{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T04:07:47Z","timestamp":1782446867341,"version":"3.54.5"},"reference-count":21,"publisher":"Acoustical Society of America (ASA)","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12074090"],"award-info":[{"award-number":["12074090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,1,1]]},"abstract":"<jats:p>Low-frequency transducers are considerably smaller than the wavelength. When multiple low-frequency transducers are closely packed, they couple with the surrounding water and form a transducer\u2013water\u2013transducer coupling structure called multi-element coupled transducers (MCT). This study presents a theoretical model of the MCT based on radiation and mutual radiation theory and analyzes it under multiple resonance frequencies and vibration modes. The MCT comprising N single-degree-of-freedom elements possesses N resonance frequencies and corresponding vibration modes, and the resonance frequency varies with the spacing between elements. Additionally, the elements have different vibration amplitudes, with the phases of vibration among the elements manifesting as different combinations of in-phase and anti-phase in different vibration modes. Validation is performed through finite element analysis (FEA) and measurements of binary and ternary coupled transducer prototypes. The prototypes comprise bender transducers closely packed in a vertical configuration. The theoretical predictions agree with the FEA and measurement results. Thus, the theoretical model contributes to enhancing the understanding of acoustic transducer behavior in coupled configurations and optimizing the design of low-frequency acoustic arrays.<\/jats:p>","DOI":"10.1121\/10.0034862","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T13:31:30Z","timestamp":1737552690000},"page":"433-444","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Theoretical modeling and modal analysis of multi-element coupled transducers"],"prefix":"10.1121","volume":"157","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2814-5899","authenticated-orcid":false,"given":"Hao","family":"Sun","sequence":"first","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 , Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0148-4871","authenticated-orcid":false,"given":"Yu","family":"Lan","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 , Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4147-8946","authenticated-orcid":false,"given":"Wei","family":"Lu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 , Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianfang","family":"Zhou","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 , Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"2025012213312295300_c1","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/978-3-319-39044-4_7","volume-title":"Transducers and Arrays for Underwater Sound","year":"2016"},{"key":"2025012213312295300_c2","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1121\/10.0024462","article-title":"A lumped-parameter model of the free-flooded ring transducer array","volume":"155","year":"2024","journal-title":"J. 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