PSI - Issue 81

Mykhailo Hud et al. / Procedia Structural Integrity 81 (2026) 434–438

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Frequency (Hz)

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Mode number

Fig 4. The bowl is not filled with water

The natural frequency spectrum (Fig. 4), constructed on the basis of the data presented, shows a gradual increase in frequencies from 87.37 Hz to 338.29 Hz, indicating the normal development of oscillatory forms as the mode number increases. In the lower range (the first two modes), the frequencies are very close together, which is characteristic of global vibrations associated with the joint operation of the entire structure. A further increase in frequencies to values of 127 – 175 Hz reflects the transition to partial modes with a more complex distribution of deformations. A pronounced increase in the range of 215 – 338 Hz indicates the activation of localized vibration modes dominated by individual rigid elements of the structure.

The bowl is completely filled

The bowl is partially filled

The bowl is not filled

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Frequency (Hz)

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Mode number

Fig 5. Comparative characteristics of different options for filling the pool bowl

The combined graph (Fig. 5) shows that the first two sets practically coincide across the entire frequency range: the difference between the corresponding modes is tenths to hundredths of a hertz and does not change the shape of the curve. In contrast, the third set shows significantly lower frequencies for all modes. For each mode number, the frequency values are noticeably lower than in the previous two, which clearly indicates a decrease in the overall stiffness of the structure. At the same time, the shape of the curve remains monotonous and fairly smooth without sharp jumps, which indicates the relative structural integrity of the model. However, the transition of the spectrum to a lower range expresses the increased sensitivity of the structure to dynamic loads, in particular to the coincidence of natural frequencies with the operating frequencies of technological or seismic influences.