Dynamic and Static Pull-in instability of electrostatically actuated nano/micro membranes under the effects of Casimir force and squeezed film damping

Document Type : Research Paper


Univ of Tehran


In the current study, the effects of Casimir force and squeeze film damping on pull-in instability and dynamic behavior of electrostatically actuated nano and micro electromechanical systems are investigated separately. Linear elastic membrane theory is used to model the static and dynamic behavior of the system for strip, annular and disk geometries. Squeeze film damping is modeled using nonlinear Reynolds equation. Both equation of motion and nonlinear Reynolds equation are first nondimensionalized, and then discretized and solved by means of finite element method. Static pullin analysis is performed and validated by previous researches, and then dynamic pull-in values are investigated and compared with static pull-in parameters. In the next step, the effect of squeeze film damping, ambient pressure and Casimir force on the system dynamics is studied. Results show significant effect of Casimir force and squeeze film damping on the system behavior which is considerable for fabrication and design


Main Subjects

[1] H. C. Nathanson, W. E. Newell, R. A. Wickstrom, J. R. Davis Jr, The resonant gate transistor, Electron Devices, IEEE Transactions on, Vol. 14, No. 3, pp. 117-133, 1967.
[2] G. Taylor, The coalescence of closely spaced drops when they are at different electric potentials, in Proceeding of, The Royal Society, pp. 423-434.
[3] H. Sadeghian, Surface stress effects on the electrostatic pull-in instability of nanomechanical systems, arXiv preprint arXiv:1611.02222, 2016.
[4] M. Weinberg, R. Candler, S. Chandorkar, J. Varsanik, T. Kenny, A. Duwel, Energy loss in MEMS resonators and the impact on inertial and RF devices, Proc. Transducers 2009, pp. 688-695, 2009.
[5] A. K. Pandey, R. Pratap, Effect of flexural modes on squeeze film damping in MEMS cantilever resonators, Journal of Micromechanics and Microengineering, Vol. 17, No. 12, pp. 2475, 2007.
[6] B. McCarthy, G. G. Adams, N. E. McGruer, D. Potter, A dynamic model, including  non-dimension displacement non-dimension time contact bounce, of an electrostatically actuated microswitch, Microelectromechanical Systems, Journal of, Vol. 11, No. 3, pp. 276-283, 2002.
[7] M. I. Younis, Modeling and simulation of microelectromechanical systems in multiphysics fields, Thesis, Citeseer, 2004.
[8] M. I. Younis, A. H. Nayfeh, Simulation of squeeze-film damping of microplates actuated by large electrostatic load, Journal of Computational and Nonlinear Dynamics, Vol. 2, No. 3, pp. 232-241, 2007.
[9] P. Y. Kwok, M. S. Weinberg, K. S. Breuer, Fluid effects in vibrating micromachined structures, Microelectromechanical Systems, Journal of, Vol. 14, No. 4, pp. 770-781, 2005.
[10] D. Yan, A. Lal, The squeeze film damping effect of perforated microscanners: modeling and characterization, Smart materials and structures, Vol. 15, No. 2, pp. 480, 2006.
[11] M. J. Martin, B. H. Houston, J. W. Baldwin, M. K. Zalalutdinov, Damping models for microcantilevers, bridges, and torsional resonators in the free-molecular-flow regime, Microelectromechanical Systems, Journal of, Vol. 17, No. 2, pp. 503-511, 2008.
[12] R. Batra, M. Porfiri, D. Spinello, Effects of Casimir force on pull-in instability in micromembranes, EPL (Europhysics Letters), Vol. 77, No. 2, pp. 20010, 2007.
[13] M. Keivani, J. Khorsandi, J. Mokhtari, A. Kanani, N. Abadian, M. Abadyan, Pull-in instability of paddle-type and double-sided NEMS sensors under the accelerating force, Acta Astronautica, Vol. 119, pp. 196-206, 2016.
[14] W.-H. Lin, Y.-P. Zhao, Nonlinear behavior for nanoscale electrostatic actuators with Casimir force, Chaos, Solitons & Fractals, Vol. 23, No. 5, pp. 1777-1785, 2005.
[15] A. Ramezani, A. Alasty, J. Akbari, Analytical investigation and numerical verification of Casimir effect on electrostatic nanocantilevers, Microsystem Technologies, Vol. 14, No. 2, pp. 145-157, 2008.
