MODELING THE SIZE DEPENDENT STATIC AND DYNAMIC PULL-IN INSTABILITY OF CANTILEVER NANOACTUATOR BASED ON STRAIN GRADIENT THEORY

It is well-established that mechanical behavior of nanoscale systems is size dependent. In this paper, strain gradient elasticity theory is used for mathematical modeling of size dependent electromechanical instability of cantilever nanoactuator. The nanoactuator is modeled using Euler–Bernoulli beam theory and equation of motion is derived using Hamilton's principle. In order to solve the nonlinear governing equation, reduced order method (ROM) is employed. The dynamic pull-in instability of the nanoactuator is investigated through plotting the time history and phase portrait of the system. Static and dynamic pull-in voltage of nanoactuator as a function of dimensionless length scale parameters is determined. The obtained results show that when thickness of the nanoactuator is comparable with the intrinsic material length scales, size effect can substantially influence the pull-in behavior of the system.

[1]  M. Abadyan,et al.  Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method , 2010 .

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

[3]  Xiangshan Chen,et al.  PULL-IN INSTABILITY OF CIRCULAR PLATE MEMS: A NEW MODEL BASED ON STRAIN GRADIENT ELASTICITY THEORY , 2012 .

[4]  Martin W. Knecht,et al.  Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers , 2013 .

[5]  H. Haddadpour,et al.  Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators , 2010 .

[6]  W. Lin,et al.  Casimir effect on the pull-in parameters of nanometer switches , 2005 .

[7]  Romesh C. Batra,et al.  Symmetry breaking, snap-through and pull-in instabilities under dynamic loading of microelectromechanical shallow arches , 2009 .

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

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

[10]  M. Ghalambaz,et al.  Influence of size effect and elastic boundary condition on the pull-in instability of nano-scale cantilever beams immersed in liquid electrolytes , 2013 .

[11]  M. Abadyan,et al.  Investigation of Size Effect on the Pull-in Instability of Beam-type NEMS under van der Waals Attraction , 2011 .

[12]  Shenjie Zhou,et al.  Pull-in instability analysis of electrostatically actuated microplate with rectangular shape , 2011 .

[13]  Ling Wen-hui,et al.  Dynamic Behaviour of Nanoscale Electrostatic Actuators , 2003 .

[14]  H. Sedighi,et al.  Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method , 2013 .

[15]  Mohammad Taghi Ahmadian,et al.  Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method , 2010 .

[17]  Jun Wang,et al.  Modeling the size-dependent elastic properties of polymeric nanofibers , 2008, Nanotechnology.

[18]  Mahdi Moghimi Zand,et al.  Effect of geometric nonlinearity on dynamic pull-in behavior of coupled-domain microstructures based on classical and shear deformation plate theories , 2009 .

[19]  R. Ansari,et al.  Size-Dependent Pull-In Instability of Hydrostatically and Electrostatically Actuated Circular Microplates , 2013 .

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

[21]  Alberto Corigliano,et al.  A PLATE MODEL FOR THE EVALUATION OF PULL-IN INSTABILITY OCCURRENCE IN ELECTROSTATIC MICROPUMP DIAPHRAGMS , 2011 .

[22]  M. Abadyan,et al.  Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS , 2011 .

[23]  Abbas S. Milani,et al.  Analytical closed-form solutions for size-dependent static pull-in behavior in electrostatic micro-actuators via Fredholm integral equation , 2013 .

[24]  Jian-Gang Guo,et al.  Influence of van der Waals and Casimir forces on electrostatic torsional actuators , 2004 .

[25]  Ya-Pu Zhao,et al.  Nonlinear behavior for nanoscale electrostatic actuators with Casimir force , 2005 .

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

[27]  Norman A. Fleck,et al.  A reformulation of strain gradient plasticity , 2001 .

[28]  N. Aluru,et al.  Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches , 2002 .

[29]  M. Pashaei,et al.  STUDY THE BEHAVIOR OF AN ELECTRICALLY EXCITING NANOTUBE USING OPTIMAL HOMOTOPY ASYMPTOTIC METHOD , 2012 .

[30]  M. Abadyan,et al.  APPROXIMATING THE EFFECT OF VAN DER WAALS FORCE ON THE INSTABILITY OF ELECTROSTATIC NANO-CANTILEVERS , 2011 .

[31]  F. Rajabi,et al.  A Nonlinear Microbeam Model Based on Strain Gradient Elasticity Theory , 2013 .

[32]  M. Ahmadian,et al.  DYNAMIC PULL-IN INSTABILITY AND VIBRATION ANALYSIS OF A NONLINEAR MICROCANTILEVER GYROSCOPE UNDER STEP VOLTAGE CONSIDERING SQUEEZE FILM DAMPING , 2013 .

[33]  Pradeep Sharma,et al.  A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies , 2007 .

[34]  H. Sedighi.  THE INFLUENCE OF SMALL SCALE ON THE PULL-IN BEHAVIOR OF NONLOCAL NANOBRIDGES CONSIDERING SURFACE EFFECT, CASIMIR AND VAN DER WAALS ATTRACTIONS , 2014 .

[35]  Randolph Rach,et al.  Modeling the pull-in instability of the CNT-based probe/actuator under the Coulomb force and the van der Waals attraction , 2014 .

[36]  Mohamadreza Abadyan,et al.  Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory , 2011 .

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

[38]  Jian-Gang Guo,et al.  Dynamic stability of electrostatic torsional actuators with van der Waals effect , 2006 .

[39]  Shenjie Zhou,et al.  Size-dependent pull-in instability of electrostatically actuated microbeam-based MEMS , 2011 .

[40]  U. Ejike.  The plane circular crack problem in the linearized couple-stress theory , 1969 .

[41]  A. Eringen,et al.  On nonlocal elasticity , 1972 .

[42]  G. J. Delben,et al.  Influence of the Casimir force on the pull-in parameters of silicon based electrostatic torsional actuators , 2007 .

[43]  M. Porfiri,et al.  Review of modeling electrostatically actuated microelectromechanical systems , 2007 .