Purpose

This paper develops a vibro-acoustic component modal synthesis method to solve the problem of high computation time in solving the eigenvalues and eigenvectors of coupled equations for noise reduction topology optimization.

Methods

The normalization condition of the left and right eigenvectors of the unsymmetrical vibro-acoustic equation is introduced, and Craig–Bampton method is extended to the structure-acoustic coupled problem, which reduces the time consumed by the response calculation part. The results show that the eigenvalues, the eigenvectors, and the response values calculated by the proposed method match well with the original model. To solve the problem of spurious eigenmodes caused by the traditional penalization model used in the classical bi-directional evolutionary optimization (BESO) method, the linear stiffness penalization model is introduced into the BESO method, and an improved penalization model is proposed.

Conclusions

Numerical examples of minimizing the response at a specified target point are studied. The results show that the iterative process is robust. Through these numerical design examples, the effectiveness and reliability of the model reduction method and the improved penalization model are verified.

中文翻译：

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基于模型约简法的声固耦合系统拓扑优化

目的

为了解决降噪拓扑优化的耦合方程的特征值和特征向量问题，本文提出了一种振动声分量模态综合方法，以解决计算时间长的问题。

方法

介绍了非对称振动声学方程左，右特征向量的归一化条件，并将Craig–Bampton方法扩展到结构声学耦合问题，从而减少了响应计算部分所花费的时间。结果表明，该方法计算出的特征值，特征向量和响应值与原始模型吻合良好。为了解决经典双向进化优化（BESO）方法中使用的传统惩罚模型所引起的伪本征模式问题，将线性刚度惩罚模型引入BESO方法中，并提出了一种改进的惩罚模型。

结论

研究了使指定目标点的响应最小化的数值示例。结果表明，迭代过程是鲁棒的。通过这些数值设计实例，验证了模型简化方法和改进的惩罚模型的有效性和可靠性。