Vibration-Based Health Monitoring in Beams Using Curve Fitting, Correlation, and Curvature Determination Methods

Health monitoring and damage detection in structures is important for maintaining the safety and health of individuals as well as for dealing with economic losses. This article compares primary and secondary modal information, including the frequency values and vibration mode shapes, for health monitoring and damage detection in beams. The impact of the damage is observed as a difference between primary and secondary frequency values, as well as a difference between the coefficients of the polynomial curves. Also, the Pearson's Correlation Coefficient (PCC) between the primary and secondary modes is calculated as values other than 1 and -1 that indicate the impact of damage on the relative displacement of degrees of freedom. However, damage locations cannot be identified by curve fitting, correlation, and comparison of natural frequencies; thus, comparison of primary and secondary shapes of vibration modes was made based on determination of central curvature. It was shown that the difference between the primary and secondary curvature graphs occurs as fractures created in damaged positions and in the curvature graph of the secondary situation; hence, the damaged locations are identifiable.