Abstract

This article presents a topology optimization (TO) method developed for maximizing the acoustic attenuation of a perforated dissipative muffler in the targeted frequency range by optimally distributing the absorbent material within the chamber. The finite element method (FEM) is applied to the wave equation formulated in terms of acoustic pressure (chamber) and velocity potential (central duct, due to the existence of thermal gradients and mean flow) in order to evaluate the acoustic performance of the noise control device in terms of transmission loss (TL). Sound propagation through the chamber fibrous material is modeled considering complex equivalent acoustic properties, which vary spatially not only as a function of temperature but also as a function of the filling density, since non-homogeneous density distributions are considered. The acoustic coupling at the perforated duct is performed by introducing a coordinate-dependent equivalent impedance. The objective function to maximize is expressed as the mean TL in the targeted frequency range. The sensitivities of this function with respect to the filling density of each element in the chamber are evaluated following the standard adjoint method. The method of moving asymptotes (MMA) is used to update the design variables at each iteration of the TO process, keeping the weight of absorbent material equal or lower than a given value, while maximizing attenuation. Additionally, several particular designs inferred from the topology optimization results are analyzed. For example, the sizing optimization of a number of rings is carried out simultaneously with the aforementioned TO process (density layout). A reactive chamber is added in order to evaluate the TL of a hybrid muffler and its shape optimization is also carried out simultaneously with the aforementioned TO. Results show an increase in the muffler’s mean TL at target frequencies, for all cases under study, while the amount of absorbent material used is maintained or even reduced.

中文翻译：

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耗散和混合消声器的拓扑和形状优化

摘要

本文介绍了一种拓扑优化（TO）方法，该方法旨在通过在腔室内最佳地分配吸收材料来最大化目标频率范围内的穿孔消声器的声衰减。为了评估噪声的声学性能，将有限元方法（FEM）应用于根据声压（腔）和速度势（中心管道，由于存在热梯度和平均流）公式化的波动方程控制设备的传输损耗（TL）。考虑到复杂的等效声学特性，对通过腔室纤维材料的声音传播进行建模，由于考虑了非均匀的密度分布，这些等效声学特性不仅在空间上随温度变化，而且随填充密度而变化。通过引入与坐标有关的等效阻抗，可以在穿孔导管处进行声耦合。最大化的目标函数表示为目标频率范围内的平均TL。遵循标准伴随方法评估此功能相对于腔室中每个元素的填充密度的敏感性。移动渐近线（MMA）的方法用于在TO过程的每次迭代中更新设计变量，使吸收性材料的重量等于或小于给定值，同时使衰减最大化。此外，分析了从拓扑优化结果中推断出的几种特殊设计。例如，多个环的尺寸优化与上述的TO处理（密度布局）同时进行。添加了一个反应室，以评估混合消声器的TL，并且其形状优化也与上述TO同时进行。结果表明，在所有研究的案例中，在目标频率下消声器的平均TL都有所增加，而所使用的吸收性材料的数量却保持不变甚至减少了。