68 Chapter V The Aeroelastic Instability Following the discussion around the effect of fiber angle and crack existence in the dynamic characteristics, the discussion continues to its effect in the aeroelastic instability limit. In this chapter, primarily discuss the aeroelastic behavior due to varying fiber angles, crack existence, and combination between both parameters. This chapter will complete the whole picture of this study due to the relation between varying parameters, dynamic characteristics that discussed in the previous chapter, and the aeroelastic behavior. Moreover, the selected mode shapes in the flutter analysis are only the first four mode shapes which are first bending (1B), second bending (2B), first torsion (1T), and third bending (3B) modes. These mode shapes are selected due to the close proximity of their respective natural frequencies. V.1 The Aeroelastic Limit of ° Undamaged Wing To begin with, the discussion starts with investigating the result of flutter analysis from 0° undamaged wing. The flutter analysis results obtained through computational processes conducted using FEM for the structural domain and DLM to generate the unsteady aerodynamic load. The flutter analysis results presented in two graphs which are velocity versus frequency (U-f) and velocity versus damping ratio (U-g). Technically, in determining the critical flutter speed, U-g graph is used to capture the phenomenon where the damping ratio of the system approaches the structural damping. In this case, the structural damping assumed to be zero. Hence, when the damping ratio of the system reaches zero in the U-g graph, the aeroelastic instability may occurred. Additionally, the U-f graph will be utilized to observe the appearance of mode coupling and divergence. The mode coupling evidenced by the values of frequency of one vibration mode along the velocity adjacent to the other mode. Moreover, the divergence speed presence can be detected when the frequency of vibration mode reaches zero. The flutter analysis results of 0° orientation , which illustrated in Figure V.1, shows that there are instability phenomenon occurred in the range of velocity between 50- 120 m/s. Based on Figure V.1.a, there are several possibilities where the instability may occurred due to the frequency value between 2B and 1T are adjacent to each 69 other approximately around 95-120 m/s. This observed result may indicate the mode coupling that will result in flutter. Additionally, at 110 m/s the frequency of first bending mode reaches 0 Hz, which means the divergence will occur. Furthermore, Figure V.1.b added more information to capture aeroelastic instability phenomenon. At exactly 100 m/s the damping ratio for 1T reaches zero. It means that the system damping ratio exceed the structural damping in this model that would lead to instability phenomenon. This result linearly related with the velocity and frequency graph that previously mentioned in Figure V.1.a that indicates mode coupling in the range of 95-120 m/s. (a) (b) Figure V.1. The Graph of (a) Velocity vs Frequency (b) Velocity vs Damping Ratio from Flutter Analysis 70 Figure V.2. The Mode Swapping Phenomenon Captured in 0° Undamaged Wing Model To provide extensive insight into the flutter analysis due to the mode coupling or swapping, it needs to prove the occurrence of its phenomenon. Figure V.2 is presented to illustrate mode swapping by selecting three velocities from three different region. The first region is before the guessed critical flutter speed, the second region selected in the system damping ratio reaching zero for 1T, and the third region is after the flutter region. The first region which selected at 80 m/s, showing a clear difference between 2B and 1T mode shape. This result indicates that in the 80 m/s, the mode swapping has not happened yet. Subsequently, when the system damping ratio reaches zero at 100 m/s, the 1T mode shape as if mixed with the 2B which proved the appearance of mode swapping. Lastly at 120 m/s, supposedly after the critical speed, the initial 1T transform into 2B and the 2B still mixed with the 1T. Perhaps, until 120 m/s the mode swapping still occurred which means the initial guess of flutter region ranged around 95-120 m/s is true. V.2 The Effect of Fiber Orientations in Aeroelastic Limit After examining the aeroelastic limit in 0° undamaged wing, which is the baseline model in this study, the analyses continue to investigate to the effect of fiber orientation in aeroelastic limit. To reduce the complexity in the process of understanding the aeroelastic instability behavior with respect to fiber orientation, this study started with analyzing its effect on each mode shapes as presented in 71 Figure V.3. This procedure is selected due to the results from dynamic characteristics show that each mode shape showing different pattern. Respectively from the left-side of the figure is U-f and U-g. Figure V.3.a illustrates the effect of fiber orientations in the first bending mode. The U-f graph of the first bending mode shows overlapping results for and 90 + orientations. However, the 60° and 75° orientation showing similarities as well. The pattern of divergence speed fluctuations is quite unique. Started at 0°, the divergence speed is at 110 m/s. Then, the divergence speed increase into 120 m/s at 15° orientation before reduces gradually to 115 m/s at 30° orientation, 100 m/s at 45° orientation, and 85 m/s at 60° and 75° orientation. Afterwards, when the fiber orientation reaches 90°, the pattern as if repeated into 0° again. The U-g graph, which depicted in the right-side, also indicates similar pattern. Furthermore, in the U-f graph of the second bending mode, which presented in the right-side of Figure V.3.b, did not indicate any instability phenomenon. However, the trendline of the frequency reduction can be analyzed. The similarities between and 90 + orientation trendlines also observed in this mode shape. However, unlike the previous pattern for the first bending mode, in this mode shape the trendline of 60° and 75° orientations are different. The order of the frequency reduction trendlines from the least respectively are 75°, 0°, 60°, 15°, 30°, and 45°. Additionally, at the damping ratio graph, depicted in the left-side of Figure V.3.b, showing similar results.