Electrothermomechanical modeling of out-of-plane deformation in single-stepped beams actuated by resistive heating

Abstract

An analytical model for the electrothermomechanical analysis of out-of-plane deformation in resistively heated single-stepped beams is presented. The model takes into account the conductive heat transfer from the beam to the substrate in which it is anchored. It also considers the temperature dependence of the beam material properties and accounts for the locally enhanced resistive heating effect around the release holes in the beam to predict temperature distribution along the beam. Energy method and Euler–Bernoulli beam theory are used for the prediction of out-of-plane deformation and stress distribution of the beam, as well as the out-of-plane rotation at the middle of the beam. The model considers the nonuniformity of the air gap between the beam and the substrate and captures the resultant asymmetric temperature distribution along the beam. The out-of-plane rotations in the middle of the single-stepped beam predicted by the analytical model and measured experimentally agree within 10%. The analytical model is then used to predict the maximum actuation current, which results in high temperature plastic deformation and agrees with the experiments within 5%. The proposed analytical model provides a good approach for systematic design and analysis of out-of-plane electrothermal microactuators based on single-stepped beam design.