Updating finite element dynamic models using an element-by-element sensitivity methodology

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared £2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of "zooming" on the detected error locations. Several simulation examples which demonstrate the potential of the proposed methodology are discussed. I. Introduction E VEN though the field of finite element analysis of structural dynamic problems has witnessed tremendous progress in the last two decades, greater confidence is still placed in experimental data. Therefore, the finite element model of a given structure is often updated to reflect the results of a particular experiment. Usually, the computed eigenmodes are compared with the measured frequencies and mode shapes. If both sets are not in agreement, the finite element model is refined via a two-step updating procedure which: 1) locates the errors and 2) corrects them. Clearly, the first step is the most challenging of the two. Once the location of the errors is known, it is relatively easy to correct them, especially if the error sources can be identified. However, locating and identifying these errors can be a difficult task for the following reasons. In general, only a few experimental modes are available, and these may be contaminated with random and systematic measuring errors. Moreover, only a subset of the degrees of freedom (DOF) in the finite element model can be monitored; and as for practical and economical reasons, only a few sensors can be utilized.