Practical applications of singular value decomposition in rotordynamics

Singular value decomposition (SVD) is used extensively in the controls community to examine the dynamic behavior of systems. SVD is one component of linear systems theory that has developed into a very mature mathematical tool for assessing systems. One objective of this paper is to illustrate the manner in which that large base of analysis can be brought to bear on both classical and emerging rotordynamics problems. This paper reviews the mathematical fundamentals of SVD and addresses its physical implications with respect to rotordynamics. To illustrate these physical concepts, simple rotor systems are examined in terms of forced response and stability margin characteristics. Additional examples are presented in which SVD is applied to more complex rotor systems for balancing, model reconciliation, and model reduction objectives.