276 C.E. Silva and S.J. Dyke Fig. 29.1 An example of a 5 5 correlation bar plot 1 2 3 4 5 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1 Experimental mode Reference mode Correlation understand. An example of this plot for a 5 5 successful correlation matrix is presented in Fig. 29.1. Model correlation matrices are very common when a mode needs to be checked for validity in cases of computational or torsional modes. For this particular project, the benefits of the modal assurance techniques are used with a distinct objective: to implement a methodology for verifying the closeness of a model boundary condition parameters to those of an experimental result. This is why the method will be further referred to as “MAC-based” instead of modal assurance criteria. 29.3 Numerical Validation As stated previously, the development of the mathematical models used in this study is the first part of a much broader procedure which is the numerical verification of the proposed technique. A model correlation method has been proposed but before it can be implemented with experimental data, it has to be tested with unpolluted data so that it can prove its reliability. In the present chapter, this verification will be performed in an iterative way so that it can be further implemented with real data. Two sources of data can be used instinctively from the mathematical models already discussed: the analytical and the finite element models. It is expected that for the analytical case, a perfect correlation occurs; whereas for the finite element case, which is an approximation, a close-to-perfect-correlation occurs. 29.3.1 Numerical Example A correlation procedure against the three developed mathematical models, each one with different parameter values will be made. This constitutes the ‘model space’, a group of distinct parametrized models to which the experimental case is going to be compared until the best match is determined. The mathematical models to be used are: 1. Simply supported beam with both ends free for rotation. 2. Simply supported with: • Rotational springs on both ends with three different k i values on one end, and five proportional values going from 20%to100%of k i on the other end. This gives a total of twenty five cases.
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