## 2 Experimental Methods
### Variation in Damping  
When a spring-mounted triangular prism is acted by the vertical flow force \(F_{\text{fluid}}\), the motion of the prism in the vertical-direction can be expressed as  
\[m\ddot{\mathbf{y}}+c\dot{\mathbf{y}}+K\mathbf{y}=F_{\text{fluid}}\mathbf{\dot{y}} \tag{1}\]  
where \(m\), \(c\) and \(K\) are the mass, the damping coefficient, and the stiffness of the oscillation system, respectively. \(\ddot{\mathbf{y}}\), \(\dot{\mathbf{y}}\) and \(\mathbf{y}\) are the acceleration, the velocity, and the displacement of the prism, respectively. \(\mathbf{\dot{y}}\) is the unit normal vector in the transverse direction. Generally, \(F_{\text{fluid}}\) can be decomposed into viscous and inviscid components [29]. Figure 3: Experimental setup: (**a**) Oscillation system and triangular prism; (**b**) Power take-off system (PTO); (**c**) Load resistance. In this paper, the variation in damping coefficient is implemented by adjusting the load resistance \(R_{\text{L}}\) in the power take-off system (PTO). The PTO has been introduced by [PERSON] [28]. The components of the PTO and the load resistance are illustrated in Figure 3b,c. In the PTO system, the rack is fixed on the transmission, and meshes with gear group to convert the linear oscillatory mechanical motion of the prism in FIM to a rotational oscillatory motion of gear. In addition, the gear group meshes with the gear of the generator to drive the rotor to rotate. When a generator runs, the wire loop, which is cutting across the magnetic induction lines, yields an induction current, resulting in an electromotive force that always resists the motion of the oscillator. As the magnitude of the electromagnetic force depends on the rotational motion of the rotor, which is related to the motion of the prism, the electromagnetic force can be regarded as part of the system damping force. In summary, the motion of the spring-mounted triangular prism with PTO can be simplified as in Figure 4.  
The system damping coefficient \(c\), which is the sum of mechanical damping coefficient \(c_{\text{m}}\) and the electromagnetic damping coefficient \(c_{\text{e}}\), can be expressed as the following equation. \[c=c_{\text{m}}+c_{\text{e}} \tag{2}\]  
The mechanical damping coefficient \(c_{\text{m}}\) is dependent on the mechanical friction in the gears, the PTO system and linear bearings. The electromagnetic damping coefficient \(c_{\text{e}}\), which includes the generator damping coefficient \(c_{\text{gen}}\) and harness damping coefficient \(c_{\text{harm}}\), is dependent on the generator internal resistance \(R_{0}\) and the external load resistance \(R_{\text{L}}\). The expression of \(c_{\text{e}}\) can be written as  
\[c_{\text{e}}=c_{\text{gen}}+c_{\text{harm}}=\frac{\beta^{2}B^{2}l^{2}R_{0}}{ \left(R_{0}+R_{\text{L}}\right)^{2}}+\frac{\beta^{2}B^{2}l^{2}R_{\text{L}}}{ \left(R_{0}+R_{\text{L}}\right)^{2}}=\frac{\beta^{2}B^{2}l^{2}}{R_{0}+R_{ \text{L}}} \tag{3}\]  
where \(B\) is the magnetic flux density, and \(l\) is the length of the wire cutting the magnetic field perpendicularly to the field lines. \(\beta\) is the speed ratio of gear group, which is associated with the radius of the gears and rotor. In order to simplify the following analysis, two dimensionless parameters are introduced for the first time in this paper: the load resistance ratio \(R^{*}\) and the short circuit equivalent damping coefficient \(c_{0}^{*}\). \(R^{*}\) is the ratio of external load resistance \(R_{\text{L}}\) to the inner resistance of the generator \(R_{0}\), which can be expressed as  
\[R^{*}=R_{\text{L}}/R_{0} \tag{4}\]  
\(c_{0}^{*}\) is the ratio of system damping coefficient \(c\) at the short circuit (S/C) case to the mechanical damping coefficient \(c_{\text{m}}\), which can be expressed as  
\[c_{0}^{*}=\left.\frac{c}{c_{\text{m}}}\right|_{R_{\text{L}}=0}=1+\frac{\beta^ {2}B^{2}l^{2}}{c_{\text{m}}R_{0}} \tag{5}\]  
Figure 4: Simple schematic of the spring-mounted triangular prism with PTO in coming flow.