Finite element model updating of smart structures with direct updating algorithm

In this paper, a finite element model updating algorithm is proposed to enhance the accuracy of the simulated finite element model of a smart structure (collocated piezoelectric patches embedded on a cantilever beam). Piezoelectric patches are used to sense and control the excessive vibrations of the structures. Mostly, they are mounted on flexible structures to measure their response at different excitations. The finite element method can be used to model the beam embedded with collocated piezoelectric patches. The complete finite element formulation of the smart structure is briefly described in this paper. There are different types of uncertainties that may be present in the simulated finite element model of a smart structure such as uncertainty in the structural boundary conditions, in the material elastic properties, the dimensions of the structure, piezoelectric elastic and electric properties, and the location of the piezoelectric patches mounted on the structure. In the present analytical study, the above uncertainties present in the smart structure are reduced by using the direct updating algorithm. It is found that the direct updating method through updating the mass and the stiffness matrices of the smart structure successfully enhance the accuracy of the simulated finite element model of the beam embedded with PZT patches. The state-space method is used to predict the response in the frequency domain. The maximum percentage error in the simulated finite element model of the piezoelectric embedded beam structure due to its structural and the electrical property uncertainty is 10.36% and 23.52% respectively and that was completely removed by using the direct updating algorithm. The optimal location of the piezoelectric patches is also taken as uncertainty which is successfully updated by using the proposed direct updating algorithm. The maximum percentage error in the natural frequencies of the smart structure due to location uncertainty is 18.39% which was also completely removed. To validate the outcomes, a frequency response function (FRF) is plotted.