Periodic Motions and Stability Analysis of a Non-linear Rotating Beam Subjected to Torsional Excitation.

摘要

The periodic motions and stability of a nonlinear rotating beam subjected to a torsional excitation is investigated in this thesis. Both quadratic and cubic geometric stiffening nonlinearities are retained in the equation of motion, and the reduced model is obtained via the Galerkin method. Saddle-node bifurcations and Hopf bifurcations of the Period-1 motions of the model were obtained via the high order harmonic balance method. The period-2 and period-4 solutions, which are emanated from the period-1 and period-2 motions, respectively, are obtained by the combined implementation of the harmonic balance method, Floquet theory, and Discrete Fourier Transform (DFT). Stabilities are detected by Floquet theory. Stable and unstable periodic motions are illustrated from numerical and analytical solutions. The analytical periodic solutions and their stabilities are verified through numerical simulation.