Modal analysis of periodically time-varying linear rotor systems

General rotor systems possess both stationary and rotating asymmetric properties, whose equation of motion is characterized by the presence of periodically time-varying parameters with the period of half the rotation. This paper takes two different approaches to develop the complex modal analysis method for periodically time-varying linear rotor systems: one approach by employing Floquet theory and another by coordinate transformation. The first approach, based on decomposition of state transition matrix, leads to the periodically time-varying eigensolutions, whereas the second approach transforms the finite order time-varying matrix equation into an equivalent infinite order time-invariant linear equation by introducing modulated coordinates, leading to an infinite set of constant eigensolutions. The relations between the eigensolutions obtained by two different approaches are derived and their features are compared.