Effects of time truncation in updating methods based on FRF data

Some techniques, which update the spatial matrices of the numerical model of a structure in order to take account of variations of the physical characteristics, use the data of measured frequency response functions (FRFs), but the passage from the time domain into the frequency domain, starting from an impulse response function (IR), could produce a biased FRF, if the IR is truncated at the end of the recording widow. The bias of the FRF, due to the truncation, is caused by complex constants, different for each mode, which multiply the residues. For this reason, the level of the FRF could be affected by the truncation, whereas no bias is present both in the natural frequencies and in the damping ratios. Therefore a structural updating is difficult (often impossible) to be successfully performed with the approaches mentioned before. Moreover, a structural updating procedure could lead to a wrong identification of the model matrices. These difficulties are more and more significant when the length of the observation window is short with respect to the time constants of the considered modes. In this paper, the time effects of the truncation in the structural updating procedures are reported by analyzing the behaviour of simple structural components, such as cantilever beams, considering both numerical simulations and experimental data.