Abstract

A method is proposed for probabilistically model updating an initial deterministic finite element model using measured statistical changes in natural frequencies and mode shapes (i.e., modal parameters). The approach accounts for variations in the modal properties of a structure (due to experimental errors in the test procedure). A perturbation of the eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix. This stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix. Monte Carlo simulations, in conjunction with the variations of the structural modal parameters, are used to determine the variations of the stiffness reduction factors. These values will subsequently be used to estimate statistics for the corrected stiffness parameters. The effectiveness of the proposed technique is illustrated using simulated data on an aluminum cantilever Euler-Bernoulli beam.

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