PSI - Issue 59

Mykhailo Hud et al. / Procedia Structural Integrity 59 (2024) 687–691 Mykhailo Hud et al. / Structural Integrity Procedia 00 (2019) 000 – 000

689

3

Table 1. Frequencies of natural oscillations without reinforcement of columns.

Frequency

Period, s

Distribution coefficient

Modal mass

N Own witnesses

Rad/S

Hz

В%

В%

1 2 3 4 5 6 7 8 9

0.02

47.26

7.52

0.13

0.29 0.16

42.47 42.47 12.27 54.74

0.007 0.007

130.45 134.81 341.65 348.77 451.56 459.31 514.32 550.05 746.13 798.42 827.77 962.47 991.19 1006.52 1084.77 1150.58 1210.86 1296.03 1312.61 1382.53 1489.97 1537.33 1664.40 1705.8 1798.53 1845.56

20.77

0.048 0.046 0.018 0.018 0.013 0.013 0.012 0.011 0.008 0.007 0.007 0.006 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003

21.4

0.0

0.00 1.81 0.00 0.02 0.00 0.00 2.10

54.74 56.56 56.56 56.58 56.58 56.58 58.69 58.69 67.55 67.55 67.55 86.98 87.30 87.57 87.57 88.11 88.11 88.11 88.11 88.53 88.53 88.62 88.62 88.62

0.0029 0.0028 0.0022 0.0021 0.0019 0.0018

54.40 55.53 71.90 73.14 81.89 87.58

0.061

0.0

-0.007

0.0

-0.0

-0.06 -0.00 -0.13 -0.00

10 0.0013 11 0.0012 12 0.0012 13 0.0010 14 0.0010 15 0.0009 16 0.0009 17 0.0008 18 0.0008 19 0.0007 20 0.0007 21 0.0007 22 0.0006 23 0.0006 24 0.0006 25 0.0005 26 0.0005 27 0.0005

118.81 127.13 131.81 153.26 157.83 160.27 172.73 183.21 192.81 206.37 209.01 220.14 237.25 244.79 265.03 271.63 286.39 293.87

0.0

8.85

0.0 0.0

-0.0

0.2

19.20 86.76

0.02 0.02 0.02

0.22 0.32 0.26 0.00 0.54

0.0

-0.03

0.0 0.0 0.0

0.

0.0 0.0

0.02

0.42 0.00 0.08 0.00 0.00

0.0

0.01

0.0 0.0

The frequency range varies between 7.5 Hz and 293.87 Hz. Modes 1 to 5 are the most dangerous. These are the frequencies that may cause resonance with industrial equipment and seismic activity. In addition, a visual indication of the shape of the vibrations has been established (Figs. 2, 3).

Table 2. Frequencies of natural oscillations with reinforcement of columns.

Frequency

Period, s Distribution coefficient

Modal mass

N Own witnesses

Rad/S

Hz

В%

В%

1 2 3 4

0.01

85.11

13.55 26.76 26.83 69.58

0.073 0.037 0.037 0.014

0.37 0.15

35.19

35.19 41.43 41.43 41.44

0.005 0.005 0.002

168.06 168.55 437.00

6.24

-0.004 -0.005

0.005 0.006