9 Vibration-Based Approach for Identifying Closely Spaced Modes in Space. . . 85 Fig . 9. 1 Physical model of a space frame structure with circular cross-section and MERO connecting nodes, threaded tension rod in red Mode 1: Torsion 92.40 Hz Mode 2: Lateral bending 126.12 Hz Mode 3: Vertical bending 143.59 Hz Mode 4: Local member bending and torsion 162.44 Hz Mode 5: Local member bending 173.84 Hz Mode 6: Local member bending and vertical bending 191.20 Hz Fig . 9. 2 First six numerical mode shapes with their corresponding frequencies Table 9.1 Quantification of percentages of axial and bending strain energies to the total modal strain energy of the first six modes Type of vibration Mode Axial modal strain energy [%] Bending modal strain energy [%] Local Globa l 1 90.7 5.9 x 2 93.3 4.5 x 3 85.3 13.1 x 4 5.3 75.7 x 5 2.2 62.5 x 6 47.3 43.7 x it was decided to simulate free-free support conditions what has also been taken into account, respectively, in the numerical model. Figure 9.2 shows the first six mode shapes of the numerical model with their frequencies. The numerical results show two types of modes indication: both global and local vibrations in conjunction with the results presented in [5]. A mode shape is considered as global if the complete structure is deforming in a way comparable to a continuum structure. For instance, the first three mode shapes in Fig. 9.2 are classified as global: torsion, lateral bending, and vertical bending. In other words, the global displacement is higher than any local member displacement. On the other hand, local modes show member vibrations with no or minimal global deformation. In other words, the deformations of vibrating members are dominating the respective mode shape. Furthermore, it is in some cases difficult to distinguish clearly between only these two types of vibration, as also mentioned in [5]. For example, mode shape six is a combination between global vibration and local member vibration. Considering that the global vibration of a space frame structure, one can conclude that they are related to longitudinal deformations of the members, while in the case of local member vibration, the bending deformation of the members is dominant. Thus, a distinction between these two types of vibration is possible based on the percentage of participation of the axial and bending strain energies to the total modal strain energy of the structure, as illustrated in Table 9.1.
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