PSI - Issue 81

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

436

Frequency (Hz)

100 150 200 250 300 350 400 450 500

Frequency (Hz)

0 50

1

2

3

4

5

6

7

8

9

10

Mode number

Fig 2. The bowl is completely filled with water

The graph (Fig. 2) shows the spectrum of natural frequencies of the structure in the high-frequency range. The frequency values show a clear trend of monotonous growth from 123.5 Hz to 473.1 Hz, indicating a gradual complication of the vibration modes as the transition to higher modes occurs. This behavior is characteristic of rigid structures in which local vibration modes manifest themselves at significantly higher frequencies.

Frequency (Hz)

600

500

400

300

200

Frequency (Hz)

100

0

1

2

3

4

5

6

7

8

9

10

Mode Number

Fig 3. The bowl is partially (half) filled with water

The provided spectrum of natural frequencies (Fig. 3) demonstrates stable and predictable dynamics of the structure in the high-frequency range. The frequencies increase monotonically — from 123.56 Hz in the first mode to 478.43 Hz in the tenth, confirming the rigid structure of the system and the uniform formation of more complex oscillatory forms. In the lower part of the spectrum (the first two modes), the frequency values are close to each other, indicating global deformations and a similar nature of the initial vibration forms. The further increase in frequencies, especially in the 180 – 250 Hz range, reflects the beginning of the transition to more complex partial forms. A significant increase in frequencies in the upper part of the spectrum (304 – 478 Hz) indicates the activation of localized vibrations with the dominance of rigid structural elements. The graph does not contain sharp jumps or dips, which is a sign of a stable modal structure and adequate spatial performance of the model.