{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T12:29:47Z","timestamp":1764937787130,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T00:00:00Z","timestamp":1724198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52174352","FRF-TP-20-027A1"],"award-info":[{"award-number":["52174352","FRF-TP-20-027A1"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities of China","doi-asserted-by":"publisher","award":["52174352","FRF-TP-20-027A1"],"award-info":[{"award-number":["52174352","FRF-TP-20-027A1"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Taking the nonlocal effect into account, the vibration governing differential equation and boundary conditions of a magnetostrictive composite cantilever resonator were established based on the Euler magnetoelastic beam theory. The frequency equation and vibration mode function of the composite cantilever were obtained by means of the separation of variables method and the analytic solution of ordinary differential equations. The lateral deflection, vibration governing equations, and boundary conditions were nondimensionalized. Furthermore, the natural frequency and modal function of the composite beam were quantitatively analyzed with different nonlocal parameters and transverse geometry dimensions using numerical examples. Compared with the results without considering the nonlocal effect, the influence of the nonlocal effect on the vibration characteristics was analyzed. The numerical results show that the frequency shift and frequency band narrowing of the magnetostrictive cantilever resonator are induced by nonlocal effects. In particular, the high-frequency vibration characteristics, such as vibration amplitude and modal node of the composite beam, are significantly affected. These analysis results can provide a reference for the functional design and optimization of magnetostrictive resonators.<\/jats:p>","DOI":"10.3390\/s24165390","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:53:19Z","timestamp":1724417599000},"page":"5390","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Vibration Characteristics of Magnetostrictive Composite Cantilever Resonator with Nonlocal Effect"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7949-6351","authenticated-orcid":false,"given":"Yan","family":"Xu","sequence":"first","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7579-3007","authenticated-orcid":false,"given":"Xinchun","family":"Shang","sequence":"additional","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1809-7413","authenticated-orcid":false,"given":"Ke","family":"Xu","sequence":"additional","affiliation":[{"name":"Collaborative Innovation Center of Steel Technology, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.sna.2012.12.013","article-title":"Magnetostrictive resonators as sensors and actuators","volume":"200","author":"Zhang","year":"2013","journal-title":"Sens. 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