Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam Authors
First Online: 05 December 2008 Received: 06 June 2008 Revised: 09 September 2008 Accepted: 14 October 2008 DOI:
Cite this article as: Fu, Y.M. & Zhang, J. Acta Mech Sin (2009) 25: 211. doi:10.1007/s10409-008-0216-4 Abstract
On the basis of the Euler–Bernoulli hypothesis, nonlinear static and dynamic responses of a viscoelastic microbeam under two kinds of electric forces [a purely direct current (DC) and a combined current composed of a DC and an alternating current] are studied. By using Taylor series expansion, a governing equation of nonlinear integro-differential type is derived, and numerical analyses are performed. When a purely DC is applied, there exist an instantaneous pull-in voltage and a durable pull-in voltage of which the physical meanings are also given, whereas under an applied combined current, the effect of the element relaxation coefficient on the dynamic pull-in phenomenon is observed where the largest Lyapunov exponent is taken as a criterion for the dynamic pull-in instability of viscoelastic microbeams.
Keywords MEMS Viscoelastic microbeam Nonlinear dynamics References
McCarthy B., Adams G.G., McGruer N.E.: A dynamic model, including contact bounce, of an electrostatically actuated microswitch. J. Microelectromech. Syst.
(3), 276–283 (2002)
Zhang W.M., Meng G.: Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitation in MEMS. Sens. Actuators A
, 291–299 (2005)
De S.K., Aluru N.R.: Complex oscillations and chaos in electrostatic microelectromechanical systems under superharmonic excitations. Phys. Rev. Lett.
94(204101), 1–4 (2005)
Xu L., Jia X.: Electromechanical coupled nonlinear dynamics for microbeams. Arch. Appl. Mech.
, 485–502 (2007)
Zhang W.M., Meng G., Chen D.: Stability, nonlinear and reliability of electrostatically actuated MEMS devices. Sensors
, 760–796 (2007)
Osterberg P.M., Senturia S.D.: M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures. J. Microelectromech. Syst.
(2), 107–118 (1997)
Younis M.I., Nayfeh A.H.: A study of nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dyn.
, 91–117 (2003)
Zhang L.X., Zhao Y.P.: Electromechanical model of RF MEMS switches. Microsyst. Technol.
, 420–426 (2003)
Krylov S., Maimon R.: Pull-in dynamics of an elastic beam actuated by continuously distributed electrostatic force. J. Vib. Acoust.
, 332–342 (2004)
Sadeghian H., Rezazadeh G.: The influence of stress gradient on the pull-in phenomena of microelectromechanical switches. J. Phys. Conf. Ser.
, 1117–1122 (2006)
Nayfeh A.H., Younis M.I., Abdel-Rahman E.M.: Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dyn.
, 153–163 (2007)
Batra R.C., Porfiri M., Spinello D.: Vibrations of narrow microbeams predeformed by an electric field. J. Sound Vib.
, 600–612 (2008)
Bethe K., Baumgarten D., Frank J.: Creep of sensor’s elastic elements: metals versus non-metals. Sens. Actuators A
, 844–849 (1990)
Flügge W.: Viscoelasticity, 2nd edn. Springer, New York (1975)
Peng F., Fu Y.M.: Characteristics of creep buckling for viscoelastic laminated plates. Acta Mech. Sin.
35(3), 353–356 (2003) (in Chinese)
Pelesko J.A., Bernstein D.H.: Modeling MEMS and NEMS. Chapman & Hall/CRC, Boca Raton (2003)
Gilat R., Aboudi J.: The Lyapunov exponents as a quantitative criterion for the dynamic buckling of composite plates. Int. J. Solids Struct.
, 467–481 (2002)
Krylov S.: Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures. Int. J. Nonlinear Mech.
, 626–642 (2007)
Goldhirsch I., Sulem P.L., Orszag S.A.: Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method. Physica D
, 311–337 (1987)
MATH CrossRef MathSciNet Copyright information
© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH 2008