# Design of a Noise Mitigation System Using Lightweight Graded Micro-Porous Material
## 3 Design, Fabrication, and Validation of Graded Micro-Porous Material System
### Design of the Graded \(\upmu\)PHB Composite Material  
Designing acoustic materials presents a significant challenge, as achieving both superior sound absorption and transmission loss simultaneously is difficult. For a micro-porous material, if the material exhibits a high sound absorption, it will correspondingly demonstrate a poor transmission loss, and vice versa. This can be resolved by careful design considerations that are crucial for achieving the desired acoustic responses.  
Based on our previous work [25; 33; 35] and the current study, the following conclusions are derived:  
Figure 11: Validation of predicted transmission loss with experiment for 25 mm thick specimens.  
* The absorption coefficient increases with the increase in microbubble size, resulting in a material with an increased pore size and porosity;
* The sound absorption coefficient increases with particle sizes up to 1 mm, but beyond this limit, the trend reverses for a specific material thickness;
* The transmission loss increases with the decrease in particle size, leading to a smaller pore size and a decrease in porosity (low permeability).
* Large particle size \(\upmu\)PHB composite material exhibits high sound absorption, while small particle size \(\upmu\)PHB composite material demonstrates high transmission loss.
* Flow properties remain unaffected by specimen geometry when the ratio of minimum specimen dimension to mean particle diameter exceeds 10;
* Flow properties depend on particle size, pore size, and their distribution within the material system;
* The pore-size distribution (PSD) model inverse method is effective for smooth-surface solid glass beads, whereas the multivariable-fit inverse method with G-ICAL/JCAPL is suitable for both smooth solid glass beads and rough-particle-surface \(\upmu\)PHB composite materials.  
Based on these findings, a nearly monodisperse particle micro-porous material will offer either good sound absorption or transmission loss, but not both. A recommended approach involves using large-size particles/granules (pore) on the sound incidence side/face and gradually decreasing the particle size or pore size (see Figure 12a) towards the material's core. This design facilitates effective sound wave penetration into the material system before the energy dissipation occurs, achieved by employing a large particle-size \(\upmu\)PHB composite material layer at the forefront. Several layer combinations were assessed and are reported in reference [33], but in this work, for concept demonstration, we have selected two different grading combinations (L\({}_{80}\), M\({}_{25}\), S\({}_{25}\), and L\({}_{37.5}\), M\({}_{37.5}\), S\({}_{25}\)) of the material system with a total thickness of 50 mm (typically used in aircraft acoustic liners) against a rigid backing, which is shown in Figure 12b. Here, the L--large, M--medium, and S--small with subscripts represent the percentage of the total thickness. The gradation of pore size should lead to the design of a \(\upmu\)PHB composite material with \(\geq\)0.50 and transmission loss \(\geq\) 20 dB over a broad frequency range (over 500 Hz).