Frequency response functions of rotating periodically time-varying systems

Differential equations of rotating elastic systems are presented which are described by non-symmetric, periodically time-varying matrices which are caused by non-axisymmetric properties of the shaft and the disc of the rotor. The modal decoupling of the periodic differential equation system by the HILL-transformation is shown and the vibration response of the harmonically excited system is presented. Theoretical wave frequency response functions (WFRFs) are then defined which form the basis for the identification of the modal parameters as function of the rotational frequency of the system. These WFRFs can be determined directly from tests. As an example the theoretical WFRFs of rotating discs are presented in detail.