Size effect on the static behavior of electrostatically actuated microbeams

2011 ◽  
Vol 27 (3) ◽  
pp. 445-451 ◽  
Author(s):  
Li Yin ◽  
Qin Qian ◽  
Lin Wang
Keyword(s):  
Size Effect ◽  
Static Behavior ◽  
Electrostatically Actuated

Static Analysis of Electrically Actuated Nano to Micron Scale Beams Using Nonlocal Theory

2011 ◽  
Author(s):  
Y. Alizadeh Vaghasloo ◽  
Abdolreza Pasharavesh ◽  
M. T. Ahmadian ◽  
Ali Fallah
Keyword(s):  
Size Effect ◽  
Algebraic Equation ◽  
Bending Moment ◽  
Nonlocal Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Beam Deflection ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Electrically Actuated ◽  
The One

In this paper, size dependent static behavior of micro and nano cantilevers actuated by a static electric field including deflection and pull-in instability, is analyzed implementing nonlocal theory. Euler-bernoulli assumptions are made to model the relation between deflection of the beam and bending moment. Differential form of the constitutive equation of nonlocal theory is used to find the revised equation for bending moment and substituting in the equilibrium equation of electrostatically actuated beams final nonlinear ordinary differential equation is arrived. Also the boundary conditions for solving the equation are revised and to analyze the size effect better governing equation is nondimetionalized. The one parameter Galerkin method is used to transform this equation to a nonlinear algebraic equation. Arrived algebraic equation is solved utilizing Newton-Raphson method. Size effect on the maximum deflection and deflection shape for various applied voltages is studied. Also effect of beam size on the static pull-in voltage is studied. Results indicate that the dimensionless beam deflection decreases as size decreases while the pull-in voltage increases and specially change of deflection and pull-in voltage is significant for nanobeams.

Static Deflection and Pull-In Instability of the Electrostatically Actuated Bilayer Microcantilever Beams

2015 ◽  
Vol 07 (06) ◽  
pp. 1550090 ◽  
Author(s):  
M. Mojahedi ◽  
M. Rahaeifard
Keyword(s):  
Scale Parameter ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Static Deflection ◽  
Static Behavior ◽  
Stress Theory ◽  
Electrostatically Actuated

This paper deals with the static behavior of an electrostatically actuated bilayered microswitch on the basis of the modified couple stress theory. The beam is modeled using Euler–Bernoulli beam theory and equivalent elastic modulus and length scale parameter are presented for the bilayer beam. Static deflection and pull-in voltage of the beam is calculated using numerical and analytical methods. The numerical method is based on an iterative approach while the homotopy perturbation method (HPM) is utilized for the analytical simulation. Results show that there is a very good agreement between these methods even in the vicinity of the pull-in instability. Moreover, the effects of different parameters such as thicknesses of layers and length scale parameter on the static deflection and instability of the microcantilever are studied. Results show that for the cases with the equivalent length scale parameter comparable to the thickness of beam, the size-dependency plays significant roles in the static behavior of the bilayer microcantilevers.

Characterization of Static Behavior of a Nonlinear Doubly Clamped Microbeam Under Electrostatic Actuation and Detection

2013 ◽  
Author(s):  
Mohammad Taghi Ahmadian ◽  
Mahdi Mojahedi ◽  
Ahmad Barari ◽  
Keikhosrow Firoozbakhsh
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Static Deflection ◽  
Static Response ◽  
Electrostatic Forces ◽  
Static Behavior ◽  
Dc Voltage ◽  
Electrostatically Actuated ◽  
Fringing Fields

In this study, the static deflection and pull-in instability of the doubly clamped microbeam with a mass attached to its midpoint are investigated. Nonlinear electrostatic forces, fringing fields, base rotation and mid-plane stretching of the beam in this model are considered. First, a system of two nonlinear integro-differential equations are expressed in partial derivatives which describe coupled flexural-flexural motion of electrostatically actuated microbeam gyroscopes under rotation. Then static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (direction and sensing) directions are studied. The equations of static motion are reduced by Galerkin’s decomposition method. The static response of the microgyroscope to variations in the DC voltage across the drive and sense electrodes is obtained.

Size Effect on Pull-In Behaviors of Electrostatically Actuated Cantilever Micro-Beams

2013 ◽  
Vol 300-301 ◽  
pp. 889-892
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Deformation Problem ◽  
Approximate Analytical Solutions ◽  
Modified Couple Stress

For the deformation problem of an electrostatically actuated cantilever micro-beam, size effect on pull-in behaviors of the micro-beams have been studied based on modified couple stress theory. The approximate analytical solutions to the pull-in voltage and pull-in displacement of the micro-beam are derived by using the Rayleigh-Ritz method. The results show that the normalized pull-in voltage of the cantilever micro-beam is size-dependent and the normalized pull-in displacement of the micro-beam is size independence.

Characterization of Static Behavior of Electrostatically Actuated Micro Tweezers Using Modified Couple Stress Theory

2012 ◽  
Author(s):  
Ali Darvishian ◽  
Hamid Moeenfard ◽  
Nasser Ghaderi ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Theory Of Elasticity ◽  
Static Behavior ◽  
Design Synthesis ◽  
Stress Theory ◽  
Electrostatically Actuated ◽  
Modified Couple Stress

In this paper, static behavior and pull-in of micro tweezers is studied. The micro tweezer is modelled as two cantilever beams. Static behavior of the micro tweezer under the effect of electrostatic actuation is modelled using the Euler-Bernoulli beam theory. In order to capture size effects on the behavior of micro tweezers, modified couple stress theory is utilized. It is shown when the voltage between two electrodes increased from some specific value, micro beams adhere to each other and it is observed that the pull-in voltage predicted by the modified couple stress theory considerably differs with that of the classical theory of elasticity. Results of this paper can be used for accurate design, synthesis and optimization of micro tweezers.

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