{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T04:57:24Z","timestamp":1768971444390,"version":"3.49.0"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,31]],"date-time":"2019-12-31T00:00:00Z","timestamp":1577750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004569","name":"Ministerstwo Nauki i Szkolnictwa Wy\u017cszego","doi-asserted-by":"publisher","award":["011 \/ RID \/ 2018\/19"],"award-info":[{"award-number":["011 \/ RID \/ 2018\/19"]}],"id":[{"id":"10.13039\/501100004569","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The paper presents research related to the functional features of a novel three-layer circular piezoelectric actuator\/sensor. The outer layers of the transducer are made of non-piezoelectric material. The middle layer comprises two elements\u2014a piezoelectric disk, and a ring made of non-piezoelectric material. The additional external passive layer has a very important function; it protects the transducer\u2019s electrical components against damage caused by external factors. Also, if sparking on the transducer wires or electrodes occurs, this layer prevents fire. So far, there is no analytical model for such a transducer. Closed-form analytical equations are important tools for predicting and optimizing the operation of devices. Thus, using both the Plate Theory and constitutive equations of piezoelectric materials, an analytical formula describing transducer deflection as a function of electrical loads has been found (electromechanical characteristic of the transducer). In addition, it is worth noting that under certain assumptions, the developed analytical model can also be used for two-layer transducers. The tests carried out show satisfactory compliance of the results obtained through the developed solution with both literature data and numerical data. Moreover, based on the obtained analytical model, the effect of selected non-dimensional variables on the actuator performance has been examined. These parameters include dimensions and mechanical properties of both piezoelectric disk and passive plates and strongly influence the behavior of the transducer.<\/jats:p>","DOI":"10.3390\/s20010222","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T03:28:53Z","timestamp":1578022133000},"page":"222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Static Electromechanical Characteristic of a Three-Layer Circular Piezoelectric Transducer"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8090-1671","authenticated-orcid":false,"given":"Grzegorz","family":"Mieczkowski","sequence":"first","affiliation":[{"name":"Bialystok University of Technology, Faculty of Mechanical Engineering, 45C Wiejska Str., 15-351 Bialystok, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej","family":"Borawski","sequence":"additional","affiliation":[{"name":"Bialystok University of Technology, Faculty of Mechanical Engineering, 45C Wiejska Str., 15-351 Bialystok, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dariusz","family":"Szpica","sequence":"additional","affiliation":[{"name":"Bialystok University of Technology, Faculty of Mechanical Engineering, 45C Wiejska Str., 15-351 Bialystok, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"\u015etef\u0103nescu, D.M. 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