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MONG the various possibilities for schemes of its kind, this study deals with the specific case where the computer model of a structure is to be upgraded on the basis of experimental measurements of normal mode frequencies only. It is implicit that the essential forms of the fundamental modes are already adequately identified in the starting computer model. The objective is to establish a rational procedure for predicting the modified structure (stiffness matrix) which correlates most closely with a given set of measured modal frequencies. The form of the computer model itself (conforming elements) is taken to be given and fixed. An existing procedure for this identification problem, as developed and used in the Viking program, apparently originates with White.' Experience with the structural modeling methods used in this program are summarized in a report of Wada et al. 2 Subsequent application of such procedures in the Skylab project is described in a recent report. 3 White's derivation establishes his model modification scheme based on the first-order terms of a Taylor expansion of the altered model about the original one. The scheme allows prediction of a set of scale parameters, in number equal to or less than the number of available test-data points. In the latter case the parameters are determined to minimize the mean-square difference between measured and computed frequencies. There is no room to improve on White's result within the framework of his analytical derivation. However, by taking a different approach, a more broadly applicable procedure becomes available. Its advantages are that 1) both the number and choice of structural parameters to be varied in the modification are arbitrary, and 2) the possibility is provided that a given revision of the computer model may be approached through a set of lower-order problems with (generally) improved efficiency. The present approach relates to modal energies; its derivation leads to a useful boundedness property for iterate steps toward the upgraded computer model.

Scaling a discrete structural model to match measured modal frequencies