文档介绍：南京航空航天大学
硕士学位论文
基础定轴转动与简谐激励下矩形板的非线性振动
姓名:王洪兵
申请学位级别:硕士
专业:一般力学与力学基础
指导教师:胡海岩
20070101
南京航空航天大学硕士学位论文
摘要
首先,本文采用 Kane 方程,并结合假设模态,在保留广义惯性力和广义作
用力中非线性项的情况下,建立了空间大范围运动弹性矩形薄板的面内及横向振
动的非线性动力学控制方程组。在此基础上,以基础定轴转动与简谐激励联合作
用下的弹性矩形薄板为研究对象,引入合理的简化,建立了其横向振动的非线性
动力学方程。
然后,运用多尺度法并结合笛卡尔坐标变换等近似解析的处理方法,较为系
统地研究了矩形薄板可能发生的非线性动力学现象。以四边简支的弹性矩形薄板
为例,分析了弹性矩形薄板发生共振时的幅频响应随转速、基础激励幅值、系统
模态阻尼比等相关参数的变化规律。具体包括:板在不发生内共振前提下的外激
励主共振、参数激励主共振、外激励次共振以及板在发生 1:3 内共振情况下的
外激励主共振、参数激励主共振。通过上述分析与研究,揭示了该系统在不同激
励条件下的一系列非线性动力学规律。
关键词:弹性矩形薄板,非线性动力学,多尺度法,外激励主共振,参数激励主
共振,次共振,内共振。
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基础定轴转动与简谐激励下矩形板的非线性振动
ABSTRACT
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 bined 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