Curve Fitting Analytical Mode Shapes to Experimental Data

In this paper, we employ the fact that all experimental vibration data, whether in the form of a set of FRFs or a set of output-only spectra, is a summation of resonance curves, each curve due to a mode of vibration. We also use this superposition property of modes to calculate a modal participation matrix, a measure of the participation of each mode in the experimental vibration data. First we show how this superposition property can be used to curve fit a set of FEA mode shapes to EMA mode shapes or ODS's. The modal participation matrix is calculated as a least-squared-error solution, so any number of FEA mode shapes can be curve fit to any number of EMA mode shapes or ODS's. Next we show how an expanded and enhanced set of FRFs, Cross spectra or ODS FRFs is obtained by curve fitting FEA mode shapes to experimental data. This approach in an alternative to FEA Model Updating, where an FEA model is modified so that its modes more closely correlate with experimental data. By curve fitting FEA shapes to experimental data, an extending and enhanced dynamic model is obtained which is more suitable for machinery & structural health monitoring, and for troubleshooting noise & vibration problems using SDM and MIMO methods.