{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:15Z","timestamp":1760242215787,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,8]],"date-time":"2017-01-08T00:00:00Z","timestamp":1483833600000},"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":["11625208","11572190","11322215"],"award-info":[{"award-number":["11625208","11572190","11322215"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010261","name":"Fok Ying Tung Education Foundation","doi-asserted-by":"publisher","award":["141050"],"award-info":[{"award-number":["141050"]}],"id":[{"id":"10.13039\/501100010261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003395","name":"Shanghai Municipal Education Commission","doi-asserted-by":"publisher","award":["15ZZ010","14SG12"],"award-info":[{"award-number":["15ZZ010","14SG12"]}],"id":[{"id":"10.13039\/501100003395","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this article, the pull-in instability and dynamic characteristics of electrostatically actuated suspended microchannel resonators are studied. A theoretical model is presented to describe the pull-in effect of suspended microchannel resonators by considering the electrostatic field and the internal fluid. The results indicate that the system is subjected to both the pull-in instability and the flutter. The former is induced by the applied voltage which exceeds the pull-in value while the latter occurs as the velocity of steady flow get closer to the critical velocity. The statically and dynamically stable regions are presented by thoroughly studying the two forms of instability. It is demonstrated that the steady flow can remarkably extend the dynamic stable range of pull-in while the applied voltage slightly decreases the critical velocity. It is also shown that the dc voltage and the steady flow can adjust the resonant frequency while the ac voltage can modulate the vibrational amplitude of the resonator.<\/jats:p>","DOI":"10.3390\/s17010114","type":"journal-article","created":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T11:03:23Z","timestamp":1483959803000},"page":"114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Pull-In Effect of Suspended Microchannel Resonator Sensor Subjected to Electrostatic Actuation"],"prefix":"10.3390","volume":"17","author":[{"given":"Han","family":"Yan","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}]},{"given":"Wen-Ming","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}]},{"given":"Hui-Ming","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}]},{"given":"Kai-Ming","family":"Hu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"},{"name":"Department of Mechanical Engineering, University of California Berkeley, Berkeley, CA 94720, USA"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s10409-011-0449-z","article-title":"Size effect on the static behavior of electrostatically actuated microbeams","volume":"27","author":"Yin","year":"2011","journal-title":"Acta Mech. Sin."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6089","DOI":"10.3390\/s130506089","article-title":"A self-sensing piezoelectric microcantilever biosensor for detection of ultrasmall adsorbed masses: Theory and experiments","volume":"13","author":"Faegh","year":"2013","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1038\/nature05741","article-title":"Weighing of biomolecules, single cells and single nanoparticles in fluid","volume":"446","author":"Burg","year":"2007","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/S0022112009993521","article-title":"Energy dissipation in microfluidic beam resonators","volume":"650","author":"Sader","year":"2010","journal-title":"J. Fluid Mech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1021\/ac503845f","article-title":"Label-Free Measurement of Amyloid Elongation by Suspended Microchannel Resonators","volume":"87","author":"Wang","year":"2015","journal-title":"Anal. Chem."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4034","DOI":"10.1002\/jps.24635","article-title":"Determination of the Density of Protein Particles Using a Suspended Microchannel Resonator","volume":"104","author":"Folzer","year":"2015","journal-title":"J. Pharm. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1109\/JMEMS.2014.2376986","article-title":"Two-Photon Polymerization Lithography and Laser Doppler Vibrometry of a SU-8-Based Suspended Microchannel Resonator","volume":"24","author":"Accoto","year":"2015","journal-title":"J. Microelectromech. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1109\/JSEN.2013.2287887","article-title":"Facile Phase Transition Measurements for Nanogram Level Liquid Samples Using Suspended Microchannel Resonators","volume":"14","author":"Minhyuk","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"116106","DOI":"10.1063\/1.4768245","article-title":"Note: precision viscosity measurement using suspended microchannel resonators","volume":"83","author":"Lee","year":"2012","journal-title":"Rev. Sci. Instrum."