# Effect of approximation fidelity on vibration-based elastic constants identification

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## Abstract

Some applications such as identification or Monte Carlo based uncertainty quantification often require simple analytical formulas that are fast to evaluate. Approximate closed-form solutions for the natural frequencies of free orthotropic plates have been developed and have a wide range of applicability, but, as we show in this article, they lack accuracy for vibration based material properties identification. This article first demonstrates that a very accurate response surface approximation can be constructed by using dimensional analysis. Second, the article investigates how the accuracy of the approximation used propagates to the accuracy of the elastic constants identified from vibration experiments. For a least squares identification approach, the approximate analytical solution led to physically implausible properties, while the high-fidelity response surface approximation obtained reasonable estimates. With a Bayesian identification approach, the lower-fidelity analytical approximation led to reasonable results, but with much lower accuracy than the higher-fidelity approximation. The results also indicate that standard least squares approaches for identifying elastic constants from vibration tests may be ill-conditioned, because they are highly sensitive to the accuracy of the vibration frequencies calculation.

## Keywords

Identification Bayesian identification Response surface approximations Dimensionality Reduction Plate vibration## Notes

### Acknowledgments

This work was supported in part by the NASA grant NNX08AB40A. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Aeronautics and Space Administration.

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