Identification of material and geometrical parameters for microstructures by dynamic finite element model updating

This paper describes a procedure to identify material and geometrical parameters for microstructures using the concept of finite element model updating. This scheme utilizes measured and finite element analysis (FEA) natural frequencies that are paired together according to their mode shapes, and it incorporates an optimization sequence that formulates the frequency differences as an error vector to be minimized. To demonstrate the effectiveness of the proposed procedure, two examples are shown in this paper. One example involves a microcantilever fabricated from a single-crystalline silicon wafer, and the updating process is applied on the cantilever to identify its Young’s modulus. The identified Young’s modulus (along <100> direction) of 130.29 GPa is very comparable to those in the literature. The other example concerns a commercial, V-shaped silicon nitride probe used in an atomic force microscope. The natural frequencies and mode shapes of the probe are measured, the FEA performed, and the probe thickness and the Young’s modulus of the silicon nitride substrate determined. The identified thickness is also verified by SEM images of the probe. Both examples show that the updating procedure converged in just a few iterations.