COMPUTATION AROUND THE CRITICAL FREQUENCY

Let ] і і+і ] the critical frequency interval, which correspond to the maximal value of the /supper bound (namely [9.93 rad/s, 10.00 rad/s]). When choosing as a frequency gridding a few points between і and Wj+i, it is interesting to point out that the same result is obtained with all three methods. The lower bound is 1.966 and the critical frequency is 9.95 rad/s.

CONCLUSION

Two different cases are to be considered: if the method of subsection

5.1 has been already applied or if our physical knowledge of the problem enables to predict the frequency domains corresponding to the peaks on the fi plot, methods (1) or (2) are the most suitable ones, since they give good results while being very simple to implement. Otherwise, if no guess of the critical frequency domains is available, method (3) is especially attractive, since it seemingly enables to detect the peaks on the і plot, even when using a rough frequency gridding (at least in the case of the example). Moreover, remember that the improved algorithm of subsection 5.2 assumes that a t1 lower bound of good quality is a priori available. When applying method (3) on a rough frequency gridding, such a lower bound may be obtained, and the associated computational burden remains reasonable.