3. Sound absorption results

In this arrangement, the idea is connecting the membrane (nanofibrous) resonator together with the mesh frame. The resonant frequencies fm,n of rectangle membrane with a variation of the side dimension are determined according to formula Eq. (10). The calculated resonant frequencies relating to vids m and n are shown in Tables 2–5. The dependence of the measured sound absorption coefficient on the sound frequency is shown in the following Figures 9–16. In Figures 9–12, the measured frequency dependence of the sound absorption coefficient for samples of the same basis weight and different mesh size is compared.

From the curves on Figures 9–12 describing the frequency dependence of the sound absorption coefficient for samples of the same basis weight and different mesh size, it can be seen that the two clear sound absorption peaks occur in the case of small mesh size (1G and 2G), while in the case of large meshes (3G and 4G), only one clear sound absorption peak exists. It can be seen, therefore, that the mesh size of the grid has a major impact on the amount of the sound absorption coefficient. It can also be observed from Figure 9 that the nanofibrous membrane of highest basis weight (6 g m<sup>2</sup> ) applied on the smaller meshes is better at dampening frequencies in the range of approximately 1500 Hz and 4000–5000 Hz, while the nanofiber layer deposited on the larger meshes is better at dampening frequencies of 2500–3000 Hz. Appearance of the peak for the smaller mesh (1G, 2G) at similar frequencies can be explained by the fact that the both meshes have the same width


#### Table 2.

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 4.1 4.3 mm side dimension; the vids m and n and rectangle dimensions a and b are mentioned.


#### Table 3.

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 9.4 4.1 mm side dimension; the vids m and n and rectangle dimensions a and b are mentioned.


of 4.1 mm, which is provides the same deviation in the one of axis, regardless of the total area of the mesh. The similar phenomenon can be seen for the highest meshes (3G and 4G) where the constant dimension of meshes is 9 mm with result of identical

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 6 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

Subsequently, the influence of the basis weight of the nanolayer spun on a grid of the same mesh size onto the maximum values of the sound absorption coefficient in relation to the frequency was examined (see Figures 13–16). By checking the grids themselves (gray curve on Figures 13–16), almost identical curves of all mesh sizes were found, with only the minimum values of the sound absorption coefficient. It can be said, therefore, that the mass of the carrier grid alone does not significantly influence the course of the sound absorption curves. The basis weight influence on the sound absorption is given by the theory Eqs. (2) and (3) where the resonant frequency of homogenous membrane decreases with its increasing basis weight. The

one of sound absorption peaks for all sample configurations (Figures 9–12).

4G Mesh size 9.0;14.2 a (m) b (m) CM (m s<sup>1</sup>

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane

DOI: http://dx.doi.org/10.5772/intechopen.82615

dimension; the vids m and n and rectangle dimensions a and b are mentioned.

Table 5.

Figure 9.

33

m 1 n 1 0.009 0.0142 11.76 773 m 1 n 2 0.009 0.0142 11.76 1055 m 2 n 1 0.009 0.0142 11.76 1370 m 2 n 2 0.009 0.0142 11.76 1547 m 3 n 1 0.009 0.0142 11.76 2003 m 3 n 2 0.009 0.0142 11.76 2127 m 3 n 3 0.009 0.0142 11.76 2320 m 1 n 3 0.009 0.0142 11.76 1403 m 2 n 3 0.009 0.0142 11.76 1803

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 9.0 14.2 mm side

) fm,n (Hz)

#### Table 4.

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 9.0 9.4 mm side dimension; the vids m and n and rectangle dimensions a and b are mentioned.

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane DOI: http://dx.doi.org/10.5772/intechopen.82615


#### Table 5.

1G Mesh size 4.1;4.3 a (m) b (m) CM (m s<sup>1</sup>

dimension; the vids m and n and rectangle dimensions a and b are mentioned.

dimension; the vids m and n and rectangle dimensions a and b are mentioned.

dimension; the vids m and n and rectangle dimensions a and b are mentioned.

