Abstract The optimization of damping composite material in a certain frequency range has become one of the critical issues in structural engineering applications due to the fact that the structures usually work in a wide vibration frequency range. This paper proposes a topology optimization method for designing the damping composite materials with high stiffness and high broadband damping. The broadband damping composite material is realized by the properly combing two phases of damping material, in which phase 1 has high loss factor in lower frequency range and phase 2 has high loss factor in higher frequency range. In order to maximize the material damping performance in a given frequency range, we suggest a new algorithm for finding the optimal two-phase damping materials layout in micro scales, while the homogenized effective complex elastic matrix is obtained by considering the two damping materials layout in the microstructure. The mathematical model with two different objective functions, which are K-S objective function and weighted objective function, has been established. The first is maximize the minimum material loss factor in the given frequency range and the second is maximize the sum of the material loss factor in the given frequency range. Several typical numerical examples are presented to demonstrate the effectiveness of the proposed optimization method. An in-depth analysis is conducted to reveal the effects of the weighting factor on the optimal solutions. The results show that the K-S function has the ability to maximize the minimum damping of composite material in the given frequency band. The material loss factor increases with the increase of weighting factor. All of the results show that the proposed method can get the optimal microstructure with clearly material layout, no matter the objective is K-S function or weighted function is used.

中文翻译：

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高宽带阻尼复合材料拓扑优化

摘要 由于结构通常在较宽的振动频率范围内工作，因此在一定频率范围内优化阻尼复合材料已成为结构工程应用中的关键问题之一。本文提出了一种用于设计高刚度、高宽带阻尼阻尼复合材料的拓扑优化方法。宽带阻尼复合材料是通过将两相阻尼材料适当组合而实现的，其中第一相在较低频率范围内具有高损耗因子，第二相在较高频率范围内具有高损耗因子。为了在给定频率范围内最大限度地提高材料阻尼性能，我们提出了一种新算法，用于在微尺度上找到最佳的两相阻尼材料布局，同时考虑微观结构中两种阻尼材料的布局，得到均质的有效复弹性基体。建立了KS目标函数和加权目标函数两个不同目标函数的数学模型。第一个是在给定频率范围内最大化最小材料损耗因子，第二个是在给定频率范围内最大化材料损耗因子的总和。给出了几个典型的数值例子来证明所提出的优化方法的有效性。进行深入分析以揭示加权因子对最优解的影响。结果表明，KS 函数具有在给定频带内使复合材料的最小阻尼最大化的能力。材料损耗因子随着权重因子的增加而增加。所有结果表明，无论目标是 KS 函数还是使用加权函数，所提出的方法都可以得到具有清晰材料布局的最佳微观结构。