Size-dependent dynamic pull-in instability of hydrostatically and electrostatically actuated circular microplates

详细信息    查看全文

• 作者：V. Mohammadi (1)
  R. Ansari (1)
  M. Faghih Shojaei (1)
  R. Gholami (1)
  S. Sahmani (1)
  
• 关键词：Micromechanics ; Pull ; in instability ; Strain gradient elasticity theory ; Electrostatic actuation ; Generalized differential quadrature method
• 刊名：Nonlinear Dynamics
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：73
• 期：3
• 页码：1515-1526
• 全文大小：702KB
• 参考文献：1. Saif, M.T.A., Alaca, B.E., Sehitoglu, H.: Analytical modeling of electrostatic membrane actuator micro pumps. J. Microelectromech. Syst. 81, 335-45 (1999) CrossRef
  2. Soleymani, P., Sadeghian, H., Tahmasebi, A., Rezazadeh, G.: Pull-in instability investigation of circular micro pump subjected to nonlinear electrostatic force. Sens. Transducers J. 69, 622-28 (2006)
  3. Sallese, J.M., Grabinski, W., Meyer, V., Bassin, C., Fazan, P.: Electrical modeling of a pressure sensor MOSFET. Sens. Actuators A, Phys. 94, 53-8 (2001) CrossRef
  4. Nabian, A., Rezazadeh, G., Haddad-derafshi, M., Tahmasebi, A.: Mechanical behavior of a circular microplate subjected to uniform hydrostatic and non-uniform electrostatic pressure. J. Microsystems Technol. 14, 235-40 (2008) CrossRef
  5. Bao, M., Wang, W.: Future of microelectromechanical systems (MEMS). Sens. Actuators A, Phys. 56, 135-41 (1996) CrossRef
  6. Younis, M.I., Abdel-Rahman, E.M., Nayfeh, A.: A reduced-order model for electrically actuated microbeam-based MEMS. J. Microelectromech. Syst. 12, 672-80 (2003) CrossRef
  7. Batra, R.C., Porfiri, M., Spinello, D.: Electromechanical model of electrically actuated narrow microbeams. J. Microelectromech. Syst. 15, 1175-189 (2006) CrossRef
  8. Nayfeh, A.H., Younis, M.I., Abdel-Rahman, E.M.: Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dyn. 48, 153-63 (2007) CrossRef
  9. Nayfeh, A.H., Younis, M.I.: Modeling and simulations of thermoelastic damping in microplates. J. Micromech. Microeng. 14, 1711-717 (2004) CrossRef
  10. Zhao, X.P., Abdel-Rahman, E.M., Nayfeh, A.H.: A reduced-order model for electrically actuated microplates. J. Micromech. Microeng. 14, 900-06 (2004) CrossRef
  11. Machauf, A., Nemirovsky, Y., Dinnar, U.: A membrane micropump electrostatically actuated across the working fluid. J. Micromech. Microeng. 15, 2309-316 (2005) CrossRef
  12. Mukherjee, S., Bao, Z.P., Roman, M., Aubry, N.: Nonlinear mechanics of MEMS plates with a total Lagrangian approach. Comput. Struct. 83, 758-68 (2005) CrossRef
  13. Batra, R.C., Porfiri, M., Spinello, D.: Reduced-order models for microelectromechanical rectangular and circular plates incorporating the Casimir force. Int. J. Solids Struct. 45, 3558-583 (2008) CrossRef
  14. Chao, P.C.P., Chiu, C.W., Tsai, C.Y.: A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force. J. Micromech. Microeng. 16, 986-98 (2006) CrossRef
  15. Lam, D.C.C., Chong, A.C.M.: Indentation model and strain gradient plasticity law for glassy polymers. Int. J. Mater. Res. 14, 3784-788 (1999) CrossRef
  16. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477-508 (2003) CrossRef
  17. McFarland, A.W., Colton, J.S.: Role of material microstructure in plate stiffness with relevance to microcantilever sensors. J. Micromech. Microeng. 15, 1060-067 (2005) CrossRef
  18. Nix, W.D.: Mechanical properties of thin films. Metall. Mater. Trans. A, Phys. Metall. Mater. Sci. 20, 2217-245 (1989) CrossRef
  19. Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475-87 (1994) CrossRef
  20. Poole, W.J., Ashby, M.F., Fleck, N.A.: Micro-hardness of annealed and work-hardened copper polycrystals. Scr. Mater. 34, 559-64 (1996) CrossRef
  21. Chasiotis, I., Knauss, W.G.: The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations. J. Mech. Phys. Solids 51, 1551-572 (2003) CrossRef
  22. Aifantis, E.C.: Exploring the applicability of gradient elasticity to certain micro/nano reliability problems, microsystem technologies-micro-and nanosystems. J. Inf. Storage Process. Syst. 15, 109-15 (2009)
  23. Yang, J., Jia, X.L., Kitipornchai, S.: Pull-in instability of nano-switches using nonlocal elasticity theory. J. Phys. D, Appl. Phys. 41, 035103 (2008) CrossRef
  24. Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal. 11, 415-48 (1962) CrossRef
  25. Koiter, W.T.: Couple stresses in the theory of elasticity I and II. Proc. K. Ned. Akad. Wet. 67, 17-4 (1964)
  26. Eringen, A.C., Suhubi, E.S.: Nonlinear theory of simple microelastic solid-I. Int. J. Eng. Sci. 2, 189-03 (1964) CrossRef
  27. Eringen, A.C., Suhubi, E.S.: Nonlinear theory of simple microelastic solid-II. Int. J. Eng. Sci. 2, 389-04 (1964) CrossRef
  28. Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51-8 (1964) CrossRef
  29. Toupin, R.A.: Theory of elasticity with couple stresses. Arch. Ration. Mech. Anal. 17, 85-12 (1964) CrossRef
  30. Mindlin, R.D.: Second gradient of strain and surface tension in linear elasticity. Int. J. Solids Struct. 1, 417-38 (1965) CrossRef
  31. Mindlin, R.D., Eshel, N.N.: On first strain-gradient theories in linear elasticity. Int. J. Solids Struct. 4, 109-24 (1968) CrossRef
  32. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703-710 (1983) CrossRef
  33. Vardoulaksi, I., Exadaktylos, G., Kourkoulis, S.K.: Bending of marble with intrinsic length scales: a gradient theory with surface energy and size effects. J. Phys. IV 8, 399-06 (1998)
  34. Yang, F., Chong, A.C.M., Lam, D.C.C., et al.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731-743 (2002) CrossRef
  35. Tsiatas, G.C.: A new Kirchhoff plate model based on a modified couple stress theory. Int. J. Solids Struct. 46, 2757-764 (2009) CrossRef
  36. Xia, W., Wang, L., Yin, L.: Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration. Int. J. Eng. Sci. 48, 2044-053 (2010) CrossRef
  37. Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T.: The modified couple stress functionally graded Timoshenko beam formulation. Mater. Des. 32, 1435-443 (2011) CrossRef
  38. Ke, L.L., Wang, Y.S.: Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory. Compos. Struct. 93, 342-50 (2011) CrossRef
  39. Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S.: Nonlinear free vibration of size-dependent functionally graded microbeams. Int. J. Eng. Sci. 50, 256-67 (2012) CrossRef
  40. Ke, L.L., Wang, Y.S., Wang, Z.D.: Thermal effect on free vibration and buckling of size-dependent microbeams. Physica E 43, 1387-393 (2011) CrossRef
  41. Fleck, N.A., Hutchinson, J.W.: Phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825-857 (1993) CrossRef
  42. Kong, S.L., Zhou, S.J., Nie, Z.F., Wang, K.: Static and dynamic analysis of microbeams based on strain gradient theory. Int. J. Eng. Sci. 47, 487-98 (2009) CrossRef
  43. Wang, B., Zhao, J., Zhou, S.: A micro scale Timoshenko beam model based on strain gradient elasticity theory. Eur. J. Mech. A, Solids 29, 591-99 (2010) CrossRef
  44. Ansari, R., Gholami, R., Sahmani, S.: Free vibration of size-dependent functionally graded microbeams based on a strain gradient theory. Compos. Struct. 94, 221-28 (2011) CrossRef
  45. Ansari, R., Gholami, R., Sahmani, S.: Study of small scale effects on the nonlinear vibration response of functionally graded Timoshenko microbeams based on the strain gradient theory. ASME J. Comput. Nonlinear Dyn. 7, 031010 (2012) CrossRef
  46. Sahmani, S., Ansari, R.: On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory. Compos. Struct. 95, 430-42 (2013) CrossRef
  47. Ghayesh, M.H., Amabili, M., Farokhi, H.: Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory. Int. J. Eng. Sci. 63, 52-0 (2013) CrossRef
  48. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1970)
  49. Shu, C.: Differential Qquadrature and Its Application in Engineering. Springer, London (2000) CrossRef
  50. Ma, H.M., Gao, X.L., Reddy, J.N.: A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. J. Mech. Phys. Solids 56, 3379-391 (2008) CrossRef
  
