Generalized Goertzel algorithm for computing the natural frequencies of cantilever beams

• The paper utilizes the recently introduced generalized Goertzel algorithm.
• The algorithm is used for accurately detecting peaks in the frequency spectrum.
• The algorithm is applied to the problem of damage detection in materials.
• The superiority of the algorithm over the Chirp Z-transform is proved for cases which appear in practice.

The paper proposes a fast algorithm for accurate estimation of frequency within a specified, narrow range. The algorithm is useful for the identification of the natural frequencies of cantilever beams for damage detections purposes. The procedure is based on the generalized Goertzel algorithm combined with apriori knowledge of the natural frequencies intervals for cantilever beams given their physical characteristics. We compare our approach with the Chirp Z-transform and several frequency or time-frequency methods to illustrate its advantages for online damage detection.