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Abstract:
This paper investigates the mechanisms that can be used to enhance the absorption performance of poro-elastic materials in the viscous regime. It is shown that by adding small inclusions in a poro-elastic foam layer, a mass–spring effect can be introduced. If the poro-elastic material has relatively high viscous losses in the frequency range of interest, the mass–spring effect can enhance the sound absorption of the foam by introducing an additional mode in the frame and increasing its out-of-phase movement with respect to the fluid part. Moreover, different effects such as the trapped mode effect, the modified-mode effect, and the mass–spring effect are differentiated by decomposing the absorption coefficient in terms of the three energy dissipation mechanisms (viscous, thermal, and structural losses) in poro-elastic materials. The physical and geometrical parameters that can amplify or decrease the mass–spring effect are discussed. Additionally, the influence of the incidence angle on the mass–spring effect is evaluated and a discussion on tuning the inclusion to different target frequencies is given.

Keywords:
meta-poro-elastic material, Biot–Allard poroelastic model, mass–spring effect, viscous regime

Abstract:
This paper discusses the potential of meta-poro-elastic systems with small mass inclusions to create broadband sound absorption performance under the quarter-wavelength limit. A first feasibility study is done to evaluate whether embedding small mass inclusions in specific types of foam can lead to near-perfect absorption at tuned frequencies. This paper includes an optimization routine to find the material properties that maximize the losses due to the mass inclusion such that a near-perfect/perfect absorption coefficient can be achieved at specified frequencies. The near-perfect absorption is due to the mass-spring effect, which leads to an increase in the viscous loss. Therefore, it is efficient in the viscous regime. The well-known critical frequency, which depends on the porosity and flow resistivity of the material, is commonly used as a criteria to distinguish the viscous regime from the inertial regime. However, for the types of foam of interest to this work, the value of critical frequency is below the mass-spring resonance frequency. Hence, the inverse quality factor is used to provides a more accurate estimation on the frequency at which the transition from the viscous regime to the inertial regime.

Abstract:
In this paper the possibility of enhancing the absorption coefficient of a poro-elastic material using small, elastic mass inclusions in frequencies lower than the quarter-wavelength resonance of the porous material is discussed. We show that absorption peaks can be achieved not only by what is known in literature as the trapped mode effect, but also by the resonance of small elastic inclusions at low frequencies, which can be interpreted as a mass-spring effect. In this work, the inclusion and the porous skeleton is considered elastic and fully coupled to each other, therefore accounting for all types of energy dissipation i.e. viscous, thermal, and structural losses and energy dissipated due to the relative motion of the fluid phase and the frame excited by the resonating inclusion. Additionally, the inclusions are also modeled as motionless and rigid to distinguish between the trapped mode and/or the modified frame mode effect and the mass-spring effect. Moreover, the distinction between these two effects are explained in more detail by comparing the dissipated energy by each mechanism (viscous, thermal and structural effect).

Keywords:
Meta-porous material, Biot-Allard poroelastic model, Mass-spring effect