Ricardo Taborda

A procedure is proposed to estimate the modal damping values of a system starting from the ratio between the Fourier transforms of the response in one of its degrees of freedom and the excitation to which the system is subjected. The method is based on the concept of modal superposition, by means of which, through a simple mathematical manipulation, it is possible to express the squared module of the transfer function as a sum of the real and imaginary components of all the transfer functions of each one of the uncoupled degrees of freedom. Starting from this expression, it is intended that the value of the transfer function associated to the resonant frequency of to the ith mode can be appropriately determined just accounting for the participations of the previous modes added to the ones of the i and i+1 modes in the sum. Once established this, if the eigenvectors are normalized with respect to the value of the mode for which the transfer function is known and the participation factors of each one of the uncoupled modes of the system are calculated, then, by an iterative process, it is possible to estimate the modal damping values associated with each one of the modes involved in the transfer function under analysis.

The previous procedure is compared against simple theoretical examples, obtaining results which validate the assumptions made. Additionally, its practical application is evaluated when making an estimation of the modal damping values of an instrumented building. The results obtained are compared with those given by the non-parametric method of dynamic amplification factor for the fundamental mode and with those obtained by a modal technique of parametric estimation (MIMO software), reaching a better estimation than the first one and similar to the second one.

Finally, the limitations and possible applications of the procedure presented are discussed, and the advantages over the other two methods are discussed.