阻尼结构的减振特性及其拓扑动力学优化研究

发布时间：2018-04-07 19:11

  本文选题：阻尼结构　切入点：减振特性　出处：《南昌航空大学》2016年硕士论文

【摘要】：阻尼结构减振是一种实用的、有效的被动控制减振技术,而黏附粘弹性阻尼材料是一种常用的方式。在一些对产品性能要求较高或近乎苛刻的行业领域,如航空航天、武器装备等,对附加减振阻尼材料势必提出更高的动力学特性要求。研究阻尼结构的振动特性和减振最优,必然显得尤为重要。本文重点研究了在动力学方面阻尼结构减振特性和阻尼材料的拓扑优化方法。构建阻尼结构的动力学有限元模型是研究工作展开的基础。考虑到阻尼材料的粘贴厚度与长宽相差较多的数量级,一般地呈现薄板壳结构的特性,进而引入了阻尼结构层与层之间位移场的连续性。在此基础上,给出了位移场方程并据此建立了结构的动力学分析有限元模型理论。基于ANSYS二次开发编程语言对模型进行求解并利用实验数据和解析数据验证了该模型的有效性,为后续研究拓扑动力学迭代优化提供了计算基础。从微分角度,研究不同体积、不同位置的阻尼材料作用于结构减振时带来的利弊,形成对阻尼材料应用拓扑优化的构想。将静力学中研究应用成熟的变密度法拓展至动力学领域。以阻尼材料用量、振动特征方程、模态频率为约束,以多模态损耗因子倒数加权和最小为目标,建立阻尼结构拓扑优化模型,并引入MAC因子控制结构的振型以避免跃阶。在引入质量阵惩罚因子基础上,推导出优化目标灵敏度。在接下来的仿真中,发现了灵敏度数值的正负性不统一影响优化迭代格未更新每一个设计变量,分析了产生不连续寻优的根本原因。鉴于考虑目标函数的非凸性,而采用常规优化准则法(OC)则寻优可能会使拓扑变量出现负值或陷入局部优化解,故引入数学规划移动渐近技术对OC法进行改进,从而将全体拓扑变量纳入改进算法的优化迭代过程,演算了其数学推导过程,提出∞-范数的概念。编程实现了阻尼结构改进OC法拓扑动力学优化并对改进算法性能进行了仿真。应用本文研究的减振有限元模型和改进算法理论,仿真常见的阻尼结构,并从单模态和多模态以及谐响应特性分析方面给予了优化结果数据分析展示。研究结果表明,引入层层位移场连续的有限元模型具有较高的精度,阻尼材料使用量50%-80%时减振效果较好以及粘贴在应变最大处减振最佳,优化中自由结构的模态损耗因子均有所下降而约束阻尼结构有一定的增加。在对OC法优化的对比分析中,改进算法迭代稳定性更好、寻优效率更高、更具全域最优性。谐响应分析进一步说明了多模态优化的改进算法更能较好地抑制共峰幅值。
[Abstract]:Damping structure is a practical and effective passive damping technique, and adhesion to viscoelastic damping material is a common method.In some industries, such as aeronautics and astronautics, weaponry and so on, it is necessary to require higher dynamic characteristics of additional damping materials.It is necessary to study the vibration characteristics and optimal damping of damped structures.In this paper, the damping characteristics of damped structures and the topology optimization method of damping materials are studied.The dynamic finite element model of damping structure is the foundation of the research work.Considering the order of magnitude between the thickness and width of damping material, the characteristics of thin shell structure are generally presented, and the continuity of displacement field between layers of damping structure is introduced.On this basis, the displacement field equation is given and the finite element model theory of the dynamic analysis of the structure is established.The model is solved based on ANSYS secondary programming language, and the validity of the model is verified by experimental data and analytical data, which provides a computational basis for further research on topology dynamics iterative optimization.In this paper, the advantages and disadvantages of damping materials with different volume and position are studied from the differential point of view, and the idea of topology optimization of damping materials is formed.The application of the mature variable density method in statics is extended to the field of dynamics.Taking damping material dosage, vibration characteristic equation and modal frequency as constraints, and taking the inverse weighted sum of multi-mode loss factor as the objective, the topology optimization model of damping structure is established, and the mode shape of the structure controlled by MAC factor is introduced to avoid the jump step.On the basis of introducing the penalty factor of mass matrix, the sensitivity of optimization target is deduced.In the next simulation, it is found that the negative and positive sensitivity values affect the optimization of the iterative lattice without updating every design variable, and the fundamental reasons for the discontinuous optimization are analyzed.Considering the non-convexity of the objective function and using the conventional optimization criterion (OC), the optimization may lead to negative value of topological variables or fall into local optimal solution, so the moving asymptotic technique of mathematical programming is introduced to improve the OC method.Thus, all topological variables are incorporated into the optimization iteration process of the improved algorithm, the mathematical derivation process is calculated, and the concept of 鈭，

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