# 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
It can be observed that the spanwise deformation still exists in this coupling flapping mode and keeps symmetrical about the flow domain's center-plane in the \(Y\)-axis direction. As shown in Figure 13b, the trailing edge's mid-point shows an \"8\" shape trajectory from the side view, as well. Generally, the deformation of the lower plate in this coupling mode is similar to that of an isolated one. Figure 14 shows the time evolutions of the vortical structures of two side-by-side flapping plates at \(G_{z}=3.0\). The instants \(t_{0}\sim t_{3}\) in the figure are equal to those in Figure 12. As the upper plate moves downwards (from \(t_{0}\) to \(t_{2}\)), a counter-clockwise vortex (labeled V2) forms on the under surface and gradually separates from the trailing edge. During the same time, the lower plate moves upwards, and a clockwise vortex (labeled V1) forms on the upper surface and gradually separates. It is observed the fully-developed vortex shed from one plate will collide with that from the other one. This collision only occurs in the domain away from the trailing edges, so the influence to the flapping motion's symmetrical characteristic is weak. However, this collision between the opposite vortex will weaken the strength of the separation flow streamwise, then lead to the phenomenon of drag reduction. Considering that the flapping motion and vortex pattern of the plates are symmetrical, we name this coupling status the symmetrical flapping mode. Figure 12: Time evolutions of the transverse displacements of points \(B_{1}\) and \(B_{2}\) at \(G_{z}=3.0\). Figure 13: Envelops of the upper flapping plate at \(G_{z}=3.0\): (a) axonometric view; (b) side view. In the decoupled flapping mode, the two plates are flapping in phase, and two rows of vortex with the same rotating direction exist in the wake. Figure 15 shows the time evolutions of the transverse displacements of points \(B_{1}\) and \(B_{2}\) at \(G_{z}=4.0\). As shown in the figure, the two plates flap synchronously with the same phase. Meanwhile, the two plates' flapping motions share equivalent frequency and amplitude. Obviously, the two periodical displacement curves almost overlap. Regarding the value of displacement, the flapping motion of each plate is symmetrical about its local \(x_{b}\)-axis. The envelops of the upper flapping plate at \(G_{z}=4.0\) are also similar to those of an isolated one (see Figure 3). Figure 16 shows the time evolutions of the vortical structures of two side-by-side flapping plates at \(G_{z}=4.0\). The instants \(t_{0}\sim t_{3}\) in the figure are equal to those in Figure 15. As the upper plate moves downwards (from \(t_{0}\) to \(t_{2}\)), a counter-clockwise vortex (labeled V2) forms on the under surface and gradually separates from the trailing edge. During the same time, the lower plate moves downwards,  
Figure 9.0 Time evolutions of the vortical structures of two side-by-side flapping plates at \(G_{z}=3.0\). Figure 9.1 Time evolutions of the transverse displacements of points \(B_{1}\) and \(B_{2}\) at \(G_{z}=4.0\). as well, and a counter-clockwise vortex (labeled V1) also forms on the under surface and gradually separates from its trailing edge. The two vortexes generated in one-half cycle keep independent without obvious collisions or other interactions. Generally, the flapping motion and vortex pattern of each plate are extremely similar to each other, so it seems like there does not exists any coupling behavior between them. Hence, this coupling status is called the decoupled mode. From the discussions above, it is obvious that the transverse gap distance can evidently change the flapping dynamics and coupling modes of the two side-by-side flexible plates. The interactions between the two plates are decreasing with the increasing gap distance. According to the characteristics of flapping motion and fluid pattern obtained in the present study, three typical wake modes in such plates' configuration are classified.