PSI - Issue 81

Mykhailo Hud et al. / Procedia Structural Integrity 81 (2026) 417–421

420

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Frequency (hz)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Mode

Fig 5. Oscillation frequencies for frame option 2

The frequency set under consideration (Fig. 5) is characterised by a stable and gradual increase in values within the range from 0.384 to approximately 1.46 Hz. This transition reflects the natural progression from simpler to more complex vibration modes. Nevertheless, a marked disturbance is discernible in the first and second modes. The observed frequency pattern is consistent with a greater effective stiffness in higher modes, which is typical for the modal behavior of frame systems.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency (hz)

1

2

3

4

5

6

7

8

9

10

11

12

Mode

Fig 6. Oscillation frequencies for frame option 3

The frequency curve, as obtained from the computational data, displays a marked tendency towards a monotonic increase in natural frequency values, with a range from 1.38 Hz for the first mode to 4.53 Hz for the highest observed mode. In the mid range, the frequencies demonstrate a uniform and uninterrupted increase, devoid of any sudden fluctuations or atypical variations, with values remaining within the range of 3.27 – 3.67 Hz. Such behaviour is indicative of the sequential development of increasingly complex geometric vibration configurations within the intermediate modes. As demonstrated in point 3, there is a marked rise in frequency, which reaches 4.53 Hz. This is indicative of a transition in the system towards a state characterised by substantially more complex or localised vibrational forms.