Statistically generated weighted curve fit of residual functions for modal analysis of structures
Abstract
A statistically generated weighting function for a secondorder polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure for modal testing large structures in an external constraintfree environment to measure the effects of higher order modes and interface stiffness. This test method is applicable to structures with distinct degreeoffreedom interfaces to other system components. A theoretical residual function in the displacement/force domain has the characteristics of a relatively flat line in the lower frequencies and a slight upward curvature in the higher frequency range. In the test residual function, the abovementioned characteristics can be seen in the data, but due to the present limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of ragged data. A second order polynomial curve fit is required to obtain the residual flexibility term. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted secondorder polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and freefree modes from testing are used to improve a mathematical model of the structure. The residual flexibility modal test method is applied to a straight beam with a trunnion appendage and a space shuttle payload pallet simulator.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1995
 Bibcode:
 1995STIN...9522950B
 Keywords:

 Curve Fitting;
 Flexible Bodies;
 Mathematical Models;
 Residual Stress;
 Structural Analysis;
 Vibration Mode;
 Weighting Functions;
 Flexibility;
 Least Squares Method;
 Resonant Frequencies;
 Space Shuttle Payloads;
 Stiffness;
 Structural Mechanics