PSI - Issue 37

Rogério Lopes et al. / Procedia Structural Integrity 37 (2022) 73–80 R. F. Lopes et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4. Frequency motion of vertical translation and dive-rise. 3 = 2 1 √ 4 = 1,154 ; 2 = 2 1 √ 2 /2 ℎ 2 /12 = 0,982

(10)

2. Numerical analysis So far, the analytical model has been presented, this section devotes to the numerical model. The bus is considered in the parked mode and the natural frequencies will be achieved considering that the wind hits its side at different velocities. Considering the status of no wind effects, a comparison is drawn with the analytical model for the validation purpose. The numerical analysis is performed through Finite Element Method (FEM) formulations simulated in ABAQUS. Regarding the Finite Element (FE) mesh, a convergence study on different mesh densities (identified as coarse, medium and fine mesh) was carried out on TET elements and Table 2 presents the number of nodes and elements. Fig. 5-a) shows the FE mesh with the medium size, the interactions between tires and batteries are demonstrated in Fig. 5-b). Besides, Fig. 5-c) depicts the front and rear regions where the wind hits. Besides, in order to represent the batteries and passengers ’ weight, an inertial interaction is used.

a) c) Fig. 5. a) FE mesh, TET and medium size, b) FE interactions and connectors and c) FE affected lateral area (red – front and yellow - rear) b)

Table 2. TET mesh characteristics for different density mesh (coarse, medium and fine).

Coarse

Medium

Fine

FE Mesh

Number of nodes

36812

172142

884167

Number of elements 620547 The numerical analyses were performed and the results have been obtained. Table 3 reports the numerical solutions on frequencies obtained for = 1. . .6 for different FE meshes. It is feasible to conclude that there is a faster stabilization on the results for the coarser mesh. The results were acquired considering that the wind impacts the lateral side, both at the front and at the rear area at the velocity of = 50 /ℎ . It can be inferred that the natural frequencies tend to be greater in the case if the wind mainly hits the rear section of the bus. However, further results will be obtained and presented for the medium FE mesh. Therefore, Fig. 6 shows the distribution of the displacement amplitude obtained for all natural frequencies in the presence of the wind with the velocity of = 50 /ℎ at rear area. It must be mentioned that the bus is with null capacity. Further studies were carried out at different velocities, with full and null bus capacity. Table 4 reports the obtained results. A closer look to the results, it can be implied that the mass increase plays the greatest contribution in reduction 22657 116291