3G Mesh size 9.0; 9.4 a (m) b (m) CM (m s<sup>1</sup>

2G Mesh size 9.4;4.1 a (m) b (m) CM (m s<sup>1</sup>

Table 2.

Acoustics of Materials

Table 3.

Table 4.

32

m 1 n 1 0.0041 0.0043 11.76 1981 m 1 n 2 0.0041 0.0043 11.76 3087 m 2 n 1 0.0041 0.0043 11.76 3177 m 2 n 2 0.0041 0.0043 11.76 3962 m 3 n 1 0.0041 0.0043 11.76 4514 m 3 n 2 0.0041 0.0043 11.76 5097 m 3 n 3 0.0041 0.0043 11.76 5943 m 1 n 3 0.0041 0.0043 11.76 4345 m 2 n 3 0.0041 0.0043 11.76 5005

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 4.1 4.3 mm side

m 1 n 1 0.0094 0.0041 11.76 1564 m 1 n 2 0.0094 0.0041 11.76 2935 m 2 n 1 0.0094 0.0041 11.76 1903 m 2 n 2 0.0094 0.0041 11.76 3129 m 3 n 1 0.0094 0.0041 11.76 2361 m 3 n 2 0.0094 0.0041 11.76 3427 m 3 n 3 0.0094 0.0041 11.76 4693 m 1 n 3 0.0094 0.0041 11.76 4347 m 2 n 3 0.0094 0.0041 11.76 4480

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 9.4 4.1 mm side

m 1 n 1 0.009 0.0094 11.76 904 m 1 n 2 0.009 0.0094 11.76 1411 m 2 n 1 0.009 0.0094 11.76 1448 m 2 n 2 0.009 0.0094 11.76 1809 m 3 n 1 0.009 0.0094 11.76 2057 m 3 n 2 0.009 0.0094 11.76 2325 m 3 n 3 0.009 0.0094 11.76 2713 m 1 n 3 0.009 0.0094 11.76 1987 m 2 n 3 0.009 0.0094 11.76 2286

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 9.0 9.4 mm side

) fm,n (Hz)

) fm,n (Hz)

) fm,n (Hz)

Calculation of resonant frequencies of a rectangle membrane with 1 g m<sup>2</sup> basis weight of 9.0 14.2 mm side dimension; the vids m and n and rectangle dimensions a and b are mentioned.

#### Figure 9.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 6 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

of 4.1 mm, which is provides the same deviation in the one of axis, regardless of the total area of the mesh. The similar phenomenon can be seen for the highest meshes (3G and 4G) where the constant dimension of meshes is 9 mm with result of identical one of sound absorption peaks for all sample configurations (Figures 9–12).

Subsequently, the influence of the basis weight of the nanolayer spun on a grid of the same mesh size onto the maximum values of the sound absorption coefficient in relation to the frequency was examined (see Figures 13–16). By checking the grids themselves (gray curve on Figures 13–16), almost identical curves of all mesh sizes were found, with only the minimum values of the sound absorption coefficient. It can be said, therefore, that the mass of the carrier grid alone does not significantly influence the course of the sound absorption curves. The basis weight influence on the sound absorption is given by the theory Eqs. (2) and (3) where the resonant frequency of homogenous membrane decreases with its increasing basis weight. The

#### Figure 10.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 3 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

#### Figure 11.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 2 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

influence of basis weight on the sound absorption coefficient is not clear for these measured configurations. For the smaller meshes (1G and 2G), the sound absorption increases with decreasing basis weight of nanofibrous membrane. Then the antiresonance effect of heavy membrane where the acoustic element loses sound absorption ability (approx. 2500 Hz) occurs due to undamped vibrating membrane. For the higher meshes, the antiresonance effect does not occur because of the grid configuration with the 30 mm air gap does not allow sound absorption below 1500 Hz where the first resonant frequency should cause the first sound absorption peak.

