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Abstract
In this paper, it is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. The matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low‐frequency part of these sums are substituted with expanded test modes. The approach is meant to update FE models in one‐step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes. A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity. Finally, the performance of the proposed updating method is assessed by means of an application example in which the FE model is updated based on the test modes of a real structure.
Highlights
Finite element models are numerical idealizations of real structures used in structural design or to predict the structural response under operational conditions. e accuracy of these models is highly dependent on how precise the localized and distributed imperfections are accounted for in the model
It is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. e matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low-frequency part of these sums are substituted with expanded test modes. e approach is meant to update FE models in one-step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes
A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity
Summary
Finite element models are numerical idealizations of real structures used in structural design or to predict the structural response under operational conditions. e accuracy of these models is highly dependent on how precise the localized and distributed imperfections are accounted for in the model. Shock and Vibration model by their experimental counterparts so that a good correlation between the updated FE and the test modal parameters is obtained In this proposed approach, the method of matrix mixing [5, 6] is used in combination with the local correspondence (LC) expansion technique [7]. Is is to assure that the FE model being updated by the one-step approach is physically equivalent to the tested structured and that the discrepancies between model and real structure are caused by perturbations distributed over the FE model. It is worth highlighting that, to any sensitive-based FE model updating technique, the one-step FE updating approach proposed is suitable for cases where the structural system being updated can be modelled by a linear FE model with orthogonal mode shape vectors. Some remarks regarding the results obtained from the application examples are presented in the last part of the paper
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