## 3 Validation
### Experiment
#### 3.3.2 Experiment 2  
The second experiment is a novel setup designed in the context of this study for dynamic verification of the proposed numerical method. A cable with a 1.272 m length was supported at its ends as illustrated in Figure 10. The distances between the supports in x and y directions were 1.2 m and 0.22 m, respectively. P6 was fixed on the ground while P0 was fixed on a shake table which has a motion in the x-direction. The cable was suspended between these supports and a catenary shape was formed. Coordinates of the initial catenary shape of the cable are given in Table 5. After achieving a stationary catenary shape, two different excitations with the same amplitude of 25 mm and with frequencies of 1.0 and 1.5 Hz were applied to P0 via the shake table. These harmonic motions are referred to as Type1 and Type2, for frequencies 1.0 and 1.5 Hz, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Point ID** & **Unstretched Cable Length Form P0 (m)** & **Coordinates (m)** \\ \hline P1 & 0.212 & (0.187, \(-\)0.127) \\ P2 & 0.424 & (0.371, \(-\)0.223) \\ P3 & 0.636 & (0.573, \(-\)0.283) \\ P4 & 0.848 & (0.782, \(-\)0.306) \\ P5 & 1.060 & (0.989, \(-\)0.288) \\ P6 & 1.272 & (1.200, \(-\)0.220) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Positions of intermediate points of cable in experiment 2. Figure 10: Setup of experiment 2 of (**a**) schematic view and (**b**) real image. The displacement in y direction of P3 was used for convergence analysis. The number of particles was defined as being 2 times the number of spherical weights and half of it. Analyses were repeated for both motion types as seen in Figure 11. Although no significant difference is observed for different numbers of particles for Type1, a noise is seen at about 2.5 s and 4.5 s for Type2. The noise exists for a greater number of particles (121 and 242). Nevertheless, a further analysis was carried out by increasing the number of particles (482). This same noise still occurs, so the number of particles is enough for the convergence analysis. For a greater number of particles, some particles in numerical analysis were in a position where no mass was defined in the experimental setup. Nevertheless, convergence parameter shows similar results for a greater number of particles than 61. In all the simulations, the number of 121 particles was preferred, because each spherical weight in the experiments was represented by an SPH particle. The simulated and measured displacement history of the defined points can be seen in Figures 12 and 13 for Type1 and Type2, respectively. In the figures, black and red continuous lines show the experimental and numerical data, respectively. Due to the harmonic excitations, the cable started to displace. The simulated excitation-driven motion of the cable perfectly matches with the experimental data in terms of the period and amplitude. After the end of excitation-driven motion, oscillations start. The oscillations should end after a while due to friction and damping. A damping term was added to the numerical model for a gradual decrease in oscillations. As expected, numerical oscillations were more regular than experimental ones. Besides, the periods of oscillations were the same for both harmonic motions (Type1 and Type2); it was 0.45 s for numerical analysis and 0.42 s for experimental investigations. Although a perfect match was obtained in the excitation-driven part of the motion of cable, there was a slight difference in the oscillations part as indicated. Additionally, reactions in x and y directions for each support at P0 and P6 are given in Figure 14. There are two verification conditions for a cable in static catenary form. First, the magnitude of reactions in x directions of both supports must be equal for any cable in its catenary action. This condition is verified for both harmonic motions, as seen in Figure 14. Second, the summation of magnitude of reactions in y direction of both supports must be equal to the weight of the hanging cable.