Modal analysis of periodically time-varying rotor systems using floquet theory and modulated coordinate transformation

Abstract

The objective of this thesis is comprised of two parts such that one is to develop the complete modal analysis of a general rotor system, as a typical case of periodically time-varying rotor systems, and the other is to conduct its application study. 1. Based upon the Floquet theory the complete modal analysis starting from the time domain approach associated with the modulated coordinate is derived. In this process the feature of dFRFs and instability are briefly treated. The coordinate transform method is not only straightforward in formulating the eigenvalue problem associated with constant system matrices of infinite order but also computationally efficient in calculating the eigensolutions and frequency response functions, whereas the Floquet method provides clear physical understanding of the eigenvalues and the corresponding eigenvectors. From the time-domain approach, the infmite inputs-outputs relations are produced in modulated coordinates, on the other hand, the infinite input-single outputs ones are produced and the clusters are more clearly configured in using Floquet theory. From the frequency-domain approach, however, the dFRFs can be handled more conveniently than those in using Floquet theory. In this case, while the modulated coordinate is physically definite in complete set of the modal components for a finite order of the reduced matrix, the Floquet theory is numerically defective in expansion of the modal components, however, mathematically for infinite order of the reduced Hill``s matrix, two methods are identical. On the other hand, in case of time domain, the results of two methods are so close even for a low order of the reduced Hill``s matrix that the identity of the two methods holds in practice by a harmonic modal analysis. Also the relations of modal spaces to those from the modulated coordinates are derived to identify two methods. 2. The modal behavior by the modal strength is also newly investigated in rigorous way. From an equiv...