{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T15:24:47Z","timestamp":1760369087815,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2012,3,28]],"date-time":"2012-03-28T00:00:00Z","timestamp":1332892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>A thermally-actuated micro-electro-mechanical (MEMS) device based on a vibrating silicon membrane has been proposed as a viscosity sensor by the authors. In this paper we analyze the vibration mode of the sensor as it vibrates freely at its natural frequency. Analytical examination is compared to finite element analysis, electrical measurements and the results obtained through real-time dynamic optical surface profilometry. The vertical movement of the membrane due to the applied heat is characterized statically and dynamically. The natural vibration mode is determined to be the (1,1) mode and good correlation is found between the analytical predictions, the simulation analysis, the observed mechanical displacement and the electrical measurements.<\/jats:p>","DOI":"10.3390\/mi3020255","type":"journal-article","created":{"date-parts":[[2012,3,28]],"date-time":"2012-03-28T11:20:43Z","timestamp":1332933643000},"page":"255-269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Mechanical Vibrations of Thermally Actuated Silicon Membranes"],"prefix":"10.3390","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2242-5937","authenticated-orcid":false,"given":"Ivan","family":"Puchades","sequence":"first","affiliation":[{"name":"Electrical and Microelectronic Engineering Department, Rochester Institute of Technology, 82 Lomb Memorial Dr., Rochester, NY 14623, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustafa","family":"Koz","sequence":"additional","affiliation":[{"name":"Microsystems Engineering Department, Rochester Institute of Technology, 82 Lomb Memorial Dr., Rochester, NY 14623, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lynn","family":"Fuller","sequence":"additional","affiliation":[{"name":"Electrical and Microelectronic Engineering Department, Rochester Institute of Technology, 82 Lomb Memorial Dr., Rochester, NY 14623, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1109\/TUFFC.2004.1386679","article-title":"1.156-GHz self-aligned vibrating micromechanical disk resonator","volume":"51","author":"Wang","year":"2004","journal-title":"IEEE Trans. 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Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Puchades, I., and Fuller, L.F. (2008, January 13\u201316). Design and Evaluation of a MEMS Bimetallic Thermal Actuator for Viscosity Measurements. Proceedings of the (University Government Industry Micro\/nano) Symposium (UGIM 2008), Louisville, KY, USA.","DOI":"10.1109\/UGIM.2008.31"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1088\/0960-1317\/16\/1\/006","article-title":"Thermally actuated, bistable, oxide\/silicon\/metal membranes","volume":"16","author":"Arya","year":"2006","journal-title":"J. Micromechanics Microengineering"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0924-4247(97)01721-4","article-title":"On the mechanisms in thermally actuated composite diaphragms","volume":"67","author":"Puers","year":"1998","journal-title":"Sens. Actuat. 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