A Reference-Based FE Model Updating to Produce Measured Eigen Data

In this paper, a reference-based model updating technique is presented which produces the measured eigen data as a subset of finite element model (FEM) eigen data and thus enables to predict responses at global modes and other important modes. The measured modes are used as a reference basis and mass and stiffness matrices of the FEM are updated in such a way that the updated model replicates the test results. The measured mode shapes at limited number of points and in limited degrees of freedom (dofs) are expanded on entire FE grid points using modified inverse Guyan reduction method. Subsequently, using the expanded mode shapes, the FE matrices are updated by minimizing objective functions and invoking constraints to retain the symmetry and orthogonality of the updated matrices through Lagrange multipliers. The effectiveness of the proposed updating procedure is demonstrated by considering a L-shaped cantilever plate. The experimental data (simulated experimental data) is produced by introducing error in the eigenvalues and eigenvectors obtained from the FEM model. In this paper, we have outlined a procedure to implement the algorithm described above in a commercial FE software ABAQUS and Python. The procedure was found to replicate the selected simulated modes by updated matrices. The procedure has been demonstrated for up to 10% erroneous modes.