{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:39:21Z","timestamp":1760243961564,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2010,12,14]],"date-time":"2010-12-14T00:00:00Z","timestamp":1292284800000},"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>This paper investigates the design optimization of an electrostatically actuated microcantilever resonator that operates in air. The nonlinear effects of electrostatic actuation and air damping make the structural dynamics modeling more complex. There is a need for an efficient way to simulate the system behavior so that the design can be more readily optimized. This paper describes an efficient analytical approach for determining the optimum design for a microcantilever resonant mass sensor. One simple case is described. The sensor design is a square plate that is coated with a functional polymer and attached to the substrate with folded leg springs. The plate has a square hole in the middle to reduce the effect of squeeze film damping. With the analytical approach, the optimum hole size for maximum sensitivity is found.<\/jats:p>","DOI":"10.3390\/microm1010112","type":"journal-article","created":{"date-parts":[[2010,12,14]],"date-time":"2010-12-14T13:26:35Z","timestamp":1292333195000},"page":"112-128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Optimization Strategy for Resonant Mass Sensor Design in the Presence of Squeeze Film Damping"],"prefix":"10.3390","volume":"1","author":[{"given":"Chengzhang","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michele H.","family":"Miller","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2010,12,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1007\/s00216-004-2694-y","article-title":"Cantilever-based biosensors","volume":"379","author":"Ziegler","year":"2004","journal-title":"Anal. Bioanal. Chem."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1021\/cr0681041","article-title":"Microcantilevers: Sensing chemical interactions via mechanical motion","volume":"108","author":"Goeders","year":"2008","journal-title":"Chem. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.sna.2007.01.008","article-title":"Squeeze film air damping in MEMS","volume":"136","author":"Bao","year":"2007","journal-title":"Sens. Actuat. A"},{"key":"ref_4","unstructured":"Starr, J.B. (, January June). Squeeze film damping in solid state accelerometer. Proceedings of Technical Digest, IEEE Solid State Sensor and Actuator Workshop, Hilton Head Island, SC, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1115\/1.3438789","article-title":"Squeeze film damper: Amplitude effects at low squeeze numbers","volume":"97","author":"Sadd","year":"1975","journal-title":"J. Eng. Indust."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1115\/1.3254692","article-title":"On isothermal squeeze films","volume":"105","author":"Blech","year":"1983","journal-title":"J. Lubric. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0924-4247(93)80144-6","article-title":"A comparison of squeeze-film theory with measurements on a microstructure","volume":"A36","author":"Andrews","year":"1993","journal-title":"Sens. Actuat."},{"key":"ref_8","unstructured":"Veijola, T., Kuisma, R.H., and Lahdenpera, J. (, January June). Circuit simulation model of gas damping in microstructures with nontrivial geometries. Proceedings of Transducers \u201995 and Eurosensors IX, Stockholm, Sweden."},{"key":"ref_9","unstructured":"Yang, Y.J., and Gretillat, S.D. (, January June). Numerical simulation of compressible squeezed-film damping. Proceedings of Technical Digest Solid-State Sensors and Actuator Workshop, Hilton Head Island, SC, USA."},{"key":"ref_10","unstructured":"Yang, Y.J., Gretillat, M.A., and Senturia, S.D. (, January June). Effect of air damping on the dynamics of nonuniform deformations of microstructures. Proceedings of International Conference on Solid-State Sensors and Actuators (Transducers \u201997), Chicago, IL, USA. Digest of Technical Papers."},{"key":"ref_11","unstructured":"Kim, E.S., Cho, Y.H., and Kim, M.U. (, January January). Effect of holes and edges on the squeeze film damping of perforated micromechanical structures. MEMS\u201999, Orlando, FL, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2939","DOI":"10.1121\/1.1798331","article-title":"Modeling of viscous damping of perforated planar microstructures: Applications in acoustics","volume":"116","author":"Homentcovschi","year":"2004","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1088\/0960-1317\/13\/6\/301","article-title":"Modified Reynolds\u2019 equation and analytical analysis of squeeze-film air damping of perforated structures","volume":"13","author":"Bao","year":"2003","journal-title":"J. Micromech. Microeng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/S0924-4247(98)00109-5","article-title":"Compact analytical modeling of squeeze film damping with arbitrary venting conditions using a Green\u2019s function approach","volume":"A70","author":"Darling","year":"1998","journal-title":"Sens. Actuat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8218","DOI":"10.1021\/jp710229a","article-title":"Evolution in the Supramolecular Complexes between Poly(phenylene ethynylene)-Based Polyelectrolytes and Octadecyltrimethylammonium Bromide as Revealed by Fluorescence Correlation Spectroscopy","volume":"112","author":"Yue","year":"2008","journal-title":"J. Phys. Chem. B"}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/1\/3\/112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:04:06Z","timestamp":1760220246000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/1\/3\/112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,14]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2010,12]]}},"alternative-id":["microm1010112"],"URL":"https:\/\/doi.org\/10.3390\/microm1010112","relation":{},"ISSN":["2072-666X"],"issn-type":[{"type":"electronic","value":"2072-666X"}],"subject":[],"published":{"date-parts":[[2010,12,14]]}}}