Ph.D. Dissertation Defense by Matt S. Allen
Wednesday, April 13, 2005
(Dr. Jerry H. Ginsberg, Chair)
"Global and Multi-Input-Multi-Output Extensions to the Algorithm of Mode Isolation"
From bridges to microchips, hard-disk-drives to airplane wings, many structures exhibit vibratory behavior. Experimental modal analysis provides a method for characterizing these vibratory systems using experimentally measured vibrations. It has become an important tool for validating finite element models and in addressing noise or vibration problems in a variety of systems. Furthermore, there is increasing interest in using experimental modal analysis for more demanding applications, such as condition monitoring or dynamic material characterization. These applications require fast and accurate methods for determining a structure's dynamic properties in the presence of measurement noise.
This presentation provides a brief introduction to experimental modal analysis, illustrating some of the steps involved in decomposing vibration data into meaningful modes of vibration. Some of the difficulties that can occur in the process using the conventional approach are highlighted. A Multi-Input-Multi-Output implementation of the Algorithm of Mode Isolation is then presented which addresses some of these difficulties.
The resulting MIMO-AMI algorithm is then evaluated by applying it to vibration data from three systems. The first system consists of two orthogonal cantilevered beams joined at their free ends. The modes of vibration of the non-proportionally damped structure are found using the Ritz method, with a sub-structuring approach used to couple torsion and bending in the two beams. The impulse response of the system is then synthesized, contaminated with noise and processed with AMI. The results of AMI are compared with those of another recently developed algorithm, the Stochastic Subspace Identification Algorithm (SSI). The second system consists of a simply supported rectangular plate. The analytical solution for the vibration of the plate is used to synthesize the plate's impulse response, which is contaminated with noise and processed with AMI. The results of AMI are compared with those of another recently developed algorithm, the poly-Reference Least Squares Complex Frequency Domain (pLSCF) algorithm. AMI is then applied to vibration measurements taken from the Z24 highway bridge in Switzerland in order to validate its performance on experimental data. This data set presents a considerable challenge because of noise, modal density and the considerable number of measurements that were processed simultaneously. The results obtained by the AMI algorithm are compared with those obtained by other groups of researchers using a variety of techniques.