无阻尼及阻尼结构BESO法拓扑减振动力学优化

发布时间：2018-03-13 07:30

本文选题：约束阻尼　切入点：无阻尼　出处：《南昌航空大学》2017年硕士论文　论文类型：学位论文

【摘要】：在对工程结构减振降噪的研究中,附加阻尼材料的方式已得到广泛应用,工程结构有不同的性能需求,过于僵化的优化目标未必能得到最优的阻尼材料铺设布局;且对结构材料及质量有特殊要求的工程领域中,对原结构本身减振方法的寻求仍不可忽略。基于以上问题,本文提出约束阻尼结构及无阻尼结构在不同优化目标下的最优拓扑优化算法,分析大纲如下:(1)通过对双向渐进法(BESO)在结构拓扑优化中的发展历程总结,阐述了该方法在结构拓扑优化领域的优越性,总结了该算法现存的弊端。双向渐进法对最优拓扑构型的寻优方式使其具有高效性,但优化过程中易出现构型更新停滞问题。基于以上问题,提出了在结构优化流程中单元删除率和添加率新的定义方式,有效抑制了震荡循环现象,且进一步提高了优化效率。(2)基于虚功原理构建了约束阻尼结构动力学有限元模型,推导出约束阻尼结构的模态参数表达式并求解了模态阻尼比和模态损耗因子灵敏度算式;建立以模态阻尼比最大化为优化目标的数学模型,通过算例,结果构型的模态阻尼比得到提升,优化过程流畅无震荡,对比不同算法下的模态参数变动幅度,以及结果构型合理性,验证了改进的双向渐进法的有效性。(3)构建无阻尼结构的动力学有限元模型,推导出无阻尼结构的振动微分方程,求得无阻尼结构的模态参数表达式并求解了频率、位移及刚度灵敏度算式;建立以结构体积最小为优化目标,以结构固有频率约束以及位移约束为限制条件的多目标拓扑优化模型。通过算例,改进的双向渐进优化算法下,无阻尼结构前三阶频率均得到提升,在频率约束下所得的拓扑构型频率曲线变动平缓,实现了频率约束目标,验证了该算法对多目标优化的有效性。
[Abstract]:In the research of reducing vibration and noise of engineering structure, the way of adding damping material has been widely used, engineering structure has different performance requirements, too rigid optimization target may not be able to obtain the optimal layout of damping material laying; In engineering fields with special requirements for structural materials and quality, the search for vibration absorption methods of the original structure itself should not be ignored. In this paper, an optimal topology optimization algorithm for constrained damped structure and undamped structure under different optimization objectives is proposed. The analysis outline is as follows: (1) the development of bidirectional asymptotic method (BESO) in structural topology optimization is summarized. The advantages of this method in the field of structural topology optimization are expounded, and the shortcomings of the algorithm are summarized. Based on the above problems, a new definition method of unit deletion rate and addition rate in the process of structural optimization is proposed, which effectively restrains the phenomenon of oscillatory cycle. Furthermore, the optimization efficiency is further improved. (2) based on the virtual work principle, the dynamic finite element model of constrained damping structure is constructed, the modal parameter expression of constrained damping structure is derived, and the formula of modal damping ratio and modal loss factor sensitivity is solved. A mathematical model with the maximum modal damping ratio as the optimization objective is established. Through an example, the modal damping ratio of the configuration is improved, and the optimization process is smooth and without vibration, and the variation amplitude of modal parameters under different algorithms is compared. The validity of the improved bidirectional asymptotic method is verified, and the dynamic finite element model of the undamped structure is constructed, and the vibration differential equation of the undamped structure is derived. The modal parameter expression of undamped structure is obtained and the sensitivity formulas of frequency, displacement and stiffness are solved. A multi-objective topology optimization model with natural frequency constraints and displacement constraints as constraints is presented. The first three order frequencies of undamped structures are enhanced by the improved bi-directional asymptotic optimization algorithm. The change of frequency curve of topological configuration under frequency constraints is smooth and the target of frequency constraint is realized. The effectiveness of the algorithm for multi-objective optimization is verified.
【学位授予单位】：南昌航空大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB535.1

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