# Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow
## 3 Results and Discussion
### Flow around Two Flexible Plates in Side-by-Side Arrangement  
#### 3.2.1 Coupling Motions and Vortical Structures  
To understand the interaction dynamics between two flexible plates in a uniform flow, we perform the simulations for side-by-side arrangement. According to the results, the flapping behavior of each plate is asymmetrical about its local \(x_{b}\)-axis when the transverse gap distance is small. Meanwhile, the flapping motion of the upper plate is similar to the lower one about the flow domain's center-plane in the \(Z\)-axis direction. For simplicity, the dynamics of the upper plate will be taken for the following description due to their symmetry or similarity. It also should be noted that the following relative flapping amplitude and force coefficient have been scaled by the result of an isolated plate under the same flow condition. Figure 8 plots the relative flapping amplitude _versus_ transverse distance, including (a) at the outer side and (b) at the inner side. As shown in Figure 8a, \(Z_{B,out}\) of the plates under a small aspect ratio (\(AR<1.0\)) increases monastically with the increasing transverse distance. For instance, as \(AR=0.5\), \(Z_{B,out}\) increases smoothly and tends to reach the value 1.0. Obviously, \(Z_{B,out}\) is less than 1.0 when the two plates are placed nearby, which means that the plates' flapping is weakened; here, the largest weakened extent is about 10%. However, as the transverse distance increases, \(Z_{B,out}\) of the plates under a large aspect ratio (\(AR>1.0\)) decreases correspondingly until reaching the lowest point, then starts to increase smoothly. For instance, as \(AR=1.5\), the value of \(Z_{B,out}\) decreases from above the 1.0 level to below the 1.0 level and then starts to increase smoothly. This trend means that the plate's flapping status transits from strengthened to weakened, and the largest varied extent is about 24% and 5%, respectively. Obviously, the wider (higher aspect ratio) plates can achieve better flapping amplification than the longer plates. In other words, the longer plates in the streamwise direction can achieve better flapping weakened performance in the side-by-side configuration. As shown in Figure 8b, the trends of \(Z_{B,in}\) of the plates under a small aspect ratio are similar to the \(Z_{B,out}\). However, the trends of \(Z_{B,in}\) of the plates under a large aspect ratio show some differences. Take \(AR=1.5\) for instance again; as the transverse distance increases, \(Z_{B,in}\) of the plate increases until it reaches the peak. The value of \(Z_{B,in}\) is less than 1.0 when the two plates are placed nearby. Recall that \(Z_{B,out}\) is increasing, and above 1.0 in this regime, it can be inferred that the flapping motions towards the inside are resisted by the advection in the gap domain. The ratio of \(Z_{B,out}\) to \(Z_{B,in}\) is always larger than 1.0, and this value gets higher as the aspect ratio increases, meaning that the gap flow has a stronger influence on the wider plates. Despite the difference in various trends, the plates share the common point that the flapping asymmetry phenomenon tends to disappear as the gap distance increases. Based on a variety of simulations, three distinct coupling modes of the two side-by-side plates are identified depending on the transverse gap distance. Hereafter, the three coupling modes of the plates'  
Figure 8: The relative flapping amplitude _versus_ transverse distance: (**a**) outer side; (**b**) inner side. motion are named as single-plate mode, symmetrical flapping mode and decoupled mode, respectively. To clearly introduce the dynamics and interaction mechanisms of these typical motion modes, the plates at \(AR=1.5\) are taken as examples. According to the computation results, the parameters at \(G_{z}=0.1\), \(G_{z}=3.0\) and \(G_{z}=4.0\) are corresponding to single-plate mode, symmetrical flapping mode and decoupled mode, respectively. The dynamics of these cases are briefly analyzed as follows.