Structures with inertia periodicity present the phenomenon of band gap formation, i.e., the appearance of regions in the frequency spectrum with a higher modal spacing and lower vibration response. Rotating machines can also present such phenomenon when their working elements are mounted periodically along the shaft (longitudinal periodicity). In the present work, this phenomenon in rotating machines is reviewed, and it is shown that band gaps can be moved toward desired locations in the frequency spectrum by mounting the working elements at optimized positions along the shaft. For that, a mathematical model of the rotating machine is correlated to experimental results, and the model is used to optimize the position of the working elements (disks) in the rotor. The optimized rotor is then experimentally tested, and the resultant band gap is measured. The obtained experimental results show that one can indeed tailor the band gaps and move them toward higher or lower frequencies as desired without changing the inertia of the working elements.