column on the right) can be compared with the calculated values from Tables 2–5. The measured values of resonant frequency are in a good agreement for samples with mesh grid 1G where the calculated value of the first and second resonant frequency f1,1 = 1981 Hz and f2,2 = 3962 Hz (Table 2) can be compared with the measured first and second resonant frequencies f1 = 1672 Hz and f1 = 3696 Hz (Table 6) given by the sound absorption peaks from Figure 12. Analogous to the results, the samples with mesh grid 2G where the calculated value of the first and second resonant frequencies f1,1 = 1564 Hz and f2,2 = 3129 Hz (Table 2) can be compared with the measured first and second resonant frequencies f1 = 1536 Hz and

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different

1 4.3 mm. 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of

; 1 N\_1 g m<sup>2</sup>

) covering the grid of mesh size 4

; 2 N\_2 g m<sup>2</sup>

; 3 N\_3 g m<sup>2</sup>

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 1 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane

DOI: http://dx.doi.org/10.5772/intechopen.82615

Figure 12.

Figure 13.

35

basis weights (6N\_6 g m<sup>2</sup>

1 mm thickness and reflective wall was 30 mm.

The resonant frequencies with relevant sound absorption coefficients are summarized in Table 6. The resonant frequency for membrane of 1 g m<sup>2</sup> (lightest

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane DOI: http://dx.doi.org/10.5772/intechopen.82615

#### Figure 12.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 1 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

#### Figure 13.

influence of basis weight on the sound absorption coefficient is not clear for these measured configurations. For the smaller meshes (1G and 2G), the sound absorption

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 2 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of 3 g m<sup>2</sup> covering the grid of different mesh sizes: 1G\_4.1 4.3 mm; 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

increases with decreasing basis weight of nanofibrous membrane. Then the antiresonance effect of heavy membrane where the acoustic element loses sound absorption ability (approx. 2500 Hz) occurs due to undamped vibrating membrane. For the higher meshes, the antiresonance effect does not occur because of the grid configuration with the 30 mm air gap does not allow sound absorption below 1500 Hz where the first resonant frequency should cause the first sound absorption peak. The resonant frequencies with relevant sound absorption coefficients are summarized in Table 6. The resonant frequency for membrane of 1 g m<sup>2</sup> (lightest

Figure 10.

Acoustics of Materials

Figure 11.

34

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different basis weights (6N\_6 g m<sup>2</sup> ; 3 N\_3 g m<sup>2</sup> ; 2 N\_2 g m<sup>2</sup> ; 1 N\_1 g m<sup>2</sup> ) covering the grid of mesh size 4 1 4.3 mm. 2G\_9.4 4.1 mm; 3G\_9.0 9.4 mm; 4G\_9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

column on the right) can be compared with the calculated values from Tables 2–5. The measured values of resonant frequency are in a good agreement for samples with mesh grid 1G where the calculated value of the first and second resonant frequency f1,1 = 1981 Hz and f2,2 = 3962 Hz (Table 2) can be compared with the measured first and second resonant frequencies f1 = 1672 Hz and f1 = 3696 Hz (Table 6) given by the sound absorption peaks from Figure 12. Analogous to the results, the samples with mesh grid 2G where the calculated value of the first and second resonant frequencies f1,1 = 1564 Hz and f2,2 = 3129 Hz (Table 2) can be compared with the measured first and second resonant frequencies f1 = 1536 Hz and

#### Figure 14.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different basis weights (6N\_6 g m<sup>2</sup> ; 3 N\_3 g m<sup>2</sup> ; 2 N\_2 g m<sup>2</sup> ; 1 N\_1 g m<sup>2</sup> ) covering the grid of mesh size 9.4 4.1 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

Figure 16.

basis weights (6N\_6 g m<sup>2</sup>

1G mesh with membrane 6 N

2G mesh with membrane 6 N

3G mesh with membrane 6 N

4G mesh with membrane 6 N

Table 6.

37

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different

α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz)

0.801 5008 0.966 4432 0.974 3896 0.906 3696

α f<sup>1</sup> (Hz) f<sup>2</sup> (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz)

0.941 4312 0.958 3560 0.943 3448 0.934 3448

α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz)

0.968 2728 0.651 3424 0.731 2872 0.349 1536

α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz) α f1 (Hz) f2 (Hz)

— —— — 0.57 3272 — —

Measured resonant frequencies of a rectangle membrane of different basis weights and different side dimensions.

