## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Rain-Wind-Induced Vibration--Aeroelasticity of the Cable System
#### 3.3.2 Wind Tunnel Studies of Rain-Wind-Induced Vibration  
Due to the obvious challenges associated with full-scale field measurements, many authors have studied RWIVs using wind tunnel tests. There are generally two methodsadopted to simulate rain conditions--the guiding water method [91; 92] and the spraying water method [85; 93; 94]. The former creates the water rivulet by installing a guiding tube on one end of the cable, while the latter simulates raining by spraying water from nozzles. [PERSON] et al. [91] investigated the aerodynamic forces involved in RWIVs by conducting wind tunnel tests on a cable model with a diameter of 350 mm and a length of 1.54 m. Experiments were performed in a closed-circuit wind tunnel, in which the cable model was suspended by a forced vibration system. Two types of surface configurations were considered--a smooth surface and a surface with an artificial upper rivulet attached. The rivulet was an arc-shaped element made of organic glass, which had a radius of 25 mm, a width of 37.6 mm and a height of 8.5 mm. Oscillating motions of the rivulet were taken into account by prescribing rotational motions of the cable. Both aerostatic tests and forced vibration tests were performed on the smooth cable and the cable with the rivulet. Time histories of surface pressure in each test were measured and compared. It was found that the vertical vibration of the cable had a marginal influence on the surface pressure distribution on the cable-rivulet system, whereas oscillations of the upper rivulet significantly amplified the fluctuations on the surface pressure. Additionally, it was found that the mean value of wind pressure was not sensitive to the vibration, indicating that aerodynamic forces extracted using quasi-steady coefficients were not suitable for the study of RWIVs and that the self-excited forces determined using the flutter derivatives of the cable would be a more accurate option. A significant limitation to this work was in treating the upper water rivulet as a solid attachment as this does not reflect its real characteristics and so compromised the reliability of the results. A better approach to simulate the rivulet was used by [PERSON] et al. [93], in which the rivulet was formed by simulating rainfall using a spraying water system. To study the effect of water rivulets on the RWIV, wind tunnel tests on a cable model with a diameter of 160 mm and a testing length of 2 m in an open-circuit wind tunnel were performed, in which the cable model was able to oscillate freely or locked in a fixed position. Characteristics of the water rivulets were extracted from videos captured by the camera installed on the cable model. A comparison was made between the motions of rivulets on the fixed cable and the free-oscillating cable. It was found that motions of the upper rivulet and the cable showed a strongly coupling effect, whereas motions of the lower rivulet appeared to be irrelevant to RWIV. When the cable was vibrating, the upper rivulet had harmonic and uniform oscillations along the longitudinal direction of the cable. It was also found that RWIV at the same wind velocity can have different amplitudes, indicating that the excited system had multiple equilibrium states induced by various initial conditions. The effect of initial conditions on RWIV was further investigated by [PERSON], [PERSON] and [PERSON] [94]. Wind tunnel tests were performed with an identical cable model, rainfall simulation and wind tunnel configurations as in [PERSON] et al. [93]. Initial excitations of different amplitudes were applied to the cable model at the beginning of the wind tunnel tests. Then, mean values of the aerodynamic damping ratio derived from the free oscillation tests were compared. It was found that small variations in the amplitude of the initial excitation led to significant changes in the aerodynamic damping ratio, and the presence of the oscillating upper rivulet always triggered a negative aerodynamic damping ratio.