The operation of a rotating machine at critical speeds frequently causes a high level of mechanical vibration, noise and excessive wear. An important objective regarding rotating machinery is either to eliminate major resonances or to avoid operating the equipment at speeds which could induce them.All shaft/bearing systems have a large number of frequencies at which they tend to vibrate. These are the so-called eigenfrequencies or natural frequencies. They are determined by the mass and stiffness distribution of the shaft as well as the location and stiffness of the supporting bearings. Sometimes the compliance of the housing also has a significant influence.Each eigenfrequency is associated with a different vibration mode, or eigenmode. In practice, engineers are mainly concerned with the modes at lower frequencies, because their vibration amplitudes are more pronounced than those at higher frequencies.