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Vibrations are often represented as a sum of standing waves in space, i.e. normal modes of vibration. While this can be mathematically accurate, the representation as travelling waves can be compact and more appropriate from a physical point of view, in particular when the energy flux along the structure is meaningful. The quantification of travelling waves assists in computing the energy being transferred and propagated along a structure. It can provide local as well as global information about the structure through which the mechanical energy flows. Presented in this paper is a new method to quantify the fraction of mechanical power being transmitted in a vibration cycle at a specific direction in space using measured data. It is shown that the method can detect local defects causing slight non-uniformity of the energy flux. Equivalence is being made with the electrical power factor and electromagnetic standing waves ratio, commonly employed in such cases. Other methods to perform experiment based wave identification in one-dimension are compared with the power flow based identification. Including a signal processing approach that fits an ellipse to the complex amplitude curve and Hilbert transform for obtaining the local phase and amplitude. A new representation of the active and reactive power flow is developed and its relationship to standing waves ratio is demonstrated analytically and experimentally.

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Structures possessing cyclic symmetry such as turbine bladed disks, ultrasonic motors, and toothed gear wheels can experience elevated vibration levels when small deviations from circumferential periodicity exist. Detection of these perturbations via classical system identification approaches is time-consuming, indirect, and exhibits low sensitivity to defects, and is affected by measurement noise. The present work utilizes low-level forces that automatically lock onto a weighted rotating projection of the system modes at resonance frequency to enhance the detectability of small structural imperfections. The spatial localization of defects is exploited to identify multiple, localized, isolated defects’ locations. The defects’ severities are estimated based on the deviation from the circular structure's analytical mode shapes. The fast and enhanced precision of defect identification is obtained by employing the modal-filtered autoresonance technique. To validate the presented method, an experimental system consisting of a ring of coupled Helmholtz acoustic resonators was developed. Experimental results show good agreement with numerical simulations, verifying the method's capabilities to identify the location and severity of multiple defects. Thus, the implementation of the suggested method provides fast and precise structural health monitoring of cyclic-symmetric systems.