## 5 Result and Discussion
### Impact of Temperature on Modal Parameters in Seeded Crack Specimens  
The impact of temperature for three crack depths 0.25, 0.50, and 1 mm were chosen for this assessment. The experimental procedures are the same for all the crack specimens as those without cracks. The natural frequency for 0.25, 0.5, and 1 mm crack depths are shown in Figures 12-14, respectively. All the graphs show a similar trend of decreasing frequency with the increase in temperature. Moreover, the trend of decaying is lesser at lower temperatures while deeper trends were observed at higher temperatures. This suggested that the material properties deteriorated at higher temperatures, meaning less elastic. These changes in the material properties were associated with the stiffness of the material at different temperatures.  
The rate of heating the specimens had little impact on the fundamental frequency. This research aims to verify this by ramping at 2, 5, and 8 \({}^{\circ}\)C/min for all three crack depths. Thus, the effect of the heating rates was compared for all the specimens as shown in respective figures. It is seen that the analytical and numerical results were comparable to the ramping at 2 \({}^{\circ}\)C/min. Although, this effect is minimal at lower temperatures and more noticeable at higher temperatures. Therefore, this signifies that the rate of heating can have a slight effect on the dynamic response of any mechanical system.  
Figure 11: Modal amplitude for an uncracked beam.  
Figure 10: Natural frequency for an uncracked beam.  
The effect of temperature on modal amplitude is plotted for all the crack depths. The modal behaviour of 0.25, 0.5, and 1 mm crack depths are shown in Figures 15-17, respectively. It was noticed that modal amplitude decreased with the increase in crack depth. The decrease in amplitude was also associated with a rise in temperature. Comparatively, the declining trend of amplitude behaviour for a 1 mm crack depth was more linear than 0.25 and 0.5 mm crack depths. This signified that the increase in crack depth reduced the beam stiffness. Thus, this evidence can be utilized for determining crack depth in structuring health monitoring. It was observed that vibration amplitude was different on all heating rates. The effect of heating rate on amplitude is obvious for higher temperatures. The vibration behaviour of a 0.25 mm crack depth was observed linear till 100 \({}^{\circ}\)C. A nonlinear response for all higher temperature ranges was also observed. Similarly, a 0.5 mm crack depth was observed.  
Figure 14: Natural frequency for a 1 mm crack depth.  
Figure 12: Natural frequency for a 0.25 mm crack depth.  
Figure 13: Natural frequency for a 0.50 mm crack depth.  
depth showed a small drop in vibrating amplitude from 25 to 100 \({}^{\circ}\)C, and then it dropped abruptly. This implied that the specimen loses its stiffness greatly when the temperature goes above 100 \({}^{\circ}\)C. Moreover, a 1 mm crack depth showed a linear response at all values of temperatures. Thus, a 1 mm crack depth was a special case where its stiffness played a bigger role in the vibrating behaviour than the temperature as shown in Figure 17. Heating at 2, 5, and 8 \({}^{\circ}\)C/min appeared to have a similar response but heating at 5 and 8 \({}^{\circ}\)C/min are small in amplitude drop compared to heating at 2 \({}^{\circ}\)C/min. This indicated ramping at 2 \({}^{\circ}\)C/min had accumulated more heat on the beam as it takes a longer duration to heat to the required temperature and through this process softens the material properties. Nevertheless, ramping at 2 \({}^{\circ}\)C/min is in good agreement with the analytical and numerical results. This signified that heating at a lower rate is more accurate for theoretical and experimental vibration testing.  
Figure 16: Modal amplitude for a 0.50 mm crack depth.  
Figure 17: Modal amplitude for a 1 mm crack depth.  
Figure 15: Modal amplitude for a 0.25 mm crack depth.