Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Acta Mechanica Sinica
Erschienen in: Acta Mechanica Sinica 1/2019

28.08.2018 | Research Paper

Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method

verfasst von: Milad Saadatmand, Alireza Shooshtari

Erschienen in: Acta Mechanica Sinica | Ausgabe 1/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Kármán plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlinear frequency response (F–R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases: (1) semi-linear vibration; (2) weakly nonlinear vibration; (3) highly nonlinear vibration, are validated by comparing with the numerical solutions. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano/microelectromechanical transducers such as microphones and pressure sensors.
Vorheriger Artikel A three-parameter single-step time integration method for structural dynamic analysis
Nächster Artikel Numerical and experimental analysis of the closed-cell aluminium foam under low velocity impact using computerized tomography technique

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Younis, M.I.: MEMS Linear and Nonlinear Statics and Dynamics. Springer, New York (2011)CrossRef
2.
Jia, X., Yang, J., Kitipornchai, S., et al.: Resonance frequency response of geometrically nonlinear micro-switches under electrical actuation. J. Sound Vib. 331, 3397–3411 (2012)CrossRef
3.
Han, J., Zhang, Q., Wang, W.: Static bifurcation and primary resonance analysis of a MEMS resonator actuated by two symmetrical electrodes. Nonlinear Dyn. 80, 1585–1599 (2015)CrossRef
4.
Zhang, Y., Zhao, Y.P.: Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading. Sens. Actuators A 127, 366–380 (2006)CrossRef
5.
Faris, W.F.: Nonlinear Dynamics of Annular and Circular Plates Under Thermal and Electrical Loadings. Virginia Tech, Blacksburg (2003)
6.
Saeedivahdat, A., Abdolkarimzadeh, F., Feyzi, A., et al.: Effect of thermal stresses on stability and frequency response of a capacitive microphone. Microelectron. J. 41, 865–873 (2010)CrossRef
7.
Talebian, S., Rezazadeh, G., Fathalilou, M., et al.: Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate. Mechatronics 20, 666–673 (2010)CrossRef
8.
Vogl, G.W., Nayfeh, A.H.: Primary resonance excitation of electrically actuated clamped circular plates. Nonlinear Dyn. 47, 181–192 (2007)CrossRefMATH
9.
Saghir, S., Younis, M.I.: An investigation of the static and dynamic behavior of electrically actuated rectangular microplates. Int. J. Nonlinear Mech. 85, 81–93 (2016)CrossRef
10.
Batra, R., Porfiri, M., Spinello, D.: Vibrations and pull-in instabilities of microelectromechanical von Kármán elliptic plates incorporating the Casimir force. J. Sound Vib. 315, 939–960 (2008)CrossRef
11.
Rombach, P., Müllenborn, M., Klein, U., et al.: The first low voltage, low noise differential silicon microphone, technology development and measurement results. Sens. Actuators A 95, 196–201 (2002)CrossRef
12.
Martin, D.T.: Design, Fabrication, and Characterization of a MEMS Dual-Backplate Capacitive Microphone. University of Florida, Gainesville (2007)
13.
Liu, J.: Nonlinear Dynamics of a Dual-Backplate Capacitive MEMS Microphone. University of Florida, Gainesville (2007)
14.
Mann, B.P., Liu, J., Hazra, S.: Correcting measurement nonlinearity in dynamic nanoindentation. In: ASME 2006 International Mechanical Engineering Congress and Exposition. 2006. American Society of Mechanical Engineers
15.
Batra, R., Porfiri, M., Spinello, D.: Reduced-order models for microelectromechanical rectangular and circular plates incorporating the Casimir force. Int. J. Solids Struct. 45, 3558–3583 (2008)CrossRefMATH
16.
Wang, Y.G., Lin, W.H., Li, X.M., et al.: Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force. Appl. Math. Modell. 35, 2348–2357 (2011)MathSciNetCrossRefMATH
17.
Kermani, M.M., Dehestani, M.: Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force. Acta Mech. Sin. 34, 528–541 (2018)MathSciNetCrossRefMATH
18.
Kim, N., Aluru, N.: Effect of intermolecular force on the static/dynamic behaviour of M/NEM devices. Nanotechnology 25, 485204 (2014)CrossRef
19.
Klimchitskaya, G., Mohideen, U., Mostepanenko, V.: Casimir and van der Waals forces between two plates or a sphere (lens) above a plate made of real metals. Phys. Rev. A: At. Mol. Opt. Phys. 61, 062107 (2000)CrossRef
20.
