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 modelled 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. The sizing optimization of these rings is carried out simultaneously with the aforementioned TO process (density layout). A reactive chamber is added in order to evaluate the TL

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