Model updating of a 'clamped'-free beam system using FEMtools
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Model updating is used to improve the match between the dynamic properties (eigenvalues and eigenmodes) of a Finite Element (FE) model and test data. In this report some parameters of initial FE models of two designs of a ‘clamped’-free beam system, are updated based on the first five eigenfrequencies of the first five bending modes of an experimental model by using FEMTOOLS 3.1.1. The goal of this traineeship is to learn about the possibilities of the FE model updating process inside the commercial software package FEMTOOLS. The beam models that are used for this purpose are a simple straight beam (‘beam a’) and a slightly different beam (‘beam b’). The difference between the beams is the height of the beams right half. In order to create an interesting updating situation a mismatch of approximately 10 − 15% between the eigenfrequencies of two beam models is chosen. In MATLAB for both beams a FE model is built of 50 Euler beam elements. The difference between the eigenfrequencies can be influenced by changing the height of ‘beam b’. This is done until the requirement is satisfied. Further initially it was required that the influence of the shear stress on the eigenfrequencies is less than 1%. Therefore, both beams model are also built using 50 Timoshenko beam elements. The influence of the shear stress can be investigated by comparing the eigenfrequencies of the FE models built using Timoshenko beam elements with the eigenfrequencies of the FE models built using Euler elements. By changing the relationship between the height and the length of the beam the influence of the shear stress on the eigenfrequencies can be reduced. Both beams are manufactured for carrying out experimental modal analysis. Eight frequency response functions (FRF’s) of both beam systems are determined with a Signal Analyzer and the software package SIGLAB. Therefore the beams are excited on eight optimal locations and the acceleration response is measured on a fixed location. These FRF’s are exported to the software package ME’SCOPE which is used to carry out the Orthogonal Polynomial modal-parameter fit procedure. The real parts of the eigenvalues are very small in comparison with the imaginary parts. Therefore the undamped angular eigenfrequencies are used in the updating process. In FEMTOOLS the initial FE model is built (based on ‘beam a’) of fifty LINE2 elements. This element type takes the shear stress into account. The initial FE element model is updated, with different update strategies, based on the first five experimental eigenfrequencies corresponding to the five bending modes of ‘beam a’ and ‘beam b’. Typical parameters which are updated are the clamping stiffnesses, the cross-section and the second moment of area of the right half of the beam. The results show a clear decrease in the discrepancies between the numerical and experimental eigenfrequencies. The correctness of the updated parameters depends on the chosen strategy. It can be concluded that FEMTOOLS is capable to improve the match between the dynamic 7 properties of a FE model and experimental data. In order to carry out a physically meaningful model update it is important that the user has knowledge about the updating process and about the system that is updated.