A Time-Domain Demodulation Approach for Extracting Natural Frequencies and Standing-Wave Mode Shapes in Non-Axisymmetric Turbomachinery Components

Abstract Measuring the natural frequencies and mode shapes of rotating turbomachinery components under real-operating conditions is particularly important to prevent dangerous operating scenarios. However, this task becomes particularly challenging for runners and impellers because they are rotating, confined, and, in hydraulic turbomachinery, submerged. Furthermore, many existing measurement techniques rely on frequency-domain analysis, where measurements taken from the stationary frame can produce complex spectral responses that complicate interpretation. To address these challenges, this work proposes a method to extract excited mode shapes and their associated vibration frequencies directly from time-domain signals. Mode shapes are recovered through demodulation of the structural response measured once the system reaches a resonant state. Measurements are performed using a laser Doppler vibrometer (LDV) in the stationary frame. To validate the method, a simplified model representing an axial turbomachinery impeller or runner is studied both experimentally and numerically. First, modal analyses under stationary (non-rotating) conditions are conducted to identify the natural frequencies and mode shapes. The structure is then set into rotation and brought to resonance using a piezoelectric actuator, with response measured by the LDV in the stationary frame and by an accelerometer installed in the rotating frame. The proposed method demonstrates the feasibility of accurately extracting mode shapes in complex rotating systems and provides valuable insights for resonance detection and monitoring of such structures. Limitations and potential applications of the methodology are also discussed.