Scale Effect On The Deformation Behavior Of Micro-beam In MEMS

In Micro Electro-Mechanical System (MEMS), when the size of the microstructure decreases to micrometer, its performance of the mechanical and physical properties will show the different characteristics with the bulk material, that is scale effect. The electrostatic driven micro-beam is often used in drivers, so it is significant to analyze the scale effects. This paper primarily analyzes the scale effect of the static analysis and the dynamic analysis of the micro-beam which is actuated by electrostatic force, details are as follows:Firstly, base on the micro-beam pull-effect phenomenon, this paper establishes the mathematical model between the threshold voltage and the critical deflection, then uses the direct coupling method-the TRANS126 reduction unit of the finite element ANSYS to set up the electromechanical coupling model. Meanwhile, obtains how the geometry structure parameters impact upon the micro-beam pull-in effect.Secondly, base on the vibration theory of micro-beam, under the variable load, the paper applies the TRANS126 reduction unit, after many times pilot calculation, gets the convergence points of the voltage and the deflection, and obtains the natural frequency and the pull time of micro-beam. Meanwhile, establishes the quantitative analysis model between the thickness and the natural frequency of intrinsic characteristics length of the micro-beam.At last, this paper establishes a static deformation analysis model of micro-beam deflection based upon the scale effect of the mechanical behavior when the micro-beam dimensions range in micron dimension. Simultaneously, combines bending theory of beam under the action of static electricity with the power series expansion, the Euler's reduction formula and the boundary conditions of the micro-beam proposes a approximation analytical model for the scale effect on the micro-beam deformation, and approximate analytical model of micro-beam under the low-voltage driven is obtained.Base on the results of the models and the ANSYS, it shows that the material and the mechanical properties will reflect the scale effect when the micro-beam structural dimension decreases to which it can compare with characteristic length.