The first half-period of pressure heads for frequency response extraction and analysis of waterhammer with fluid–structure interaction

This paper details an efficient procedure to extract and analyze the pipe system characteristics from the pressure and stress waves generated during the first half-period of the water hammer with fluid–structure interaction (FSI). To this end, a new transient signal is generated using the first half-period of pressure heads through verified mathematical and numerical computations in the time domain. Then, the system's resonant frequencies are extracted from the new transient signal by employing a fast Fourier transform (FFT) algorithm. The extraction procedure is verified using the analytical results from the literature. The analytical relations of the dominant resonant frequencies corresponding to the pressure and stress waves in the new transient signal are also derived to analyze the frequency data captured using the proposed approach. The effects of the stress wave (structural) frequencies are closely investigated, considering several hypothetical case studies. Both major FSI mechanisms during water hammer in a reservoir–pipe–valve​ system, namely Poisson and junction, are taken into account. The results demonstrate that the presented approach can manifest the hydraulic and structural properties of the pipeline system. The main stress wave frequencies result in a considerable increase in the amplitude of the extracted resonant frequencies, whereas a reduction effect is revealed due to the reflected stress wave frequencies. This research is of crucial importance for system identification in pipelines.