Generalized closed-form models for pull-in analysis of micro cantilever beams subjected to partial electrostatic load

This work presents a new approach for the pull-in analysis of micro cantilever beams subjected to partial electrostatic actuation. A novel generalized closed-form models for the pull-in instability position and pull-in voltage of a cantilever beam with partial overlap of the beam and fixed actuation electrode is developed. The model benefits from including the effect of non-uniform loading and the fringing field effect into consideration, therefore, no correction factor is required. The accuracy of the model is validated through comparison with Finite Element Method (FEM) simulation results and correlation to within 6.6% error is obtained. The model is also validated against other existing empirical and analytical models and is demonstrated to be of equal accuracy with a more generalized model framework.

► Error of uniform load analysis is highest at full electrode.
► Pull-in position varies with electrode length, from 0.33 to 0.44.
► Generalized closed-form model is derived including non-uniform load.
► The method is applicable to other structures with known shape function.
► Simpler than the energy principle method with similar accuracy.