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Shock and Vibration
Volume 4, Issue 4, Pages 211-222

Statistically Generated Weighted Curve Fit of Residual Functions for Modal Analysis of Structures

Paul Stanley Bookout

Marshall Space Flight Center (MSFC), Structural Analysis Division, ED23, AL 35812, USA

Revised 8 May 1995

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure to modal test large structures in a free-free environment to measure the effects of higher order modes and stiffness at distinct degree of freedom interfaces. Due to the present damping estimate limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of irregular data, which should be a smooth curve in a second-order polynomial form. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure, which is used to predict constrained mode shapes.