Fixed Axis Rotation And Base Excitation Of The Flexible Beam Under The Combined Effects Of Nonlinear Dynamical Behavior Research

In this thesis, a set of nonlinear dynamic governing equations is established by using Kane's method for the flexible slender beams undergoing a large planar motion, with the nonlinearities of both geometrical and inertial types taken into consideration. Based on these equations, the flexible beams under both rotation and parametric excitations are mainly concerned with, and the nonlinear dynamic equations of their lateral vibrations are derived.Many of the possible nonlinear dynamic behaviors of the beams are systematically investigated, and the method of multiple scales combined with the Cartesian transformation is used to solve directly the nonlinear differential equations. The frequency-response curves of variously supported beams are given according to the different parameters such as rotating speed, exciting amplitude, and damping coefficients. The nonlinear dynamic phenomenon studied in this thesis include the secondary resonance and their stabilities under the external excitations without internal resonance, the primary resonance and their stabilities under the external excitations without internal resonance, the principal parametric resonance and their stabilities under the parametric excitations without internal resonance, the principal parametric resonance with 3:1 internal resonance and their stabilities, the primary resonance with 3:1 internal resonance and their stabilities, the principal parametric resonance combined with the primary resonance and 2:1 internal resonance and their stabilities.This thesis enables one to gain an insight into the inherent nonlinear dynamics of the flexible beams under both rotation and parametric excitation, and the numerously complicated nonlinear dynamic behaviors of the beams. It also offers theoretic references for relevant experiments.