| The objective of this dissertation in part is to mathematically prove that the Random Decrement signatures are indeed the free decay responses of the system, at the measured locations, for a class of problems widely encountered in structural dynamics. This is accomplished by first relating the technique to other well established time series techniques, such as the correlation function and the Fourier series.; A general relationship is developed between the cross-Random decrement signature and the cross-correlation function for two linear, stationary processes. Since most processes in nature exhibit Gaussian distributions, the relationship is reduced to include a joint Gaussian probability distribution function.; Several single degree-of-freedom and two degrees-of-freedom systems are studied analytically using the mathematical model of the Random Decrement signature and the results compared to the free decay responses of the system. A variety of input load conditions are incorporated to analyze the effect of uncorrelated and strongly correlated inputs. The results indicate that for relatively wide band-limited inputs, the signatures are identical to the free decay responses of the system. Furthermore, if more than one discrete input is introduced into the system, the shape of the signature will depend on the relative intensity of the inputs. For continuous inputs spread over a large area of the system, the shape of the signature is independent of the input intensity and is therefore unique to the system.; A system identification technique is developed based upon a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices.; Finally, an experiment was conducted on a scale model of an offshore platform structure. Random data measured at different locations on the structure are analyzed and the corresponding signatures obtained. The system parameters are calculated from the signatures. The validity of the mathematical model is tested by comparing the results with another experiment where the input load was also measured as a function of time. A damage site was introduced in the structure and the proposed system identification technique employed to detect its location. The off-diagonal elements in the flexibility matrix were used; the damage location was successfully identified. (Abstract shortened with permission of author.)... |
