Publications Details
Stability analysis and modeling of rotating flexible structures
A method is presented for determining the nonlinear stability of undamped flexible structures spinning about a principal axis of inertia. Equations of motion are developed for structures that are free of applied forces and moments. The development makes use of a floating reference frame which follows the overall rigid body motion. Within this frame, elastic deformations are assumed to be given functions of n generalized coordinates. A transformation of variables is devised which shows the equivalence of the equations of motion to a Hamiltonian system with n + 1 degrees of freedom. Using this equivalence, stability criteria are developed based upon the normal form of the Hamiltonian. It is shown that a motion which is spin stable in the linear approximation may be unstable when nonlinear terms are included. A stability analysis of a simple flexible structure is provided to demonstrate the application of the stability criteria. Results from numerical integration of the equations of motion are shown to be consistent with the predictions of the stability analysis. A new method for modeling the dynamics of rotating flexible structures is developed and investigated. The method is similar to conventional assumed displacement (modal) approaches with the addition that quadratic terms are retained in the kinematics of deformation. Retention of these terms is shown to account for the geometric stiffening effects which occur in rotating structures. Computational techniques are developed for the practical implementation of the method. The techniques make use of finite element analysis results, and thus are applicable to a wide variety of structures. Motion studies of specific problems are provided to demonstrate the validity of the method. Excellent agreement is found both with simulations presented in the literature for different approaches and with results from a commercial finite element analysis code. The computational advantages of the method are demonstrated.