Discrete and continuous mathematical models for torsional vibration of micromechanical scanners

Abstract

Micromechanical scanners are used in various industrial scanning applications like. display and imaging technologies. The desired vibration mode is often the torsional mode, so derivation of an accurate mathematical model for calculation of torsional mode frequency has great importance. In this work, discrete and continuous mathematical models are given for free torsional vibration of a box shaped scanner suspended with two beams. Numerical calculation of torsional rigidity using energy methods is shown. The derivations are extendible to scanners that have non-rectangular beam cross-sections, orthotropic material anisotropy, and different mirror geometries. Analytical formulas are compared with three-dimensional FEM simulations using ANSYS commercial software. The FEM simulations and analytical formulas are verified with experimental results. FEM simulations and experimental results showed that simple discrete models can be used for a wide range of beam dimensions except for the cases where beam inertia is comparable to mirror inertia.