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

696

5

oscillations. Instead, there are triple forms of natural oscillations. Just as in the previous scenario, as the number of modes increases, the natural frequency increases. Table 4 shows the numerical values of the natural oscillation frequencies of the third stage of the research.

Table 4. Numerical data of natural frequencies when loading 7-9 floors.

Frequency

Modal mass

Distribution coefficient

Own witnesses

Period, s

N

Rad/S 14.81 29.43 38.23 51.11 57.30 86.22 90.14 91.82 94.53 103.63

Hz

В%

В%

1 2 3 4 5 6 7 8 9

0.06 0.03 0.02 0.01 0.01 0.01 0.01 0.01 0.01

2.35 4.68 6.08 8.13 9.12

0.42 0.21 0.16 0.12 0.10

8.09 0.60 7.19

49.61

49.61 49.89 89.06 89.06 89.06 89.06 89.11 89.21 90.24 90.24

0.27

39.17

0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 1.0 0.0

13.72 14.35 14.62 15.05 16.50

0.072 0.069 0.068 0.066 0.060

0.25 0.34 1.17

10

0.009

-0.004

When the upper floors are loaded, which corresponds to the third stage of the study, a decrease in the number of modes to 10 is observed. However, the frequency range has increased and is in the range from 14.81 Hz to 103.6 Hz. It is important to note that the presence of paired forms of natural oscillations is not clearly observed. However, the 7th and 8th modes are quite close in terms of their values and can be considered as paired. 4. Conclusion As a result of finite-element modelling, the natural vibration frequencies of a multi-storey building with a reinforced concrete frame were obtained. Four modelling stages were carried out. At stage 0, the parameters of natural vibrations were determined without taking into account the uneven distribution of loads. At the first stage, additional loads were applied on floors 1-3, at the 2nd stage on floors 4-6, and at the 3rd stage on floors 7-9. It was found that the lowest values of vibrations would be when the load was distributed on floors 7-9. At stages 1 and 2, the frequencies are almost the same, but at stage 3, the number of modes increased. References Avramov, K. V., Mikhlin, Y. V., Kurilov, E., 2007. Asymptotic analysis of nonlinear dynamics of simply supported cylindrical shells. Nonlinear Dyn. 47. Bardell, N.S., Dunsdon, J.M., Langley, R.S., 1997. On the free vibration of completely free, open, cylindrically curved, isotropic shell panels. J Sound Vib. 207. Iasnii, V., 2020. Technique and some study results of shape memory alloy-based damping device functional parameters. Scientific Journal of TNTU 97(1), 37 – 44. Pellicano, F., Avramov, K. V. 2007. Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk. Communicaoins in Nonlinear Science Numerical Simulation 12(4), 496-518. Pradyumna, S., Bandyopadhyay, J.N., 2008. Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation. Journal of Vibration and Acoust. 318(1), 176-192. Yasniy, P.V., Mykhailyshyn, M.S., Pyndus, Y.I., Hud, M., 2020. Numerical Analysis of Natural Vibrations of Cylindrical Shells Made of Aluminum Alloy. Materials Science 55(1), 502 – 508.