• 作者单位：V. Mohammadi (1)
  R. Ansari (1)
  M. Faghih Shojaei (1)
  R. Gholami (1)
  S. Sahmani (1)
  
  1. Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
  

文摘

In the present study, the dynamic pull-in instability and free vibration of circular microplates subjected to combined hydrostatic and electrostatic forces are investigated. To take size effects into account, the strain gradient elasticity theory is incorporated into the Kirchhoff plate theory to develop a nonclassical plate model including three internal material length scale parameters. By using Hamilton’s principle, the higher-order governing equation and the corresponding boundary conditions are obtained. Afterward, a generalized differential quadrature (GDQ) method is employed to discritize the governing differential equations along with simply supported and clamped edge supports. To evaluate the pull-in voltage and vibration frequencies of actuated microplates, the hydrostatic-electrostatic actuation is assumed to be calculated by neglecting the fringing field effects and utilizing the parallel plate approximation. Also, a comparison between the pull-in voltages predicted by the strain gradient theory and the degenerated ones is presented. It is revealed that increasing the dimensionless internal length scale parameter or decreasing the applied hydrostatic pressures leads to higher values of the pull-in voltage. Moreover, it is found that the value of pull-in hydrostatic pressure decreases corresponding to higher dimensionless internal length scale parameters and applied voltages.