Caruntu, D.I., Oyervides, R.: Frequency response reduced order model of primary resonance of electrostatically actuated MEMS circular plate resonators. Commun. Nonlinear Sci. Numer. Simul. 43, 261–270 (2017)CrossRef
21.
Khodaparast, H.H., Madinei, H., Friswell, M.I., et al.: An extended harmonic balance method based on incremental nonlinear control parameters. Mech. Syst. Sig. Process. 85, 716–729 (2017)CrossRef
22.
Liang, B., Zhang, L., Wang, B., et al.: A variational size-dependent model for electrostatically actuated NEMS incorporating nonlinearities and Casimir force. Physica E 71, 21–30 (2015)CrossRef
23.
Peng, Z.K., Meng, G., Lang, Z.Q., et al.: Study of the effects of cubic nonlinear damping on vibration isolations using harmonic balance method. Int. J. Nonlinear Mech. 47, 1073–1080 (2012)CrossRef
24.
Vogl, G.W.: Nonlinear Dynamics of Circular Plates Under Electrical Loadings for Capacitive Micromachined Ultrasonic Transducers (CMUTs). Virginia Tech, Blacksburg (2006)
25.
Osterberg, P.M., Senturia, S.D.: M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures. J. Microelectromech. Syst. 6, 107–118 (1997)CrossRef
26.
Zhao, X., Abdel-Rahman, E.M., Nayfeh, A.H.: A reduced-order model for electrically actuated microplates. J. Micromech. Microeng. 14, 900–906 (2004)CrossRef
27.
Zhang, Y.: Large deflection of clamped circular plate and accuracy of its approximate analytical solutions. Sci. China Phys. Mech. 59, 624602 (2016)CrossRef
28.
Liu, J., Martin, D.T., Kadirvel, K., et al.: Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone. J. Sound Vib. 309, 276–292 (2008)CrossRef
29.
Liu, J., Martin, D.T., Nishida, T., et al.: Harmonic balance nonlinear identification of a capacitive dual-backplate MEMS microphone. J. Microelectromech. Syst. 17, 698–708 (2008)CrossRef
30.
Fang, F., Xia, G., Wang, J.: Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations. Acta Mech. Sin. 34, 561–577 (2018)MathSciNetCrossRefMATH
31.
Firouzi, B., Zamanian, M., Hosseini, S.A.A.: Static and dynamic responses of a microcantilever with a T-shaped tip mass to an electrostatic actuation. Acta. Mech. Sin. 32, 1104–1122 (2016)MathSciNetCrossRefMATH
32.
Caruntu, D.I., Oyervides, R.: Voltage response of primary resonance of electrostatically actuated MEMS clamped circular plate resonators. J. Comput. Nonlinear Dyn. 11, 041021 (2016)CrossRef
33.
Sheikhlou, M., Shabani, R., Rezazadeh, G.: Nonlinear analysis of electrostatically actuated diaphragm-type micropumps. Nonlinear Dyn. 83, 951–961 (2016)MathSciNetCrossRefMATH
34.
Li, Z.K., Zhao, L.B., Jiang, Z.D., et al.: Mechanical behavior analysis on electrostatically actuated rectangular microplates. J. Micromech. Microeng. 25, 035007 (2015)CrossRef
35.
Nayfeh, A.H., Pai, P.F.: Linear and Nonlinear Structural Mechanics. Wiley, London (2008)MATH
36.
Chia, C.Y.: Nonlinear Analysis of Plates. McGraw-Hill, New York (1980)
37.
38.
Nayfeh, A.H., Lacarbonara, W.: On the discretization of distributed-parameter systems with quadratic and cubic nonlinearities. Nonlinear Dyn. 13, 203–220 (1997)MathSciNetCrossRefMATH
39.
Batra, R.C., Porfiri, M., Spinello, D.: Vibrations of narrow microbeams predeformed by an electric field. J. Sound Vib. 309, 600–612 (2008)CrossRef
40.
Kacem, N., Hentz, S., Pinto, D., et al.: Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors. Nanotechnology 20, 275501 (2009)CrossRef
41.
Meirovitch, L.: Fundamentals of Vibrations. Waveland Press, New York (2010)
Metadaten
Titel
Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method
verfasst von
Milad Saadatmand
Alireza Shooshtari
Publikationsdatum
28.08.2018
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 1/2019
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-018-0794-8

Weitere Artikel der Ausgabe 1/2019

Acta Mechanica Sinica 1/2019 Zur Ausgabe

Research Paper

Mechanism of wavy vortex and sign laws in flow past a bluff body: vortex-induced vortex

Research Paper

Numerical and experimental analysis of the closed-cell aluminium foam under low velocity impact using computerized tomography technique

Research Paper

Damage and fracture model for eutectic composite ceramics

Research Paper

Mechanical properties of 65Mn chiral structure with three ligaments

Research Paper

Effects of aspect ratio on shock-cylinder interaction

Research Paper

An R(x)-orthonormal theory for the vibration performance of a non-smooth symmetric composite beam with complex interface

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise