Fig. 1. Overview of the template replication technique. The polymer template foam is immersed in the metal slurry to fully coat the struts. The excess slurry is removed by repeated compression. The green bodies are then dried and sintered to form the metal foam.

Fig. 2. Representative sample of a functionally graded foam (PPI 45-80-60).

Fig. 3. SEM images of PU template foam and the corresponding metal foam for (a) PPI 45, (b) PPI 60, (c) PPI 80. Notice the similar pore morphology between the PU and metallic foam for the same PPI. The pore sizes for the metallic foam are smaller than that of the respective PU foams.

Fig. 4. SEM images of the boundary between two metallic foam layers of different PPI: (a) PPI 45 and PPI 80, (b) PPI 80 and PPI 60, (c) PPI 60 and PPI 45. By layering the PU green bodies together before sintering, the particles on the struts at the boundary may bond together, such that the adjacent layers are sintered together.

Fig. 5. Sound absorption coefficient curves (experimental and TMM predictions) for metallic foam: (a) PPI 80, (b) PPI 60-45 and (c) PPI 60-80-45. The observed experimental and predicted curves are close to each other, suggesting that the method in Section 2.4 was adequate in predicting the sound absorption coefficients of functionally graded metallic foam in this study.

Fig. 6. Sound absorption coefficient distribution of metallic foam of one pore size with different pore sizes for thicknesses of (a) 20 mm; (b) 40 mm; and (c) 60 mm, respectively.

Fig. 7. Phasor representation diagram of the impedance of metallic foam of one pore size with different pore sizes for thicknesses of (a) 20 mm; (b) 40 mm; and (c) 60 mm, respectively. The dotted lines represent ellipses with constant absorption coefficients.

Fig. 8. Sound absorption coefficient distribution of metallic foam of one pore size with different thicknesses for (a) PPI 45; (b) PPI 60; and (c) PPI 80, respectively.

Fig. 9. Plots of average sound absorption coefficient between 1000 and 5000 Hz with varying thicknesses for PPI 45, 60 and 80. Generally, the average sound absorption increases with increasing thickness or decreasing pore size.

Fig. 10. Sound absorption coefficient of functionally graded metallic foam of thickness 40 mm with different layer arrangements for (a) PPI 45 and 60; (b) PPI 45 and 80; (c) PPI 60 and 80. Marked in a cross in each figure is the intersection points between the two curves.

Fig. 11. (a) Sound absorption coefficient distribution of the functionally graded metallic foam of thickness 40 mm for PPI 45 and 80, calculated from DB and TMM models for frequencies below 6000 Hz. (b) Plots of Eq. (26) with frequency. Notice the closeness in intersection points with the line $\text{ }\!\!\Delta\!\!\text{ }\alpha =0$.

Fig. 12. Sound absorption coefficient distribution of functionally graded metallic foam of thickness 60 mm with different layer arrangements for (a) PPI 45 (2 layers) and 60 (1 layer); (b) PPI 45 (2 layers) and 80 (1 layer); (c) PPI 60 (2 layers) and 45 (1 layer); (d) PPI 60 (2 layers) and 80 (1 layer); (e) PPI 80 (2 layers) and 45 (1 layer); (f) PPI 80 (2 layers) and 60 (1 layer).

Fig. 13. Sound absorption coefficient distribution of functionally graded metallic foam of thickness 60 mm with different layer arrangements for PPI 45, 60 and 80, each of thickness 20 mm.