PSI - Issue 37

Rogério Lopes et al. / Procedia Structural Integrity 37 (2022) 81–88 R. F. Lopes et al./ Structural Integrity Procedia 00 (2019) 000 – 000 5 Since the vertical force, over the axis, was generated by the passenger ’s weight , thus such force contributed to the strain variation in the corresponding direction being higher in the joint section. The logarithmic strain is reached its maximum in the contact between the joint and the trailer as shown in Fig. 4. In addition, high values are also achieved in the area surrounding the rear wheel hub, therefore, this zone is considered as one of the most critical areas in the structure. 85

× 10 −4

Fig. 4. Logarithmic strain in direction. Another important aspect is related to the vertical displacement variation, wherein the structure undergoes a downward displacement depending on the passenger weight. Fig. 5 shows the vertical displacement variation. It is feasible to state that the displacement is not uniform, since the tractor possesses four supports at the wheels, whereas the trailer includes only two. It is possible to quantify the chassis structure deflation in relation to the initial stage when measured at a central section, where the scale factor is five times enlarged. The rear edge undergoes a relative displacement of about 103 ( ). The following analysis corresponds to the natural frequencies vibration, in which this type of analysis led to the identification of various vibration modes of the whole structure. It is remarkable that this multi-body system exhibits an increase in structural instability if it is not adequately damped. Table 3 presents all modes of vibrations i ( = 1, … ,8) obtained from numerical analyses for both bus payload cases: the full and null capacity. It can be inferred that mass increase led to the frequency reduction tending to a rigid body motion. Besides, the modes corresponding to the lowest frequency showed that the articulation reflects the instability. For higher frequencies, the frame bending and twisting deformation modes, directly damaging its integrating members. When external factors bias the frame such as instability of the road, which the suspension receives and transmits this frequency to the frame and therefore it caused amplifying the behavior. The red region represents the area with the greatest amplitude of vibration (displacement) within the range, which are the most critical for both passengers and bus equipment. Notice that the vibrational modes are similar by varying the amplitude of frequency for every case. This behavior is shown in the displacement contour, as presented in Fig. 6. 4 −6.49 −3.93 −1.38 1.18 3.73 6.28 Fig. 5. Vertical displacement caused by the people weight, along the axis, values are in [mm]. Table 3: Natural frequencies in different boundary conditions. Capacity ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Null 0.4817 0.9266 1.3487 1.7553 2.0661 2.6404 2.8368 3.8117 Full 0.0000 0.3901 0.5026 0.9556 1.6653 2.0962 2.4521 2.7186 3.1. Articulation system behavior This section is devoted to the analysis of the articulation system affecting the global behavior of the structure by −10.3 −8.56 −6.85 −5.13 −3.42 −1.71 −9.0 0.00 × 10 −1