# Design of a Noise Mitigation System Using Lightweight Graded Micro-Porous Material
## 3 Design, Fabrication, and Validation of Graded Micro-Porous Material System
### Validation by Normal Incidence Impedance Tests
#### 3.4.2 Graded uPHB Composite Material Combination of L37.5, M37.5, S25  
In this graded material combination, the layer with a large particle size and medium particle size are of equal thickness, being 1.5 times thicker than the layer with a small particle size, with a total thickness of 50 mm. The predictions have been validated through experiments, and detailed discussions are provided. Figure 16: Validation of predictions with experimental absorption coefficient versus frequency for graded (L50, M25, S25) uPHB composite material. Figure 17: Validation of predictions with experimental transmission loss versus frequency for graded (L50, M25, S25) μPHB composite material. * Absorption Coefficient Response Figure 18 shows the experimental absorption coefficient alongside the predicted response for a graded material configuration composed of L37.5, M37.5, S25 with a total thickness of 50 mm. The predictions demonstrate good agreement with the experimental data. Specifically, excellent agreement is observed between 250 to 500 Hz, with slight underestimation, ranging from 0 to 0.05, between 500 to 950 Hz, and an excellent fit beyond 1000 Hz up to 1600 Hz. Additionally, the absorption coefficient bounds of medium and large particle-size uPHB composite materials are presented. This comparison highlights the superior performance of the graded material system over the medium and large particle-size uPHB composite materials beyond 700 Hz and throughout the specified frequency range. Consequently, it can be concluded that the L37.5, M37.5, S25 graded material system stands out, achieving an absorption coefficient \(\geq\)0.50 over 500 Hz, which continues to increase with frequency and reaches a value of 0.82 @ 1600 Hz. * Transmission Loss Response Figure 19 shows the experimental transmission loss versus frequency alongside predictions for a graded material configuration composed of L37.5, M37.5, S25 with a total thickness of 50 mm. The prediction demonstrates reasonably good agreement with the experimental data. However, in the low-frequency range of 250 to 800 Hz, there is a noticeable difference, with predictions showing an overestimation ranging from 0 to 6 dB relative to the experiment, peaking at 250 Hz and gradually decreasing with increasing frequency. Between 800 to 1600 Hz, the prediction shows an excellent fit with the experiment. Additionally, Figure 19 shows the transmission loss test response for medium and large particle-size uPHB composite materials. As observed in the previous case, it can be concluded that the transmission loss response for the selected graded material combination falls between the transmission loss bounds of the medium and large particle-size materials. Similar to the previous case, a design transmission loss \(\geq\) 20 dB over a broad frequency range (over 500 Hz) is achieved for the L37.5, M37.5, S25 graded material system. Comparing the two graded uPHB composite material combinations, both systems exhibit a designed sound absorption of \(\geq\)0.50 across a broad frequency range. However, it is evident that L50, M25, S25 performed better than L37.5, M37.5, S25 in terms of the absorption coefficient. Additionally, it can be concluded that incorporating a thicker layer of large particle-size uPHB composite material on the front side of the graded material system enhances sound absorption. Figure 18: Validation of predictions with experimental absorption coefficient versus frequency for graded (L37.5, M37.5, S25) uPHB composite material. Moreover, this study indicates that employing a graded system with a large particle/pore size facing the sound wave, followed by a gradually decreasing pore size, offers a favorable balance between absorption coefficient and transmission loss. Similarly, the current approach allows for the design of material systems tailored to any desired combination of absorption coefficient and transmission loss based on specific requirements. This design technology was used to build an acoustic liner of 4-foot inner diameter, 9-inch axial length, and 2-inch thickness.