Experimental Ritz vector identification and application to finite element model validation and structural damage detection

During the last two decades, the development of the methodology to experimentally verify complex structural analytical models and damage detection has been an area of intense research. To aid in the development of a verified model, many practicing engineers as well as researchers utilize experimentally measured modal properties (natural frequencies, damping ratios, and mode shapes) to adjust/verify the analytical model.; Ritz vectors represent an alternative to mode shape vectors. In numerical analysis, Ritz vectors have been shown to offer superior performance in model reduction and time simulation. However, until this study no technique existed to extract Ritz vectors from the vibration response of real structures. In this dissertation, a unique procedure to extract Ritz vectors from measured dynamic response data is developed and investigated. It is shown that the numerically simulated Ritz vectors are identical to the base line Ritz vectors when dynamic test shaker locations and directions are used as reference force locations in the direct derivation. The sensitivity of the extraction algorithm to measurement noise is shown to be comparable to the sensitivity of modal parameters extracted from the same data set. To verify the feasibility and accuracy of the extraction algorithm, measured dynamic response data and static test results from the Space Shuttle vertical stabilizer assembly experimental data base are utilized. Compare to static test data, accurate Ritz vectors were extracted using both accelerometer and laser-scanning vibrometer-based modal survey tests.; Taking advantage of the facts that Ritz vectors can be extracted from dynamic response data and demonstrated in numerical simulations to be more sensitive to structural damage than traditional mode shapes, a technique using load dependent Ritz vectors for analytical model validation and damage detection was developed. In this technique, Ritz vectors are divided into ‘static’ and ‘dynamic’ sets. These two sets of vectors ate used in conjunction with a modified Minimum Rank Perturbation Theory to detect both the location and extent of structural damage. Both numerical simulation and experimental data were used to demonstrate the feasibility of using experimental Ritz vectors to validate analytical model and monitor structural health.