{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:22:48Z","timestamp":1762917768796,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,6]],"date-time":"2017-04-06T00:00:00Z","timestamp":1491436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach.<\/jats:p>","DOI":"10.3390\/s17040779","type":"journal-article","created":{"date-parts":[[2017,4,6]],"date-time":"2017-04-06T04:23:30Z","timestamp":1491452610000},"page":"779","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7100-1321","authenticated-orcid":false,"given":"Attilio","family":"Frangi","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engng., Politecnico di Milano, 20133 Milano, Italy"}]},{"given":"Andrea","family":"Guerrieri","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engng., Politecnico di Milano, 20133 Milano, Italy"}]},{"given":"Nicol\u00f3","family":"Boni","sequence":"additional","affiliation":[{"name":"MSH Division, ST Microelectronics, 20010 Cornaredo (MI), Italy"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,6]]},"reference":[{"key":"ref_1","unstructured":"(2017, April 01). 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