The Timoshenko Beam Theory based Spectral Finite Element to Analyse Effects of Shear Deformation on Electrostatically Actuated Narrow Thick Clamped Microbeams

Abstract MEMS devices utilize electrostatics as preferred actuation method. The accurate determination of pull-in instability parameters (i.e., the pull-in voltage and pull-in displacement) of such devices is critical for their correct design. In the literature, these devices have been majorly analyzed as Bernoulli-Euler microbeams. However, Dileesh et al. (doi: 10.1115/ESDA2012-82536) have studied the pull-in instability behavior of thin microcantilevers by developing a six-nodded Timoshenko beam theory based spectral finite element (TBT-SFE). They have demonstrated the effectiveness of the TBT-SFE by comparing their results with corresponding results of COMSOL-based three-dimensional finite element simulations. In addition, effects of shear deformation also start to play significant role as the beam’s slenderness decreases. In this paper, authors have developed the TBT-SFE based on the work by Dileesh et al. for the case of statics. However, unlike Dileesh et al. where they have developed a six-nodded TBT-SFE, authors have investigated the best combination of number of nodes per element and total number of elements to carry out the proposed study. This finalized TBT-SFE is then utilized to determine static pull-in instability parameters of narrow clamped microbeams with various beam thickness-to-length ratios. This study highlights the importance of transverse shear effects on pull-in instability parameters of Timoshenko microbeams.