Nonlinear Vibration Of A Rectangular Plate Subject To Basement Rotation And Harmonic Excitation

With the nonlinearities of both general geometrical and general inertial types reserved, a set of nonlinear dynamic governing equations for an elastic rectangular plate undergoing a large overall motion is established by using Kane's equation in this thesis. Based on these equations, the plate subject to the basement rotation and harmonic excitation is mainly studied, and the nonlinear dynamic equation of its lateral vibration is derived.Many of the possible nonlinear dynamic behaviors of the plate are systematically investigated, and the method of multiple scales combined with the Cartesian transformation is used directly to solve the nonlinear differential equation. The frequency-response curves of the plate simply supported along its four edges are shown versus the parameters such as rotating speed, excitation amplitude, and modal damping ratio. The nonlinear dynamic phenomena of concern in the thesis include the primary resonance under the external excitations without internal resonance, the principal parametric resonance under the parametric excitations without internal resonance, the secondary resonance under the external excitations without internal resonance, the primary resonance with 1:3 internal resonance, and the principal parametric resonance with 1:3 internal resonance. The study reveals the inherent nonlinear dynamics of the elastic rectangular plate subject to the basement rotation and harmonic excitation.