【作者】 李红影；

【导师】 谢里阳； 郭星辉；

【作者基本信息】 东北大学 ， 机械设计及理论， 2012， 博士

【摘要】 壳板、局部浸液板普遍存在于工程中的各个领域,其应用之一是航空发动机叶片和钢铁行业中连续热镀锌钢板,它们在工作状态下表现出的不同振动特性引起了各国学者的广泛和高度关注。叶片在很长一段时间内被简化为梁和板模型来研究,这种简化对于中等或小展弦比叶片的动力学研究会产生很大误差,而对于壳板模型叶片的振动研究,在最近十几年才逐渐活跃起来。叶片在工作过程中易产生振动,由此引起疲劳损伤,利用凸肩干摩擦阻尼结构能够有效抑制叶片振动,增加叶片的高周疲劳寿命。但是由于壳板模型比较复杂以及干摩擦阻尼结构接触特性和运动行为的复杂性,同时考虑叶片振动而伴随的几何非线性,这些因素使得在应用近似解析方法来研究壳板凸肩叶片模型的非线性动力学特性时遇到很大困难,故多集中于分析其固有特性,对工程较为常见的受迫振动研究关注较少。轴向移动局部浸液板模型取自钢铁行业中连续热镀锌钢板生产线,目前连续热镀锌生产线普遍由于带钢的振动,而造成镀锌板产生振动纹、镀层量不符合标准等质量问题,开展其相应的研究工作有非常现实的理论和工程意义。本文针对特殊移动构件(壳板、局部浸液板)在工程中的两种应用实例(航空发动机叶片、连续热镀锌钢板),结合其应用背景分别简化为模型：旋转壳板凸肩叶片、轴向移动局部浸液板,并分别对其非线性动力学特性进行了理论和数值研究。本文旨在通过对两个典型实例模型的非线性动力学分析,提供一种研究这些特殊移动构件非线性动力学特性的有效研究方法。论文主要工作和成果如下：(1)研究壳板凸肩叶片的非线性振动特性。提出一种新的计算壳板凸肩叶片固有特性、非线性振动响应的解析方法,并通过数值算例进行了验证。采用薄壁壳板模型模拟叶片结构,将凸肩简化为弹簧系统,考虑相邻凸肩之间的相互作用、几何非线性、阻尼、安装角及周期激励等因素,应用Donnell’s简化壳理论建立旋转壳板凸肩叶片的非线性振动方程。针对悬臂壳板叶片模型复杂的边界条件,介绍了一种利用单向解析函数代入变分方程降为另一方向的常微分方程的解析方法来求解其固有特性。在此基础上,分别采用Runge-Kutta法和多尺度法对旋转壳板凸肩叶片系统的非线性振动特性进行了研究,两种方法所得结论一致,并对系统进行了参数振动分析。研究结果表明,凸肩干摩擦阻尼结构使得系统的振动不连续,致使叶片系统振动能量无法连续积累,从而有效减小叶片的振动幅值。(2)研究旋转壳板凸肩叶片系统的稳定性和全局动态分岔特性。揭示了壳板凸肩叶片系统参数在整个参数空间内变化时系统周期解的变化过程及其具有的非线性动力学特性。应用李雅普诺夫一次近似理论对其稳定性进行分析。采用多尺度法获得系统主共振情况下的平均方程和分岔方程。通过研究整个参数空间内,不同参数集合上平均方程的全局行为,揭示了壳板凸肩叶片系统各运动状态之间的相互联系和转化。分析结果显示,系统参数集合处在某些特定区域时,系统具有运动性态发生变化的分岔特性。(3)研究轴向移动局部浸液板的非线性振动特性。首次揭示轴向移动局部浸液板存在1：3内共振,讨论轴向移动局部浸液板产生1：3内共振的机理。利用液体与薄板法向速度保持一致的液固耦合界面条件,将液体对薄板的作用等效为附加质量,进而将局部浸液板简化为刚度相同而密度、阻尼不同的阶梯板。基于Von Karman薄板大挠度方程,建立考虑几何非线性、轴向张力、轴向运动速度、液固耦合作用、阻尼及外激励等诸多耦合因素共同作用下薄板的非线性振动方程。通过实测发现镀锌板在实际载荷作用下,仅产生弯曲振动,并未发生扭转振动,故仅研究了轴向移动局部浸液板弯曲振动特性。应用奇异函数理论研究了系统的固有特性。选用两个相邻模态,分别采用Runge-Kutta法和多尺度法对系统进行研究,两种方法所得结论吻合较好,研究了不同参数对内共振系统的影响。结果表明,1：3内共振系统具有复杂而多变的非线性振动特性。(4)研究轴向移动局部浸液板1：3内共振系统的稳定性和运动分岔现象。第一次描绘出轴向移动局部浸液板1：3内共振系统复杂的分岔曲线。在第一阶模态附近,系统由于存在1：3内共振,两阶模态相互耦合,无法得到参数平面上分界曲线的解析表达式,通过数值方法揭示了1：3内共振系统复杂的分岔现象。通过与系统在第二阶模态附近的分岔曲线比较,展示出了1：3内共振系统模态耦合的特性及其复杂的动力学行为。更多还原

