Model updating of microsystems using test data

Abstract

In modern electronics technology, the rapid advances of microsystems present an imperative requirement in the modeling and the testing of their dynamic characteristics. Due to particular sophistication of microsystems in design and fabrication, finite element (FE) method has limitations to produce accurate mathematical models for microsystems. To obtain a credible analytical model of a microsystem, model updating is employed as an effective approach for improving the FE model using vibration test data. Considering particular testing techniques and damped microstructures of microsystems, this dissertation deals with the research on development of identification of damped structures and suitable updating methods for microsystems. The relationship between structural and viscous damping models in damped systems has been addressed. A complex FRF method has been proposed for generally damped structures. A novel method directly using base excitation test data has been developed successfully for model updating. The modal identification procedure, where a damping model is arbitrarily chosen for a damped system in the cases of viscous and structural damping, has been studied. It is shown that an exact relationship exists between structural and viscous damping models in a proportionally damped system. The identified damping matrix is not proportional though the equivalent mode shapes remain real. For a non-proportionally damped system, the equivalent mode shapes consist with their counterparts of the original system except differing by a complex scaling factor. It is demonstrated efficiently by numerical studies and an experimental example that the error in estimating modal parameters induced by wrong interpretation of damping model is quite small. In addition, the equivalent damping matrix is physically meaningful in the case of a system with distributed damping while there is no such equivalent damping matrix if the damping is localized.