薄壁构件约束阻尼结构动力学拓扑优化研究

发布时间：2019-02-21 16:40

【摘要】：薄壁构件不仅能够以很小的重量代价,承担相当大的载荷,而且具有散热性能良好等特性,在航空航天和汽车等行业上获得了广泛的应用。随着现代工业节能环保的要求,轻量化成为产品设计中一个重要的部分,随之而来的薄壁构件的振动噪声问题也日益突出。约束阻尼结构能有效地抑制结构宽频振动噪声,在传统的约束阻尼结构减振设计中,将约束阻尼材料覆盖于整个结构的表面,有效抑制结构振动和噪声的同时,增加了结构的附加质量。本文以约束阻尼薄板结构为研究对象,在深入研究约束阻尼板结构有限元建模的基础上,将动力学拓扑优化方法引入到约束阻尼材料在薄板结构上的布局优化问题中,提出了约束阻尼薄板结构的动力学拓扑优化方法,为提高约束阻尼材料的利用率和抑制振动的能力提供了一种新的方法。本文的研究成果主要有一下几个方面:根据弹性材料和粘弹性材料的本构关系,采用能量法,建立了约束层阻尼板的有限元动力学模型,通过算例验证了有限元模型的正确性。分析了约束阻尼悬臂板的约束阻尼材料使用量和分布位置对约束阻尼结构的振动特性的影响,阐明了对约束阻尼材料的布局进行优化的必要性。建立了以模态损耗因子最大化为目标函数的约束阻尼板的拓扑优化模型,基于模态应变能方法,推导了目标函数对设计变量的灵敏度,采用独立网格滤波技术消除棋盘格式,制定了删除和添加约束阻尼单元的规则,编制基于双向渐进优化算法的约束阻尼结构的拓扑优化流程,对约束阻尼悬臂板结构的约束阻尼材料的布局进行了优化,并与渐进优化算法的优化结果进行对比分析,结果显示:本文提出的基于双向渐进优化算法的约束阻尼拓扑优化方法具有更好的优化能力,得到的拓扑构型比渐进优化算法更优。基于SIMP插值模型,重新组装了约束阻尼板的质量矩阵和刚度矩阵。建立以模态损耗因子倒数最小化为优化目标的约束阻尼结构的拓扑优化模型。为了避免模态交换的问题,跟踪计算迭代过程中的MAC值。推导了目标函数对设计变量的灵敏度,采用独立网格滤波技术消除棋盘格式。编制基于SIMP插值模型和MMA算法的约束阻尼结构的拓扑优化流程,以约束阻尼悬臂板和两短边固定的约束阻尼板为研究对象,对约束阻尼材料的布局进行了优化,验证了提出的优化方法的有效性和适用性。提出了在对指定频带简谐激励下,以约束阻尼结构的某些位置的共振峰值的平方最小化为优化目标的约束阻尼结构动力学拓扑优化模型。针对传统的灵敏度分析方法未考虑模态阻尼比的灵敏度,会产生较大的误差的问题,对传统的灵敏度分析方法进行改进,提出了考虑模态阻尼比灵敏度的灵敏度分析方法。采用渐进优化算法对建立的优化模型进行求解,编制了其优化流程。以悬臂的约束阻尼板和四边固定的约束阻尼板为研究对象,对拓扑优化结果进行了分析,结果表明:两种灵敏度分析方法的优化结果均能够降低优化目标值,并且本文提出的考虑了模态阻尼比灵敏度的灵敏度分析方法得到的优化结果比未考虑模态阻尼比灵敏度的灵敏度分析方法的优化结果的模态阻尼比更大共振峰值更小,验证了本文提出的考虑了模态阻尼比灵敏度的灵敏的方法更有效。提出了在约束阻尼结构受简谐激励或频带简谐激励时,以约束阻尼结构的某些位置的频响位移最小化为优化目标约束阻尼结构的动力学拓扑优化模型。采用复模态叠加法对约束阻尼动力学方程求解,分析了直接法和伴随法计算灵敏度的特点和适用范围,通过算例分析确定了采用伴随法对建立的动力学优化模型进行灵敏度分析。采用MMA算法对优化模型进行求解,编制以频响位移最小化为优化目标的约束阻尼结构的拓扑优化流程。通过算例分析,验证了提出的优化方法的有效性。最后,对约束阻尼板结构的优化布局进行了实验研究,验证了本文提出的拓扑优化方法的正确性和有效性。
[Abstract]:The thin-wall component not only can bear a considerable load at a small weight, but also has the characteristics of good heat dissipation performance and the like, and has wide application in the fields of aerospace and automobile and the like. With the requirement of energy-saving and environmental protection in the modern industry, the light weight becomes an important part in the product design, and the problem of vibration noise of the thin-wall component is also becoming more and more prominent. The constrained damping structure can effectively restrain the broadband vibration noise of the structure, and in the traditional constrained damping structure vibration reduction design, the constraint damping material is covered on the surface of the whole structure, the vibration and the noise of the structure are effectively restrained, and the additional quality of the structure is increased. In this paper, based on the study of the finite element modeling of the constrained damping plate structure, the dynamic topology optimization method is introduced to the optimization of the layout of the constrained damping material in the thin plate structure. The dynamic topology optimization method of constrained damping thin plate structure is put forward, and a new method is provided to improve the utilization rate of the constrained damping material and to suppress the vibration. The results of this paper have several aspects: according to the structure of the elastic material and the viscoelastic material, the energy method is used to establish the finite element dynamic model of the damping plate of the constrained layer, and the correctness of the finite element model is verified by the calculation example. The influence of the applied amount and the distribution position of the constrained damping cantilever plate on the vibration characteristics of the constrained damping structure is analyzed, and the necessity of the optimization of the layout of the constrained damping material is explained. Based on the modal strain energy method, the sensitivity of the objective function to the design variable is derived based on the modal strain energy method, and the board format is eliminated by adopting the independent mesh filtering technology. the rule of deleting and adding the constraint damping unit is established, the topological optimization flow of the constraint damping structure based on the two-way progressive optimization algorithm is prepared, the layout