[16] G. Xie, J. Ding, S. Liu, W. Xue, J. Luo, Interfacial properties for real rough MEMS/NEMS surfaces by incorporating the electrostatic and Casimir effects–a theoretical study, Surface and Interface Analysis, Vol. 41, No. 4, pp. 338-346, 2009.
[17] Y. T. Beni, A. Koochi, M. Abadyan, Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS, Physica E: Lowdimensional Systems and Nanostructures, Vol. 43, No. 4, pp. 979-988, 2011.
[18] J. Duan, Z. Li, J. Liu, Pull-in instability analyses for NEMS actuators with quartic shape approximation, Applied Mathematics and Mechanics, Vol. 37, No. 3, pp. 303-314, 2016.
[19] Y. Tadi Beni, F. Mehralian, The effect of small scale on the free vibration of
functionally graded truncated conical shells, Journal of Mechanics of Materials and Structures, Vol. 11, No. 2, pp. 91-112, 2016.
[20] Y. G. Wang, H. F. Song, W. H. Lin, Nonlinear Pull-In Characterization of a Nonlocal Nanobeam with an Intermolecular Force, Journal of Mechanics, pp. 1-11, 2016.
[21] A. Kanani, A. Koochi, M. Farahani, E. Rouhic, M. Abadyan, Modeling the size dependent pull-in instability of cantilever nano-switch immersed in ionic liquid electrolytes using strain gradient theory, Scientia Iranica. Transaction B, Mechanical Engineering, Vol. 23, No. 3, pp. 976, 2016.
[22] E. M. Abdel-Rahman, M. I. Younis, A. H. Nayfeh, Characterization of the mechanical behavior of an electrically actuated microbeam, Journal of Micromechanics and Microengineering, Vol. 12, No. 6, pp. 759,
[23] S. Krylov, B. R. Ilic, D. Schreiber, S. Seretensky, H. Craighead, The pull-in behavior of electrostatically actuated bistable microstructures, Journal of Micromechanics and Microengineering, Vol. 18, No. 5, pp. 055026, 2008.
[24] S. Pamidighantam, R. Puers, K. Baert, H. A. Tilmans, Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions, Journal of Micromechanics and Microengineering, Vol. 12, No. 4, pp. 458, 2002.
[25] A. Alipour, M. M. Zand, H. Daneshpajooh, Analytical solution to nonlinear behavior of electrostatically actuated nanobeams incorporating van der Waals and Casimir forces, Scientia Iranica, Vol. 22, No. 3, pp. 1322-1329, 2015.
[26] M. M. Zand, M. Ahmadian, Dynamic pull-in instability of electrostatically actuated beams incorporating Casimir and van der Waals forces, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 224, No. 9, pp. 2037-2047, 2010.
[27] M. M. Zand, M. T. Ahmadian, Application of homotopy analysis method in studying dynamic pull-in instability of microsystems, Mechanics Research Communications, Vol. 36, No. 7, pp. 851-858, 2009.
[28] M. M. Zand, M. Ahmadian, B. Rashidian, Semi-analytic solutions to nonlinear vibrations of microbeams under suddenly applied voltages, Journal of Sound and Vibration, Vol. 325, No. 1, pp. 382-396, 2009.
[29] S. Tajalli, M. M. Zand, M. Ahmadian, Effect of geometric nonlinearity on dynamic pull-in behavior of coupled-domain microstructures based on classical and shear deformation plate theories, European Journal of Mechanics-A/Solids, Vol. 28, No. 5, pp. 916- 925, 2009.
[30] M. M. Zand, M. Ahmadian, Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, pp. 1664-1678, 2009.
[31] S. Saghir, M. I. Younis, Approaches for Reduced-Order Modeling of Electrically Actuated von-Karman Microplates, Journal of Computational and Nonlinear Dynamics, Vol. 12, No. 1, pp. 011011, 2017.
[32] E. Ventsel, T. Krauthammer, 2001, Thin plates and shells: theory: analysis, and applications, CRC press,
[33] T. Veijola, H. Kuisma, J. Lahdenperä, T. Ryhänen, Equivalent-circuit model of the squeezed gas film in a silicon accelerometer, Sensors and Actuators A: Physical, Vol. 48, No. 3, pp. 239-248, 1995.
[34] S. Krylov, R. Maimon, Pull-in dynamics of an elastic beam actuated by continuously distributed electrostatic force, Journal of vibration and acoustics, Vol. 126, No. 3, pp. 332-342, 2004.
Volume 47, Issue 2
December 2016
Pages 219-230
  • Receive Date: 13 August 2016
  • Revise Date: 24 October 2016
  • Accept Date: 02 November 2016