The present study has focused on the estimation of normal modes and their mode shapes from experimental data. The determination of accurate undamped modal parameters from experimental data in the presence of damping is critical for the construction or reconciliation of structural dynamics models, in which the physical mass and stiffness properties are isolated from the dissipative effects of damping. The response functions measured from experimental data are generally approximated by finite-dimensional first-order difference equations in the time-domain using algorithms such as ERA. Such models, or realizations, do not directly determine the mass and stiffness matrices, except under special restrictions. This thesis develops a family of transformation-based methods for the construction of second-order structural dynamic models from first-order system realizations of experimental data. Transformations to a second-order canonical basis are effective for the systematic extraction of the normal modes from the first-order realizations.;Two separate transformations are developed: the Common Basis-Normalized Structural Identification (CBSI) procedure and the Uncoupled Nonproportional Damping (UNDAMP) procedure. CBSI transforms the first-order state space realizations to the well-known form of second-order proportionally-damped equations of motion. The resulting structural dynamics models are shown not only to yield the accurate normal modes for proportionally damped cases, but also improved estimates of the normal mode shapes in the presence of nonproportional damping as compared to existing methods. The UNDAMP algorithm extends the CBSI method to a global transformation spanning up to the full space of the damped modes. As such, UNDAMP is capable of filtering out the contaminating attributes of nonproportional damping from the CBSI-determined normal modal parameters. Furthermore, UNDAMP is applicable to the extracting of non-proportional damping when the number of measured sensors is less than the number of identified modes.;Using normal modal parameters determined by CBSI or UNDAMP, a method for determining minimal-order mass and stiffness matrices is presented. The resultant model is an alternative second-order realization with measured physical variables as degrees of freedom, and the derived mass and stiffness matrices are shown to have asymptotic equivalence to Guyan-reduced and/or Craig-Bampton-synthesized structural models.;The efficiency and accuracy of the present transformation methods are demonstrated through simulated numerical examples and experimental data. In particular, the present methods are used to reconstruct frequency response functions and applied to damage detection in truss structures. Finally, the implications of these analytical techniques for structural system identification and directions for future research are also discussed.
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