【Abstract】 Cylindrical panels and plates partially immersed in fluid are widely used in various fields of engineering. For example, aero engine blades and continuous hot-dip galvanizing steel plates in steel industry. Experts pay more and more attentions to their different vibration characteristics under working state. For a long time, vibrations of blades have been studied by simplifying them as models of beams or plates. This simplification will lead to error in terms of dynamic research on moderate or low aspect ratio blades. In recent ten years study on the model of cylindrical panels begins to warm up. Under the state of working, blades are easy to resonate and arose to fatigue damage. The shrouded dry friction damper can effectively suppresses vibration of blades and increases high cycle fatigue life. However, due to the complex model of cylindrical panels, and the complexity of contact characteristics and movement behavior for dry friction damper, together with the geometric nonlinearity accompanied with the vibration of blades, it would be hard to study the dynamic characteristics of shrouded blade of cylindrical panel. For this reason, most of studies focus on its inherent characteristic, while the study of forced vibration, frequently appeared in engineering, draws few attentions. The model of axially moving plates partially immersed in fluid comes from line of hot galvanized zinc in steel industry. Because of vibration of steel plate in continually hot galvanized zinc line, quality problems, like vibration ripple and failure to reach standard galvanized depth, appear in the steel industry. So it would be of great theoretical and engineering importance to make relative study in this area.Through aero engine blade and continually hot zinc-galvanized steel plate, application instances of which in engineering, and by simplifying the models of them as shrouded blade of rotating cylindrical panel and axially moving plates partially immersed in fluid while considering their application background, this paper studies theoretical and numerical analysis of nonlinear dynamic characteristic for especial moving components(cylindrical panels and plates partially immersed in fluid). By studying the nonlinear dynamic analysis of two typical examples, this paper aims to provide an effective method to study this kind of components. Main tasks and results of this paper are as following:(1) Study vibration characteristic of shrouded blade of rotating cylindrical panel. A new analytic approach for calculating natural properties and nonlinear vibration response for shrouded blade of cylindrical panel is developed.A numerical example is solved to verity the accuracy of the proposed methed.Adopting thin-walled cylindrical panel to simulate the structure of blade, and simplify the shroud as spring system, the nonlinear vibration equations are obtained by using Donnell’s nonlinear shallow-shell theory, the process of which also consider interaction force between shrouds, geometric nonlinearity, damping, installation angle and periodic stimulation. Considering complex boundary conditions of cantilever cylindrical panel, one-way analytic function is introduced to variation equation to reduce it into ordinary equation in another way and so to solve its inherent characteristic. Then, Runge-Kutta method and multiple scale method are also introduced to study the characteristic of nonlinear vibration for shrouded blade of rotating cylindrical panel. Conclusions drawn by these two methods are the same. Parameter vibration analysis is also made. Studying results show that shrouded dry friction damper structure leads to incontinuity of system vibration, and the vibration energy of the blade system fails to accumulate continually, thus effectively reduce the vibration amplitude.(2) Study stability and dynamic bifurcation phenomenon of shrouded blade of rotating cylindrical panel. The changing process of periodic solution and nonlinear dynamic characteristics for shrouded blade of cylindrical panel are analysed,while system parameter changes in the whole parametric space. Using Lyapunov first approximate theory to analyze system stability, and multiple scale method to obtain average equation and bifurcation equation. Through studying global behavior of average equation in different parameter sets in the whole parametric space, the connection and conversionof moving states for shrouded blade of cylindrical panel are showed Analytic results show that, while system parameter locates in specific area, system has the phenomenon of changing property of moving, namely bifurcation.(3) Study characteristic of nonlinear vibration of axially moving plates partially immersed in fluid.For the first time reveals that there is1:3internal resonance in plates partially immersed in fluid,and discusses the mechanism that1:3internal resonance produces. Using the liquid-solid interface coupling conditions of that the speed of liquid keeps the same with the normal speed of thin plate, the action of liquid on thin plate is regarded as equivalent to added mass, furtherly, plates partially immersed in fluid are simplified as step plate with equal rigidity and different damp and density. Based on Von K arman thin plate large deflection equation, nonlinear bending equation of thin plate is established, which consider geometric nonlinearity, axial tension, axial moving speed, fluid-solid interaction, damp and external stimulation etc. It was found that, under the action of actual load, zinc-galvanized plate only has bending vibration, not torsional vibration, thus only the bending vibration of axial moving plates partially immersed in fluid was studied. And also, strangeness theory is introduced to study the inherent characteristic of system. With this basis, two neighbour modalities are chosen to study, separately under Runge-Kutta method and multiple scale method, results of these two methods mate well. The influences of different factors on internal resonate system are also carried out, and the creating mechanism of1:3internal resonate system is also investigated. Results show that1:3internal resonate system has complex and variable nonlinear vibration characteristics.(4) Study stability and dynamic bifurcation phenomenon of1:3internal resonate system. Firstly describes the complex bifurcation curves of axially moving plates partially immersed in fluid which contain1:3internal resonance. Near the first order modality, due to1:3internal resonance, two order modalities coupled each other, and the analytic expression of boundary curve in parameter plane can be drawn. Through numerical method, this paper firstly displays the complex bifurcation phenomenon of system which contains1:3internal resonance. Compared with bifurcation curve of the system in the second modality, this paper shows modal coupling characteristics of1:3internal resonance system and its complex dynamics behavior.更多还原