Identification of linear structural models

Abstract

With a great amount of research currently being aimed towards dynamic analysis and control of very large, flexible structures, the need for accurate knowledge of the properties of a structure in terms of the mass, damping, and stiffness matrices is of extreme importance. Typical problems associated with existing structural model identification methods are: (i) non-unique solutions may be obtained when utilizing only free-response measurements (unless some parameters are fixed at their nominal values), (ii) convergence may be difficult to achieve if the initial estimate of the parameters is not "close" to the truth, (iii) physically unrealistic coupling in the system matrices may occur as a consequence of the identification process, (iv) large, highly redundant parameter sets may be required to characterize the system, and (v) large measurement sets may be required. To overcome these problems, a novel identification technique is developed in this dissertation to determine the mass, damping, and stiffness matrices of an undamped, lightly damped, or significantly damped structure from a small set of measurements of both free-response data (natural frequencies, damping factors) and forced-response data (frequency response functions).

The identification method is first developed for undamped structures. Through use of the spectral decomposition of the frequency response matrix and the orthogonality properties of the mode shapes, a unique identification of the mass and stiffness matrices is obtained. The method is also shown to be easily incorporated into a substructure synthesis package for identifying high-order systems. The method is then extended to include viscous damped structures. A matrix perturbation approach is developed for lightly damped structures, in which the mass and stiffness matrices are identified using the imaginary components of the measured eigenvalues and, as a post-processor, the damping matrix is obtained from the real components of the measured eigenvalues. For significantly damped structures, the mass, dauping, and stiffness matrices are identified simultaneously.

A simple, practical method is also developed for identification of the time-varying relaxation modulus associated with a viscoelastic structure. By assuming time-localized elastic behavior, the relaxation modulus is determined from a series of identification tests performed at various times throughout the response history.

Many interesting examples are presented throughout the dissertation to illustrate the applicability and potential of the identification method. It is observed from the numerical results that the uniquely identified structure agrees with simulated measurements of both free and forced·response records.