A NUMERICAL TECHNIQUE FOR NONLINEAR EIGENVALUE EQUATIONS WITH COMPLEX ROOTS AND ITS APPLICATION TO FLUIDELASTIC VIBRATION

摘要

A sophisticated analytical model for fluidelastic vibration introduces the equations of fluid motion in addition to the customary equations for structural motion. This results in a set of nonlinear eigenvalue equations with complex roots. The standard methods for eigenvalue and eigenvector extraction are not applicable mainly because of non-proportional damping and the dependency of the dynamic characteristics of the fluid-structure system on the flow velocity. This paper presents a numerical technique for solving nonlinear eigenvalue equations with complex roots. A set of reduced homogeneous equations, which resemble the linear eigenvalue equations of a system with non-proportional damping, are first derived. These equations are then solved for the true eigenvalues and eigenvectors by using a numerical iteration technique. An algorithm has been developed to carry out the iteration process.