Optimal spatial sampling interval for damage detection by curvature or strain energy mode shapes

Vibration-based methods of non-destructive damage detection utilizing curvature or strain energy mode shapes have been applied in a variety of applications. Attractive features of these methods include high sensitivity to damage and instant determination of the damage location. However, the quality of damage detection achieved in practice depends upon determining a proper sampling interval for discretization of the displacement mode shapes. Experimental observations show that both undersampling and oversampling of the displacement mode shapes may have adverse effects on the quality of damage detection. This paper presents an analysis aimed at determining the optimal sampling interval that would minimize the effects of measurement noise and truncation errors on the calculation of the curvature and strain energy mode shapes, thus maximizing sensitivity to damage and accuracy of damage localization. Derivation of the formulas for the optimal sampling interval is based on the most commonly used numerical methods for the computation of the curvature and the strain energy mode shapes. Numerical verification has shown very good performance of the suggested formulas in predicting the optimal sampling interval.