Procedure to Extract Ritz Vectors from Dynamic Testing Data

Ritz vectors represent an alternative to mode shape vectors as suitable basis vectors for n-dimensional space. In numerical analysis, Ritz vectors have been shown to offer superior performance in model reduction and time-simulations. In this paper, we develop a methodology that is able to extract Ritz vectors from single and multiple shaker dynamic tests. It is shown that the identified “experimental” Ritz vectors are identical to the analytically derived Ritz vectors when the dynamic test shaker locations and directions are used as the reference force locations in the analytical 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. Finally, to verify the feasibility and accuracy of the extraction algorithm, dynamic response data and static test results from the Space Shuttle vertical stabilizer assembly experimental database are utilized. Compared to static test data, accurate Ritz vectors were extracted using data from both accelerometer and laser-scanning vibrometer-based modal survey tests.