; 1 N\_1 g m<sup>2</sup>

1G mesh with membrane 2 N

2G mesh with membrane 2 N

3G mesh with membrane 2 N

4G mesh with membrane 2 N

) covering the grid of mesh size

1G mesh with membrane 1 N

2G mesh with membrane 1 N

3G mesh with membrane 1 N

4G mesh with membrane 1 N

; 2 N\_2 g m<sup>2</sup>

1G mesh with membrane 3 N

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane

DOI: http://dx.doi.org/10.5772/intechopen.82615

2G mesh with membrane 3 N

3G mesh with membrane 3 N

4G mesh with membrane 3 N

9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

0.858 1600 0.858 1600 0.95 1592 0.867 1672

0.944 1456 0.943 1456 0.95 1592 0.867 1536

0.677 1512 0.863 2816 0.51 1536 0.25 1056

0.95 2656 0.783 2816 0.586 2840 — —

The sound absorption coefficient α is mentioned for each resonant frequency rectangle membrane.

; 3 N\_3 g m<sup>2</sup>

#### Figure 15.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different basis weights (6N\_6 g m<sup>2</sup> ; 3 N\_3 g m<sup>2</sup> ; 2 N\_2 g m<sup>2</sup> ; 1 N\_1 g m<sup>2</sup> ) covering the grid of mesh size 9.0 9.4 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

f1 = 3448 Hz (Table 6) given by the sound absorption peaks from Figure 12. The samples with mesh grid 3G where the calculated value of first and second resonant frequency f1,1 = 904 Hz and f2,2 = 1809 Hz (Table 2) can be compared with the measured first and second resonant frequencies f1 = 1056 Hz and f1 = 1536 Hz (Table 6) given by the sound absorption peaks from Figure 12. The clear sound absorption peaks of sample with mesh grid 4G do not occur. That is why the comparison cannot be done.

Sound Absorbing Resonator Based on the Framed Nanofibrous Membrane DOI: http://dx.doi.org/10.5772/intechopen.82615

#### Figure 16.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different basis weights (6N\_6 g m<sup>2</sup> ; 3 N\_3 g m<sup>2</sup> ; 2 N\_2 g m<sup>2</sup> ; 1 N\_1 g m<sup>2</sup> ) covering the grid of mesh size 9.0 14.2 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.


#### Table 6.

f1 = 3448 Hz (Table 6) given by the sound absorption peaks from Figure 12. The samples with mesh grid 3G where the calculated value of first and second resonant frequency f1,1 = 904 Hz and f2,2 = 1809 Hz (Table 2) can be compared with the measured first and second resonant frequencies f1 = 1056 Hz and f1 = 1536 Hz (Table 6) given by the sound absorption peaks from Figure 12. The clear sound absorption peaks of sample with mesh grid 4G do not occur. That is why the

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different

; 1 N\_1 g m<sup>2</sup>

; 2 N\_2 g m<sup>2</sup>

9.0 9.4 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

Frequency dependence of the sound absorption coefficient; comparison of nanofibrous membrane of different

; 1 N\_1 g m<sup>2</sup>

) covering the grid of mesh size

) covering the grid of mesh size

; 2 N\_2 g m<sup>2</sup>

9.4 4.1 mm. The air gap between the sample of 1 mm thickness and reflective wall was 30 mm.

; 3 N\_3 g m<sup>2</sup>

; 3 N\_3 g m<sup>2</sup>

comparison cannot be done.

Figure 14.

Figure 15.

36

basis weights (6N\_6 g m<sup>2</sup>

basis weights (6N\_6 g m<sup>2</sup>

Acoustics of Materials

Measured resonant frequencies of a rectangle membrane of different basis weights and different side dimensions. The sound absorption coefficient α is mentioned for each resonant frequency rectangle membrane.
