PSI - Issue 73

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

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As can be seen from the results in Eqs. (9) and (10), if we increase the total weight of the structure, the value of the first natural frequency will also increase. This fact is important in terms of resonance, because excitation of the higher frequencies is usually more energy intensive. 3.4. Mode shapes of MRF structures The procedure described in chapter 2 allows the determination of the mode shapes of structures. For example, for the MRF structure with five floors and five columns on each floor, which is shown in Fig. 1, we can determine up to 210 values of natural frequencies and mode shapes. Figure 5 shows the mode shapes corresponding to the natural frequencies 185.95 rad/s and 392.66 rad/s. In the first case, the structure oscillates in the horizontal direction. In the second case, also in the vertical direction.

(b)

(a)

Fig. 5. (a) Mode shape for ω n = 185.95 rad/s; (b) mode shape for ω n = 392.66 rad/s.

4. Conclusions The study deals with the influence of the moment-resisting frame (MRF) structure parameters on its natural frequencies. Specifically, it deals with the influence of the number of floors of the MFR structure, the influence of the number of columns per floor, and the influence of its total weight. To determine the natural frequencies, a computational model was created in which each element (column or beam) was divided into two parts, and each joint and the center of the element has three degrees of freedom. The stiffness constant method and numerical solution were used. It was found that if the MRF structure consists of the elements with the constant cross-section and the same material, the value of the first natural frequency decreases with the inverse value of the number of floors, while it is minimally dependent on the number of columns in each floor. To verify this, a model with a single degree of freedom was created to determine the first natural frequency, where this is evident from the equation for its determination. The paper presents the solution of the frame structure only as a planar structure. If we were to solve the problem as a spatial one, in real structures where there are more columns on one floor, the overall lateral stiffness of the structure increases. Each column contributes to the structure's ability to withstand horizontal loads because it transfers part of these forces to the foundations. More columns mean that these forces are distributed over more vertical elements, which reduces the deformation of the entire structure under horizontal loads. This higher lateral stiffness has a direct impact on the dynamic behavior of the structure, especially on its natural frequency of oscillation. Since a structure with higher stiffness is "harder," its natural frequency tends to be slightly higher. Furthermore, the dependence of the natural frequency on the total weight of the MRF structure was studied. At first, the weight was increased by changing the material. By increasing the modulus of elasticity, the stiffness of the structure increased. As expected, it was found that with increasing weight, i.e. stiffness, the value of the first natural frequency also increases.