{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T13:23:30Z","timestamp":1791897810883,"version":"4.3.4"},"reference-count":26,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005073","name":"Agency for Defense Development","doi-asserted-by":"publisher","award":["16CM0071"],"award-info":[{"award-number":["16CM0071"]}],"id":[{"id":"10.13039\/501100005073","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Tonpilz is a popular transducer for underwater projector arrays for sonar systems. For low-frequency transmission, a larger axial dimension of the conventional Tonpilz transducer is required. However, a bulky and heavy Tonpilz element is not suitable due to limitations in terms of the space and payload of the array platform. To address this problem, we developed a rear-mounted Tonpilz transducer to generate a sub-fundamental resonance in addition to the common longitudinal resonance. For this purpose, we developed a new equivalent circuit model that can reflect all the effects of the key design parameters of the transducer, such as suspension thickness (stiffness), tail mass thickness, and head mass thickness. The impedance and transmitting voltage response were evaluated as performance factors at both resonance frequencies. The validity of the circuit was verified by comparing the analysis results with those from the finite element analysis of the same transducer. Based on the results, the transducer structure was designed to have comparable transmitting performance at both resonance frequencies by employing relatively high suspension stiffness, light tail mass, and heavy head mass. The novel design can permit the dual-band operation of the transducer so that the transducer can operate as a wideband projector.<\/jats:p>","DOI":"10.3390\/s20247085","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T08:59:34Z","timestamp":1607590774000},"page":"7085","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modeling and Design of a Rear-Mounted Underwater Projector Using Equivalent Circuits"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2072-3922","authenticated-orcid":false,"given":"Jinwook","family":"Kim","sequence":"first","affiliation":[{"name":"Joint Department of Biomedical Engineering, The University of North Carolina at Chapel Hill and North Carolina State University, Chapel Hill, NC 27599, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2749-199X","authenticated-orcid":false,"given":"Yongrae","family":"Roh","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Kyungpook National University, Daegu 41566, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sherman, C.H., and Butler, J.L. 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Sensors, 19.","DOI":"10.3390\/s19030580"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7085\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:43:23Z","timestamp":1760179403000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7085"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":26,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20247085"],"URL":"https:\/\/doi.org\/10.3390\/s20247085","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,10]]}}}