# Key Action Mechanisms of Intentional Mistuning
## 4 Beyond Alternate Mistuning Pattern  
Rotor B has \(N=21\) sectors and is shown in Figure 10. The frequency versus nodal diameter (ND) diagram for the tuned modes is plotted in Figure 11, with the \(EO=8\) forcing of the first modal family indicated. We are now to design an intentional mistuning pattern for rotor B, and validate its effectiveness computing the forced response for 50 random mistuning distributions, with zero average and maximum amplitude 4%, and with the material damping is set to \(\xi=10^{-2}\). In order to design an effective intentional mistuning pattern for rotor B, we look at the elastic coupling influence coefficients for the first modal family presented in Figure 12.  
In this case the coupling coefficients \(a_{1}\) and \(a_{2}\) have both a value that is not negligible as compared to the material damping \(\xi=0.01\). Following the AMM theory, an effective intentional mistuning pattern should separate one blade from its two adjacent ones in order to remove the effect of the coupling induced by the coefficients \(a_{1}\) and \(a_{2}\). The intentional mistuning pattern selected is then \([1,0,-1,\ldots,1,0,-1]\). The resulting maximum vibration amplitude for increasing intentional mistuning amplitude is shown in Figure 13.  
Figure 11: Rotor B natural vibration frequencies. Red thick line indicates the forcing case considered with engine order \(EO=8\). Figure 10: Rotor B with 21 blades and approximately 3600 DOF per sector: (**a**) Blisk model. (**b**) Sector mesh. Again, the intentional mistuning pattern is effective: it clearly reduces the vibration amplification and the sensitivity to random mistuning. This pattern is less effective than the alternate pattern for Rotor A (see Figure 5) because: (i) the difference in terms of intentional mistuning between adjacent blades was \(2 Aim\) for the alternate pattern and now is smaller, only \(Aim\), and (ii) the remaining coupling coefficients after applying the intentional mistuning pattern have now higher amplitude (compare \(a_{3}\) in Figure 12 with \(a_{2}\) in Figure 4). Figure 12: (**Top**): relative frequency deviations for the first modal family of Rotor B. (**Bottom**): corresponding influence coefficients. Figure 13: Maximum vibration amplitude for increasing intentional mistuning amplitude for 50 random mistuning patterns. Rotor B, \([1,0,-1,\ldots,1,0,-1]\) pattern, \(\xi=10^{-2}\). The frequency sweeps corresponding to the random pattern marked with a thick line in Figure 13 are shown in Figure 14. The main difference with the case of the alternate mistuning pattern is that, for large intentional mistuning, the resonance curve is now split into three peaks, and the blade displacement at the maximum shows larger motion in one blade out of every three, indicating that there are three types of blades decoupled by the intentional mistuning pattern. In order to evidence again the importance of the relative value of the damping compared to the remaining coupling coefficient \(a_{3}\), a new set of forced response simulations is performed on Rotor B leaving unchanged all parameters except for the value of the material  
Figure 14: Frequency sweep and (inset) blade displacement at the maximum (black line corresponds to the tuned amplitude), for \(Aim=0\%\) (**top**), \(Aim=5\%\) (**middle**), and \(Aim=10\%\) (**bottom**). Rotor B, \([1,0,-1,\ldots,1,0,-1]\) pattern, \(\xi=10^{-2}\). damping that is reduced to \(\xi=10^{-3}\). Note that the material damping is now comparable to the remaining coupling coefficient \(a_{3}\) (see Figure 12), and, therefore, according to the AMM theory, the intentional mistuning pattern is not necessarily going to have any beneficial effects in this case. The vibration amplitude for this case with reduced material damping is shown in Figure 15. No clear trend of vibration amplitude reduction can be appreciated, and the sensitivity to random mistuning is now much higher than in the previous simulations with larger material damping (Figure 13).