*3.3. Structural Dynamic Characteristics*

The first eight orders of vibration modes simulated and analyzed by the finite element model are shown in Figure 4. The natural frequency and participating mass ratios in the main directions are shown in Table 1. It can be seen from the model analysis that the first-order vibration mode demonstrates the torsion of the middle ring cable, the second one as the torsion of the inner and outer ring cables, the third as the torsion of the inner ring cable, the fourth as the antisymmetric vertical vibration of the whole roof along the short span, the fifth as the antisymmetric vertical vibration of the whole roof along the long span, the sixth as the symmetric vertical vibration of the whole roof along 45 degree, the seventh as the outer vibration of the south outer ring cables, and the eighth as the coupling of the translational motion and antisymmetric vibration of roof along the long-span direction. Therefore, the first three vibration modes are dominated by the torsional deformation of square ring cables while the last five ones are mainly the overall roof plane vibration and antisymmetric vibration.

**Figure 4.** Schematic diagram of the first eight-order vibration modes. (**a**) First-order; (**b**) second-order; (**c**) third-order; (**d**) fourth-order; (**e**)fifth-order; (**f**) sixth-order; (**g**) seventh-order; (**h**) eighth-order.

