## 3 Validation
### Experiment
#### 3.3.1 Experiment 1  
This experiment is inspired by the experiments available in the literature. It was first presented by [47], used in [48] and repeated in the study of [49]. It is a basic experiment for the investigation of dynamic motion of cables. In the previous versions of this experiment, the cable was released from the support of a catenary position defined in Figure 5 and the dynamic motion of it was supplied via camera. Snapshots from a camera were given. No additional numerical data were presented. In the research of [47], experimental data were supplied by using the recorded snapshots via camera. However, cable positions were not given in equally spaced time intervals [47]. A numerical solution was also presented with given time intervals. In [48], the experimental data supplied by [47] was used to verify the cable model. Positions of a free-falling cable for specified time intervals were presented as numerical results of that research. The experiment of [PERSON] [47] was repeated in [49]. In that study, configuration of the cable was compared with the experimental snapshots. In this research, time intervals of numerical analysis were supplied, however time instants of experimental snapshots were not presented. A brief discussion of numerical methods used to simulate the free-falling cable is given as follows. In the research of [PERSON] and [PERSON] [48], the finite element method was used with the following assumptions: cables possess only axial stiffness, material is linearly elastic and only small strains are involved. The same assumptions were used in the finite element model of [PERSON] [47] which was called a chain model. [PERSON] et al. [49] also used the finite element method for the cable and Akaike-Iwatani model [50] for wind effect on cable. Notably, none of these studies included the damping effect in their finite element model. Similar to the previous studies conducted with the finite element method, SPH equations are derived with the same assumptions. Since a cable has no stiffness in its transverse direction, either singularity of stiffness matrix or high displacements can be observed. This is the main drawback of finite element models. Proper algorithms should be proposed to deal with this problem as in [6]. The nature of SPH minimizes this type of problem. Figure 5: Initial geometry of the cable in experiment 1 of (**a**) schematic view and (**b**) real image. Initial geometry of the cable was defined as in previous studies mentioned above. A cable with a 1 m length was supported at its ends as illustrated in Figure 5. Supports were placed at the same elevation, and the distance between the supports in x direction was defined as 0.88 m. The cable is supported at end points, P0 and P5. A cable with 95 spherical weights was suspended as defined in Figure 5 and released from P5. Intermediate points were defined through the geometry of the cable with the cable length measured from P0 as given in Table 4 where P5 is the free end. The experiment was repeated in the context of this research to digitize the motion of the cable in detail. Accordingly, the displacements of specified intermediate points throughout the cable are supplied. The main contribution of this experiment is to give the digitized time history of a free-falling cable. In the numerical model, 95 particles were used. Due to the Lagrangian nature of the SPH method, the positions of all the particles were followed. Therefore, the number of particles used in the simulations was taken to be the same as the number of spherical weights, although a convergence analysis was performed and according to the convergence analysis it was found that less particles can be used. Convergence analysis results are given for the following experiment. Figures 6 and 7 show the displacement of intermediate points and the free end. The simulated displacements of intermediate points are close to the experimental data. However, the displacement of the free end is slightly overestimated in SPH.