PSI - Issue 59

Mykhailo Hud et al. / Procedia Structural Integrity 59 (2024) 692–696 Mykhailo Hud et al. / Structural Integrity Procedia 00 (2024) 000 – 000

695

4

The frequency range of the building frame without additional loading is between 29.07 Hz and 100 Hz. As the number of modes increases, the frequency of natural oscillations increases. The waveforms 1, 2, and 3 are not paired. Waveforms 4 to 10 have the same frequencies, and the frequencies of waveforms 11 to 14 are the same. The numerical determinations of the frequencies of natural oscillations at the first stage of research are given in Table 2.

Table 2. Numerical data of natural frequencies when loading 1-3 floors.

Frequency

Modal mass

Distribution coefficient

Own witnesses

Period, s

N

Rad/S 41.03 41.03 45.51 45.51 59.46 59.46 62.67 62.67 91.15 91.15 93.31

Hz

В%

В%

1 2 3 4 5 6 7 8 9

0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01

6.53 6.53 7.24 7.24 9.46 9.46 9.97 9.97

0.15 0.15 0.13 0.13 0.10 0.10 0.10 0.10 0.06 0.06 0.06

-0.013 -0.004

0.0 0.0

0.0 0.0

9.74 1.41

36.98

36.98 37.76 37.76 37.76 37.76 37.76 37.76 37.76 37.76

0.77

0.003 0.005 -0.001 -0.002 0.005 -0.005 -0.003

0.0 0.0

0

0.0 0.0 0.0 0.0

14.51 14.51 14.85

10 11

When the lower floors are loaded, there is a decrease in natural frequency modes from 14 to 11. The frequency range is from 41 Hz to 93 Hz. The presence of paired waveforms is also clearly visible. Also, as the frequency of natural oscillations increases, the oscillation periods decrease, which corresponds to the accepted laws of physics. Just as in the previous scenario, as the number of modes increases, the natural frequency increases. Table 3 contains the numerical values of the natural frequencies of the second stage of the research.

Table 3. Numerical data of natural frequencies when loading 4-6 floors.

Frequency

Modal mass

Distribution coefficient

Own witnesses

Period, s

N

Rad/S 41.03 41.03 41.03 45.51 45.51 45.51 59.46 59.46 59.46 62.67 62.67 62.67

Hz

В%

В%

1 2 3 4 5 6 7 8 9

0.024 0.024 0.024 0.021 0.021 0.021 0.016 0.016 0.016 0.015 0.015 0.015

6.53 6.53 6.53 7.24 7.24 7.24 9.46 9.46 9.46 9.97 9.97 9.98

0.15 0.15 0.15 0.13 0.13 0.13 0.10 0.10 0.10 0.10 0.10 0.10

0.02 -0.03 -0.01 -0.78 12.03 -0.17

0.0 0.0 0.0

0.0 0.0 0.0

0.15

0.15

37.59

37.75 37.76 37.76 37.76 37.76 37.76 37.76 37.76

0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

10 11 12

0.09

0.

0.0

0.0

In contrast to stage 1 of the study, the number of modes increased to 12. However, the frequency range decreased and is in the range from 41 Hz to 62 Hz. Also, unlike stage 2, there is no presence of paired forms of natural