PSI - Issue 73

Lenka Koubova et al. / Procedia Structural Integrity 73 (2025) 66–72 Lenka Koubova / Structural Integrity Procedia 00 (2025) 000–000

69

4

3.2. Dependence of the natural frequency on the parameters of the MRF structure Table 1 presents the values of the first natural frequencies depending on the number of floors and the number of columns on each floor. This dependence is also shown in the graph in Fig. 2. The results show that the values of the first natural frequency, at which the structure oscillates horizontally in the first mode shape, are minimally dependent on the number of columns per floor. However, as regards the number of floors, the value of the first natural frequency decreases approximately inversely with the number of floors.

Table 1. 1 st natural frequency ω n 1 . ω n 1 [rad/s]

Number of columns per floor

Number of floors

2

3

4

5

1 2 3 4 5

133.94

123.60

120.16

118.25

61.96 38.91 28.05 21.79

59.96 38.49 28.16 22.13

59.27 38.30 28.22 22.24

58.88 38.30 28.25 22.34

Fig. 2. Dependency of the first natural frequency on the number of floors and the number of columns on each floor.

3.3. Solution using a single degree of freedom model If we solve these MRF structures as a system with one degree of freedom (Fig. 3), we find the following. Let n c be the number of columns per floor and n f be the number of floors; then we can determine the total mass m and stiffness k of the frame structure. = � ∙ ∙ ℎ + ∙ ( − 1) ∙ � ∙ ∙ = [ ∙ ℎ +( − 1) ∙ ] ∙ ∙ ∙ (5) = 1ℎ2 3 ∙ (6) 1 = ∙ 1 → = = 1ℎ2 3 ∙ (7)