## 4 Results and Discussions
### Vortex Induced Vibration Response
Hence, the larger term, \(\beta\), will then maximize the amplitude vector, \(y\). In this study, the vibrational amplitude of 19 m/s wind speed generating 75.8 Hz of vortex frequency is the nearest to the model's first natural frequency of 76 Hz, thus giving the largest vibrational amplitude. Referring to Section 4.2 and Table 4, as the resultant vibrational frequency stayed between 20 and 100 Hz only the first 2 natural modes of the structure are observed to be contributing. Displayed in Figure 18 the trend of VIV amplitude to wind speed is a bell curve. Increment in vibrational amplitude occurred with the increment of wind speed until it reached the highest point during 19 m/s wind speed then proceeded to decrease. This phenomenon can well be explained by resonance theory when referred to Table 4. When vortex and vibrational frequency is near to the model's natural frequency, higher vibrational amplitude is being produced. Vortex frequency of 75.758 Hz produced at 19 m/s is almost similar to the model's natural frequency of 76.9 Hz, resonance occur, thus producing highest VIV amplitude with maximum value reaching 2.09 mm and a RMS value of 1.26 mm. Wind speed past 19 m/s showed a decrease in VIV amplitude as the vortex frequency values generated shy away from the model's natural frequency. 25 m/s wind speed having 100 Hz vortex frequency is far away from the model's natural frequency and received less contribution from the vibrational mode hence vibrating at relatively lower VIV amplitude although having a higher level of fluctuating lift force. Figure 18: Graph of vibrational amplitude of the model vs. wind speed. It is noted in this research that vortex frequency is more influential than lift force in affecting the amplitude of vortex induced vibration. Although higher wind speeds of 20, 22.5 and 25 m/s produced larger lift force acting on the flexible PVEH plate, the vibrational amplitude generated was not as high as 19 m/s wind speed because the vortex frequency produced does not resonate with the model's natural frequency. Referring to Figure 18, RMS vibrational amplitude of PVEH plate increased from 19 m/s with 1.26 mm to 20 m/s with 0.633 mm by a margin of 49.76%. Comparison could be made between 20 and 22.5 m/s where 20 m/s wind speed produced VIV with an amplitude of 0.633 mm while 22.5 m/s wind speed only achieved 0.258 mm although the latter applies 0.03 N more lift force. 20 m/s wind speed produced a vortex frequency of 80.808 Hz, which is nearer to the fundamental frequency of 76.9 Hz compared to a 22.5 m/s wind speed with a vortex frequency of 82.418 Hz. 25 m/s wind speed showed slight twisting in structural vibrational pattern compared to 19 m/s wind speed results shown in Figure 19 which is a pure bending mode. This is because the vortex frequency value of 100 Hz from 25 m/s wind speed moved away from the model's fundamental frequency but started approaching the structure's second natural frequency, creating the slight contribution of second vibrational mode or the first twisting mode onto the vibration pattern although the first bending mode is still the dominant vibrational pattern.