Nonlinear pull-in instability and free vibration of micro/nanoscale plates with surface energy - A modified couple stress theory model

Abstract Effects of surface energy on the pull-in instability and free vibration of electrostatically actuated micro/nanoscale plates are analyzed based on the modified couple stress theory. A reduced-order model is derived to consider the geometrically nonlinear strain, surface energy, the Casimir force and the material length scale simultaneously. Results show that the pull-in voltage and fundamental frequency of the plate are considerably enhanced by the material length scale, surface energy and geometrically nonlinear deformation. However, these quantities are weakened with the inclusion of Casimir force. The effects of surface energy and the material length scale become more significant if the thickness decreases. In addition, the effects of surface energy and geometrically nonlinear strain on the pull-in voltage are the largest for a square plate.

[1]  Jin He,et al.  Surface effect on the elastic behavior of static bending nanowires. , 2008, Nano letters.

[2]  F. F. Mahmoud,et al.  Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects , 2014 .

[3]  F. F. Mahmoud,et al.  Bending analysis of ultra-thin functionally graded Mindlin plates incorporating surface energy effects , 2013 .

[4]  David Elata,et al.  An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices , 2002 .

[5]  J. Pelesko,et al.  Modeling MEMS and NEMS , 2002 .

[6]  K. Minoshima,et al.  Size effect on fracture toughness of freestanding copper nano-films , 2011 .

[7]  Mohamadreza Abadyan,et al.  Influence of surface effects on size-dependent instability of nano-actuators in the presence of quantum vacuum fluctuations , 2012 .

[8]  F. F. Mahmoud,et al.  A new Bernoulli–Euler beam model incorporating microstructure and surface energy effects , 2014 .

[9]  Jin He,et al.  Surface stress effect on bending resonance of nanowires with different boundary conditions , 2008 .

[10]  Yael Nemirovsky,et al.  A membrane micropump electrostatically actuated across the working fluid , 2005 .

[11]  Daolin Xu,et al.  Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Davide Spinello,et al.  Vibrations and pull-in instabilities of microelectromechanical von Kármán elliptic plates incorporating the Casimir force , 2008 .

[13]  M. Shaat,et al.  Pull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force , 2015 .

[14]  Ali H. Nayfeh,et al.  A reduced-order model for electrically actuated clamped circular plates , 2005 .

[15]  Sritawat Kitipornchai,et al.  Electro-dynamic behavior of an electrically actuated micro-beam: Effects of initial curvature and nonlinear deformation , 2012 .

[16]  Mohsen Asghari,et al.  Geometrically nonlinear micro-plate formulation based on the modified couple stress theory , 2012 .

[17]  M. Shaat,et al.  Modeling of mechanical resonators used for nanocrystalline materials characterization and disease diagnosis of HIVs , 2016 .

[18]  B. Zhang,et al.  Anomalous plasticity in the cyclic torsion of micron scale metallic wires. , 2013, Physical review letters.

[19]  H. Tilmans,et al.  Electrostatically driven vacuum-encapsulated polysilicon resonators part II. theory and performance , 1994 .

[20]  T. Kitamura,et al.  Applicability of Fracture Mechanics on Brittle Delamination of Nanoscale Film Edge , 2004 .

[21]  Xi-Qiao Feng,et al.  Effects of surface elasticity and residual surface tension on the natural frequency of microbeams , 2007 .

[22]  S. Mukherjee,et al.  Nonlinear mechanics of MEMS plates with a total Lagrangian approach , 2005 .

[23]  Davide Spinello,et al.  REDUCED-ORDER MODELS FOR MICROELECTROMECHANICAL RECTANGULAR AND CIRCULAR PLATES INCORPORATING THE CASIMIR FORCE , 2008 .

[24]  P. Tong,et al.  Couple stress based strain gradient theory for elasticity , 2002 .

[25]  C. Ru.  Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions , 2010 .

[26]  Jorge P. Arenas,et al.  On the vibration analysis of rectangular clamped plates using the virtual work principle , 2003 .

[27]  Behrooz Farshi,et al.  Size dependent dynamic analysis of nanoplates , 2010 .

