PSI - Issue 81

Mykhailo Hud et al. / Procedia Structural Integrity 81 (2026) 486–492

491

The graph (Fig. 9) shows the change in the natural frequencies of the structure depending on the mode number and illustrates the gradual development of the modal pattern. Initially, the observed frequencies ranged narrowly from 1.352 to 1.355 Hz. These correspond to low-frequency global vibration modes, where deformations have the capacity to affect a significant proportion of the structure. The frequencies then increase smoothly, from 2.111 up to 7.994 Hz, reflecting a gradual rise in the system's stiffness and a transition to more complex mid-frequency deformation modes. The highest frequencies, within the range of 12.179 and 12.578 Hz, correspond to localised high-energy vibration modes, characterised by concentrated deformations occurring in individual elements or limited regions of the frame. Absence of sudden drops or irregular changes in the spectrum is indicative of the stability of the modal structure.

Fig 10. First form oscillations of balcony frame model

Basic frame model

1 opening frame model Balcony frame model

10 12 14

2 opening frame model

0 2 4 6 8

Frequency (Hz)

1

2

3

4

5

6

7

8

9 10 11 12

Mode

Basic frame model 1.38 3 3.275 3.275 3.354 3.457 3.554 3.566 3.61 3.637 3.669 4.533 1 opening frame model 1.331 1.342 2.16 4.276 4.309 6.859 8.003 8.058 12.584 12.728 12.834 2 opening frame model 1.294 1.328 2.137 4.178 4.273 6.809 7.879 8.02 12.572 12.644 12.808 Balcony frame model 1.352 1.355 2.111 4.321 4.331 6.703 7.977 7.994 12.179 12.578

Fig 11. Combined frequency graph

The combined graph (Fig. 11) clearly shows the division of models into two groups: flexible (Basic frame model) and rigid (1 opening frame model, 2 opening frame model, Balcony frame model). Low-frequency vibration modes dominate in the first group. The second group, on the other hand, is characterized by high modal frequencies. Despite the outward similarity in the structural diagrams of the models, their dynamic behaviour demonstrates discrepancies in their spatial operation. The basic frame model is distinguished by its notably low range of natural frequencies, which extends only up to 4.53 Hz. In contrast, the models with one opening, two openings, and balconies have much higher frequencies, extending up to 12.6 – 12.8 Hz. Despite the increased stiffness, the mid- and high-frequency portions of the spectra for these three models are very similar, suggesting that these changes do not significantly affect the dynamic properties. It is also noteworthy that, in all three of the "stiffer" models, the high-frequency modes are concentrated within a narrow range.