## 4 Results and Discussions
### Vortex Induced Vibration Response  
The Strouhal number of the model shown in Table 3 indicated that under high wind speeds, the Strouhal number deviates from the theoretical value calculated by Equation (1). [PERSON] (1949) had mentioned in a proceeding that the theoretical Strouhal number of a model is relevant with a Reynolds number below 10\({}^{4}\)[54]. Therefore, by applying Equation (1), the Strouhal number for a lower Reynolds number of 8.76 \(\times\) 10\({}^{4}\) is 0.89, but as the Reynolds number moves to a value more than  
Figure 16: Graph lift force vs time at 19 m/s. Figure 15: Graph lift force vs. wind speed. 1.81 \(\times\) 10\({}^{5}\), the Strouhal number increases to a range between 0.108 and 0.12. This value is important in predicting the critical velocity generated from a certain frequency using Equation (1). Mentioned in Section 4.5, it is proven in Table 4 that wind speed magnitude contributes proportionally to the vortex and vibrating frequency of the model, as the higher the wind speed velocity, the higher is the vortex frequency induced. This research observed that vibrational frequency of the PVEH plate always locked-in a similar frequency value to the vortex frequency produced from flow separation across the bluff splitter body. This is because a structure will always be affected and synchronized with the surrounding vibrating frequency it came across. The vortex frequency value thus being similar to the vibrational frequency of PVEH plate induced a high impact on the resultant vortex induced vibration amplitude of the PVEH plate. Complete results of tip mesh displacement against time are displayed in Figure 16. In all of the test cases illustrated in Figure 6, the displacement starts from a low and unsteady vibration and reaches a period where the tip displacement value is relatively constant around a range. This is because when vortex is unstable; the starting force due to flow instabilities acting on the PVEH plate is weak and uneven, creating unsteady and smaller tip displacement. From Figure 17a-e, (i.e., 7 to 16 m/s), the tip displacement graph shows non-periodic occurrence after reaching steady condition. This is mostly because the vortex frequency is not near to the natural frequency of the model and the tip displacement is mainly contributed by the fluctuating lift force acting on the PVEH plate. In Figure 17f-h (i.e., 18, 19 and 20 m/s), steady and periodic tip displacement is achieved. This is due to resonance or near resonance phenomena where the vortex frequencies generated by these 3 wind speeds are near to the natural frequency of the model. During resonance, the matched vortex frequency and natural frequency amplifies the tip displacement giving periodic pattern which is purely governed by the damping of the system. Lastly, Figure 17i,j shows a different vibrational curve compared  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Wind Speed (m/s)** & **Resultant Frequency (Hz)** & **Natural Frequency (Hz)** & **Difference (\%)** \\ \hline
7.00 & 20.020 & & \(-\)73.73\% \\
10.00 & 30.303 & & \(-\)60.59\% \\
12.00 & 41.958 & & \(-\)45.44\% \\
14.00 & 50.505 & & \(-\)34.32\% \\
1  
Structural resonance is a phenomenon defined as maximum structural vibration amplitude when the vibrational frequency of the structure lies near or similar to the model's natural frequency. This is because, in terms of pure structural dynamics, the local amplitude vector can be expressed as:  
\[\{y(t)\}=\ \sum\{\Phi\}_{r}\{\Phi\}_{r}^{T}\{F\}\beta\cos(\omega t-\theta) \tag{22}\]  
where \(\Phi_{r}\) is the normalized mode shape or the eigenvector of the mode, \(\sigma_{r}\) is the decay rate and \(\beta\) is the magnification factor which can be expressed as:  
\[\beta=\ 1/\sqrt{\left(\omega_{o}^{2}-\omega^{2}\right)^{2}+\left(2\sigma_{r} \omega\right)^{2}} \tag{23}\]  
This explains that when a vortex frequency is near to the model's natural frequency the term \(\omega_{o}^{2}-\omega^{2}\) in Equation (23) is being eliminated, producing the largest amount of magnification.