Measurements and Simulation of the Dynamic Characteristics of Micro-Machined Torsion Mirrors

A cross-shaped torsion mirror, fabricated by a micro-machining process, was analyzed by finite element analysis with ANSYS and COMSOL software packages. The micro-structure's resonance frequencies and mode shapes were also measured by using the Electronic Speckle Pattern Interferometry and Stroboscopic Interferometry techniques, which both are full-field and non-contact experimental procedures. Four sets of modal data, two from FE analysis and two from experiments, were compared and shown having a significant discrepancy in their frequency values, although their mode shapes were quite consistent. Inconsistency in the frequency results due to erroneous inputs that included geometrical and material parameters to the FE analysis could be salvaged by applying the finite element model updating procedure. When administrating the updating technique, the number of updating parameters should be kept small and only the uncertain ones should be selected as the updating parameters. Such a parameter that was mostly doubtful as the depth dimension of a micro-structure should definitely be included in the optimization process. Two updating cases showed that the optimization sequence converged rather quickly for both cases and significant improvements in frequency prediction were achieved. With the inclusion of the thickness parameter, the second case yielded frequency differences under 5% in all three modes, and its all three updating parameters attained final updated values that were much more reliable.