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.snb.2013.04.095","article-title":"Online measurement of mass density and viscosity of pL fluid samples with suspended microchannel resonator","volume":"185","author":"Khan","year":"2013","journal-title":"Sens. Actuators B Chem."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7650","DOI":"10.3390\/s150407650","article-title":"Highly Sensitive Measurement of Liquid Density in Air Using Suspended Microcapillary Resonators","volume":"15","author":"Malvar","year":"2015","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2698","DOI":"10.1063\/1.1611625","article-title":"Suspended microchannel resonators for biomolecular detection","volume":"83","author":"Burg","year":"2003","journal-title":"Appl. Phys. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"023704","DOI":"10.1063\/1.3534825","article-title":"High precision particle mass sensing using microchannel resonators in the second vibration mode","volume":"82","author":"Lee","year":"2011","journal-title":"Rev. Sci. Instrum."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7070","DOI":"10.1038\/ncomms8070","article-title":"High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions","volume":"6","author":"Olcum","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"228103","DOI":"10.1103\/PhysRevLett.102.228103","article-title":"Nonmonotonic Energy Dissipation in Microfluidic Resonators","volume":"102","author":"Burg","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114507","DOI":"10.1063\/1.3514100","article-title":"Energy dissipation in microfluidic beam resonators: Dependence on mode number","volume":"108","author":"Sader","year":"2010","journal-title":"J. Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"026304","DOI":"10.1103\/PhysRevE.84.026304","article-title":"Energy dissipation in microfluidic beam resonators: Effect of Poisson\u2019s ratio","volume":"84","author":"Sader","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.jsv.2016.01.029","article-title":"Dynamics of suspended microchannel resonators conveying opposite internal fluid flow: Stability, frequency shift and energy dissipation","volume":"368","author":"Zhang","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1088\/0960-1317\/16\/5\/003","article-title":"The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation","volume":"16","author":"Rhoads","year":"2006","journal-title":"J. Micromech. Microeng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mahmoodi, S.N., and Jalili, N. (2008). Coupled flexural-torsional nonlinear vibrations of piezoelectrically actuated microcantilevers with application to friction force microscopy. J. Vib. Acoust., 130.","DOI":"10.1115\/1.2948379"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.ijnonlinmec.2013.04.003","article-title":"The non-linear dynamics of electromagnetically actuated microbeam resonators with purely parametric excitations","volume":"55","author":"Rhoads","year":"2013","journal-title":"Int. J. Nonlinear Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1109\/JMEMS.2006.883568","article-title":"Vacuum-Packaged Suspended Microchannel Resonant Mass Sensor for Biomolecular Detection","volume":"15","author":"Burg","year":"2006","journal-title":"J. Microelectromech. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.sna.2014.04.025","article-title":"Electrostatic pull-in instability in MEMS\/NEMS: A review","volume":"214","author":"Zhang","year":"2014","journal-title":"Sens. Actuator A Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s11071-006-9079-z","article-title":"Dynamic pull-in phenomenon in MEMS resonators","volume":"48","author":"Nayfeh","year":"2007","journal-title":"Nonlinear Dyn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.ijnonlinmec.2012.08.002","article-title":"A comprehensive study of stability in an electro-statically actuated micro-beam","volume":"48","author":"Mobki","year":"2013","journal-title":"Int. J. Nonlinear Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1016\/j.jsv.2008.11.046","article-title":"A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams","volume":"322","author":"Chaterjee","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jabbari, G., Shabani, R., and Rezazadeh, G. (2016). Frequency response of an electrostatically actuated micro resonator in contact with incompressible fluid. Microsyst. Technol.","DOI":"10.1007\/s00542-016-2965-5"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hosseini, I.I., Zand, M.M., and Lotfi, M. (2016). Dynamic pull-in and snap-through behavior in micro\/nano mechanical memories considering squeeze film damping. Microsyst. Technol.","DOI":"10.1007\/s00542-016-3026-9"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2646","DOI":"10.1088\/0960-1317\/16\/12\/018","article-title":"A hybrid full-Lagrangian technique for the static and dynamic analysis of magnetostatic MEMS","volume":"16","author":"Aluru","year":"2006","journal-title":"J. Micromech. Microeng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1109\/JMEMS.2004.835773","article-title":"Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS","volume":"13","author":"De","year":"2004","journal-title":"J. Microelectromech. Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1016\/j.apm.2009.07.013","article-title":"Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method","volume":"34","author":"Mojahedi","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1016\/j.jsv.2009.10.025","article-title":"Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability","volume":"329","author":"Rinaldi","year":"2010","journal-title":"J. Sound Vib."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.ijengsci.2013.06.006","article-title":"Flexural vibrations of microscale pipes conveying fluid by considering the size effects of micro-flow and micro-structure","volume":"71","author":"Wang","year":"2013","journal-title":"Int. J. Eng. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.jsv.2014.12.014","article-title":"Damping analysis of a flexible cantilever beam containing an internal fluid channel: Experiment, modeling and analysis","volume":"340","author":"Wang","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s10404-015-1577-1","article-title":"Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory","volume":"19","author":"Ansari","year":"2015","journal-title":"Microfluid. Nanofluid."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s10404-015-1584-2","article-title":"Stability analysis of a piezoelectrically actuated micro-pipe conveying fluid","volume":"19","author":"Abbasnejad","year":"2015","journal-title":"Microfluid. Nanofluid."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.jfluidstructs.2014.05.014","article-title":"Fluid-dynamic loading of pipes conveying fluid with a laminar mean-flow velocity profile","volume":"50","author":"Kutin","year":"2014","journal-title":"J. Fluid Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1115\/1.4001183","article-title":"Flexural vibration band gap in a periodic fluid-conveying pipe system based on the Timoshenko beam theory","volume":"133","author":"Yu","year":"2011","journal-title":"J. Vib. Acoust."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s10404-014-1407-x","article-title":"Dynamics and pull-in instability of electrostatically actuated microbeams conveying fluid","volume":"18","author":"Dai","year":"2015","journal-title":"Microfluid. Nanofluid."},{"key":"ref_40","unstructured":"Paidoussis, M.P. (1998). Fluid-Structure Interactions: Slender Structures and Axial Flow, Academic Press."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s10404-016-1801-7","article-title":"Dynamical characteristics of fluid-conveying microbeams actuated by electrostatic force","volume":"20","author":"Yan","year":"2016","journal-title":"Microfluid. Nanofluid."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1063\/1.4770321","article-title":"Beam model and three dimensional numerical simulations on suspended microchannel resonators","volume":"2","author":"Huang","year":"2012","journal-title":"AIP Adv."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11071-005-2809-9","article-title":"Reduced-order models for MEMS applications","volume":"41","author":"Nayfeh","year":"2005","journal-title":"Nonlinear Dyn."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.sna.2003.12.012","article-title":"Some design considerations on the electrostatically actuated microstructures","volume":"112","author":"Hu","year":"2004","journal-title":"Sens. Actuator A Phys."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Dohn, S., Svendsen, W., Boisen, A., and Hansen, O. (2007). Mass and position determination of attached particles on cantilever based mass sensors. Rev. Sci. Instrum., 78.","DOI":"10.1063\/1.2804074"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1088\/0960-1317\/12\/6\/306","article-title":"Characterization of the mechanical behavior of an electrically actuated microbeam","volume":"12","author":"Younis","year":"2002","journal-title":"J. Micromech. Microeng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1088\/0960-1317\/19\/3\/035008","article-title":"Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems","volume":"19","author":"Das","year":"2009","journal-title":"J. Micromech. Microeng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/114\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:25:43Z","timestamp":1760207143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/1\/114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,8]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["s17010114"],"URL":"https:\/\/doi.org\/10.3390\/s17010114","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,1,8]]}}}