[28]  Xi-Qiao Feng,et al.  Surface effects on buckling of nanowires under uniaxial compression , 2009 .

[29]  E. S. Hung,et al.  Extending the travel range of analog-tuned electrostatic actuators , 1999 .

[30]  R. Ansari,et al.  Surface stress effects on the free vibration behavior of nanoplates , 2011 .

[31]  Ali H. Nayfeh,et al.  A reduced-order model for electrically actuated microbeam-based MEMS , 2003 .

[32]  M. Gad-el-Hak.  Design and Fabrication , 2001 .

[33]  Mohammad Taghi Ahmadian,et al.  Static pull-in analysis of microcantilevers based on the modified couple stress theory , 2011 .

[34]  Mostafa Baghani,et al.  Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory , 2012 .

[35]  A. Alasty,et al.  Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces , 2007 .

[36]  Casimir effect for a sphere and a cylinder in front of a plane and corrections to the proximity force theorem , 2006, hep-th/0602295.

[37]  Huu-Tai Thai,et al.  SIZE-DEPENDENT FUNCTIONALLY GRADED KIRCHHOFF AND MINDLIN PLATE MODELS BASED ON A MODIFIED COUPLE STRESS THEORY , 2013 .

[38]  R. Ansari,et al.  A geometrically non-linear plate model including surface stress effect for the pull-in instability analysis of rectangular nanoplates under hydrostatic and electrostatic actuations , 2014 .

[39]  Vijay B. Shenoy,et al.  Atomistic calculations of elastic properties of metallic fcc crystal surfaces , 2005 .

[40]  Anthony G. Evans,et al.  A microbend test method for measuring the plasticity length scale , 1998 .

[41]  Ali H. Nayfeh,et al.  Dynamic pull-in phenomenon in MEMS resonators , 2007 .

[43]  Ali H. Nayfeh,et al.  Modeling and simulations of thermoelastic damping in microplates , 2004 .

[44]  Baolin Wang,et al.  Influence of surface energy on the non-linear pull-in instability of nano-switches , 2014 .

[45]  Morton E. Gurtin,et al.  A continuum theory of elastic material surfaces , 1975 .

[46]  H. Gies,et al.  Casimir effect for curved geometries: proximity-force-approximation validity limits. , 2006, Physical review letters.

[47]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[48]  M. Shaat,et al.  Nonlinear-electrostatic analysis of micro-actuated beams based on couple stress and surface elasticity theories , 2014 .

[49]  F. F. Mahmoud,et al.  Static analysis of nanobeams including surface effects by nonlocal finite element , 2012 .

[50]  Fan Yang,et al.  Experiments and theory in strain gradient elasticity , 2003 .

[51]  M. Ghayesh,et al.  Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory , 2015 .

[52]  Andrew W. Mcfarland,et al.  Role of material microstructure in plate stiffness with relevance to microcantilever sensors , 2005 .

[53]  Paul C.-P. Chao,et al.  A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force , 2006 .

[54]  A. Nayfeh,et al.  Institute of Physics Publishing Journal of Micromechanics and Microengineering a Reduced-order Model for Electrically Actuated Microplates , 2022 .

[55]  H. P. Lee,et al.  Nonlinear Dynamic Analysis of MEMS Switches by Nonlinear Modal Analysis , 2003 .

[56]  H. Tilmans,et al.  Electrostatically driven vacuum-encapsulated polysilicon resonators Part I. Design and fabrication , 1994 .

[57]  Horacio D. Espinosa,et al.  Numerical Analysis of Nanotube Based NEMS Devices — Part II: Role of Finite Kinematics, Stretching and Charge Concentrations , 2005 .

[58]  M. Porfiri,et al.  Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates , 2008, Sensors.

[59]  S. Asokanthan,et al.  Influence of surface effects on the pull-in instability of NEMS electrostatic switches , 2010, Nanotechnology.

[60]  Behrooz Farshi,et al.  Vibration characteristics of circular nanoplates , 2010 .

[61]  Lin Wang,et al.  Size effect on the static behavior of electrostatically actuated microbeams , 2011 .