【作者】 何运成；

【导师】 张伟；

【作者基本信息】 北京工业大学 ， 工程力学， 2009， 硕士

【摘要】 柔性梁和板结构无论是在大型空间站等航空、航天领域中,还是在船舶、汽车、建筑等民用工程领域中都是非常重要的组成部分。随着工程结构的大型化、柔性化和轻质化,以及对结构的高可靠性、高精度、高稳定性的要求越来越高,对柔性梁和薄板结构的动力学与振动控制的研究日益重要。非线性因素对机械柔性结构的动力学特性有非常重要的影响,因此,研究柔性梁和板结构的非线性振动具有非常重要的理论意义和实际应用价值,能够为结构的设计和控制提供重要的理论指导依据。本论文主要对具有方形截面的柔性悬臂梁、金属材料矩形薄板和碳纤维复合材料层合矩形薄板进行系统的非线性振动实验研究。主要研究内容有如下几个方面:1.研究了简谐参数激励作用下方形截面悬臂梁系统非线性振动响应,主要内容如下:1)通过理论计算、Ansys有限元模拟给出了方形截面梁的固有频率并同实验观测到的共振频率对比,发现了超谐和亚谐共振等非线性现象;2)实验研究了共振区域悬臂梁模态阶次和振动方向的转变过程;绘制了频响和力幅值曲线;讨论了系统受迫响应与初始振幅之间的关系;3)研究了由于模态相互耦合作用,梁的响应在倍周期、概周期和混沌之间转化的非线性动力学行为;观察到了两类多模态组合共振的组合方式以及不同方式所对应的混沌脉冲跳跃现象;发现了梁的大幅回转运动和阵发混沌运动;4)实验测定了梁对应不同模态的相对阻尼系数。2.研究了几何尺寸、边界条件、激励等因素对金属材料矩形薄板和碳纤维复合材料层合矩形薄板系统振动响应的影响。具体内容如下:1)通过理论计算、Ansys有限元模拟给出了矩形薄板的固有频率和模态;2)通过锤击法、扫频等方法给出了板系统的共振频率,分别讨论了几何尺寸、边界条件、激励等因素对系统共振的影响;基于扫频结果,讨论了板的非线性频响特性;3)实验发现了一类高阶激励频率激发起低阶非固有频率所对应的共振现象。更多还原

【Abstract】 Flexible beam and plate structures have been increasingly used in fields of aerospace and civil engineering. Correspondingly, more and more requirements of reliability, precision and stability become considered due to the special characteristics of these structures such as light aromatics and flexibility. Research on the dynamics and vibration control of these structures, therefore, are of great importance. Nonlinear vibration, bifurcations and chaotic dynamics play an important role in nonlinear science. Specific researches on nonlinear dynamics of mechanical flexible structures can provide essential theoretical guidance for their design and control in engineering applications.In this paper, nonlinear dynamic characteristics of flexible cantilever beam with square section, metallic plate and Composite Laminated Plate have been investigated in detail using experimental method. The main contents are as follow:1. For cantilever beam, the case with harmonic parametric excitation has been maily discussed with the following details:1) Natural frequencies obtained mathematically have been compared with those of experiments, by which sub-harmonic and super harmonic resonance has been found;2) Translating processes between different mode orders and mode directions have been researched experimentally. Frequency and amplitude response curves have been drawn based on the observed points. Nonlinear character of sensitivity toward initial values has been studied and regareded to cause the curves;3) Chaotic phenomena as a result of interaction of different modes have been studied. In resonant zones, two kinds of multi-mode combination have been found; two correspongding kinds of pulse jumping phenomena have been observed as well;4) Relative damping coefficients have been determined experimentally.2. With regard to rectangular thin plates, influences from geometric dimension, boundary conditons and kinds of excitations have been studied with the details as follow:1) By means of theoretical calculation and finite element imitaiton, natural frequencies and modes have been obtained;2) Resonant frequencies have been obtained using hammering method and frequency sweeping method. Effects from boundary conditons and excitions have been discussed;3) A kind of low frequency mode resonance has been found.更多还原