of the constrained damping material of the constrained damping cantilever plate structure is optimized, The result shows that the constrained damping topology optimization method based on the two-way progressive optimization algorithm has better optimization ability, and the obtained topological configuration is better than the progressive optimization algorithm. The mass matrix and stiffness matrix of the constrained damping plate are re-assembled based on the SIMP interpolation model. and a topological optimization model of a constrained damping structure with the inverse of the modal loss factor is minimized to the optimization target is established. In order to avoid the problem of modal exchange, the MAC value in the iterative process is tracked. The sensitivity of the objective function to the design variable is derived, and the checkerboard format is eliminated by using the independent mesh filtering technique. The topology optimization process of the constrained damping structure based on the SIMO interpolation model and the MMA algorithm is developed to restrain the damping cantilever plate and the two short side fixed constrained damping plates as the research object, and the layout of the constrained damping material is optimized, and the validity and the applicability of the proposed optimization method are verified. In this paper, a constrained damping structure dynamic topology optimization model is proposed to minimize the square of the resonance peak at certain positions of the damping structure under the simple harmonic excitation of the specified frequency band. For the traditional sensitivity analysis method, the sensitivity of the modal damping ratio is not considered, the problem of large error can be generated, the conventional sensitivity analysis method is improved, and the sensitivity analysis method considering the modal damping ratio sensitivity is provided. The optimization model of the established optimization model is solved by the gradual optimization algorithm, and the optimization process is developed. Based on the constrained damping plate of the cantilever and the constrained damping plate with four sides fixed, the topological optimization results are analyzed. The results show that the optimization results of the two sensitivity analysis methods can reduce the optimization target value. and the modal damping ratio of the optimization result of the sensitivity analysis method without considering the modal damping ratio sensitivity is smaller than that of the sensitivity analysis method without considering the modal damping ratio sensitivity, It is proved that the sensitive method considering the modal damping ratio is more effective. It is proposed that the dynamic topology optimization model of the constrained damping structure is optimized by minimizing the frequency response displacement of certain positions of the damping structure when the constrained damping structure is excited by the simple harmonic excitation or the frequency band simple harmonic excitation. In this paper, a complex mode superposition method is used to solve the constraint damping dynamic equation, and the characteristics and the application range of the direct method and the adjoint method are analyzed, and the sensitivity analysis of the established dynamic optimization model by the adjoint method is determined by the calculation example analysis. The optimization model is solved by using the MMA algorithm, and the topological optimization process of the constrained damping structure with the minimum frequency response displacement as the optimization objective is prepared. The effectiveness of the proposed optimization method is verified by the analysis of the example. Finally, the optimal layout of the constrained damping plate structure is studied, and the correctness and validity of the topology optimization method proposed in this paper are verified.
【学位授予单位】：重庆大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB535.1

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