A method is disclosed for analyzing the vibrational characteristics of
rotating devices, such as hard disk drives and jet engines, that are
coupled through bearings to flexible supports. In the method, the
rotating device is discretized, for example, using a mesh suitable for
finite element analysis. The support is also discretized. The natural
frequency of elastic vibration modes for the rotating device is
calculated and the natural frequency of vibration modes for the support
is calculated. The mode shapes are then calculated and a set of modal
basis corresponding to the mode shapes is utilized. Bearing stiffness and
damping matrices are input, and the Lagrangian equations of motion are
integrated numerically in the modal space, to calculate the vibrational
response of the rotating device and support. The modal space results are
then transformed into ordinary space. The vibrational analysis may be
used to design devices having desired vibrational characteristics.