenhead, 1986. Scholar
30.Bathe, K.J. Finite element procedures in engineering anal- ysis / K.J. Bathe. – Prentice-Hall, Englewood Cliffs, 1982. Scholar

Article information

Published: 8 April 2024
Issue date: 8 April 2024
Issue: No. 1 (2024)