## 6 Conclusions  
The soft galloping (SG) and hard galloping (HG) of spring-mounted triangular prisms with \(D=10\) cm and \(L\approx 0.9\) m in water flow were investigated experimentally. A power take-off system (PTO), a spring system, additional weights, and different triangular prisms were introduced to achieve the variations in damping coefficient \(c\), system stiffness \(K\), oscillation mass \(m\) and section aspect ratio \(\alpha\), respectively. Corresponding parameters related to the experimental setup were then deduced and verified by free-decay tests. Based on the experimental setup, the complete SG and HG responses of triangular prisms were exhibited and analyzed. The evolution of the oscillation mode of prisms by varying \(c\), \(K\), \(m\), and \(\alpha\) were revealed afterwards. Based on numerous experimental results, the reason for self-excited galloping was explained and the occurrence conditions of SG and HG were demonstrated. The following conclusions can be drawn from the present paper. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\alpha\) & \(m_{\text{d}}\)/kg & \(K\)/N\(\cdot\)m\({}^{-1}\) & \(m\)/kg & \(c_{\text{c-cal}}\)/N\(\cdot\)m\(\cdot\)s\({}^{-1}\) & \(c_{\text{c-mea}}\)/N\(\cdot\)m\(  
1. In an oscillation system with PTO, the damping coefficient \(c\) is a function of mechanical damping coefficient \(c_{\mathrm{m}}\), short-circuit equivalent damping coefficient \(c_{0}^{*}\) and load resistance ratio \(R^{*}\). Among them, \(c_{\mathrm{m}}\) and \(c_{0}^{*}\) are the internal factors which are dependent on the oscillation system, \(R^{*}\) is the external factor which is dependent on the external load resistance \(R_{L}\). For fixed-magnetic PTO, \(c_{\mathrm{m}}\) and \(c_{0}^{*}\) remain constant; \(c\) is only related to \(R^{*}\). As \(R^{*}\) increases, \(c\) gradually decreases and then levels off at \(c_{\mathrm{m}}\). 2. Complete soft galloping (SG) responses: The present paper proves that the vortex-induced vibration (VIV) lower branch can also be observed in the SG response by decreasing the flow velocity in addition to the VIV initial branch, VIV-galloping transition branch and developed galloping branch. In the complete SG responses, a self-excited region exists. When \(U_{r}\) is in the self-excited region, the triangular prism can be self-initiated from VIV to galloping, regardless of velocity increase or decrease. 3. Complete hard galloping (HG) responses: VIV branches, which consist of the initial, the upper and the lower branch are complete. However, the VIV-galloping transition branch disappears and the galloping branch is incomplete. There is no self-excited region: instead, there is critical velocity (CV). The triangular prism cannot be self-initiated from VIV to galloping in any cases, but when \(U_{r}\) is beyond CV, galloping can be initiated by appropriate external excitation. 4. Complete critical galloping (CG) responses: CG is the critical oscillation mode between SG and HG. In the responses, the VIV branches and the galloping branch are all complete and intersect at a specific flow velocity (For equilateral triangular prism, \(U_{r}\approx 9\)). Although the self-excited region cannot be observed, the prism can also be self-initiated from VIV to galloping only at the specific flow velocity. 5. Evolution of oscillation mode: As \(c\) and \(m\) increase, or \(K\) and \(\alpha\) decrease, the oscillation mode of a triangular prism gradually transitions from SG to CG, continues to HG, and ends in VIV. The VIV branches, especially the upper branch, gradually become complete while the galloping branches including the VIV-galloping transition branch gradually become incomplete. Meanwhile, the self-excited region narrows and gradually disappears. The critical velocity (CV) appears and gradually increases. As a result, the ability to be excited (self and external) from VIV to galloping is continuously weakened. 6. The amplitude in VIV branches is the direct reason for the onset of the galloping in SG response.