Flow-induced vibration of a pump-turbine runner is a major challenge in practical operation

and modal analysis is key to understanding its characteristics. This study uses an acoustic-structure coupling method to determine the natural modes of a prototype pump-turbine runner in the flow passage. The nodal diametrical numbers in each mode are identified through Fourier series expansion of the distribution of the runner outer rim displacement along its circular path. Based on the rotor-stator interaction (RSI) theory

the harmonic responses of the runner under specific excitations are calculated using an acoustic-structure coupling model

and its frequency avoidance range is then examined. The results show each runner mode contains multiple diametrical components. For a 9-blade runner

its natural mode numbers always couple with those associated components taking values with a difference of ±9. It is noteworthy that an excitation force that matches the derived diametrical number can effectively excite the natural mode dominated by the original one. In addition

under specific excitations

certain higher-order modes exhibit strong resonance with amplitudes comparable to those of lower-order modes. These findings indicate the real excitation characteristics of pump-turbine runners are more complicated than commonly assumed

posing greater challenges in vibration avoidance.