Theoretical Analysis of Low-Frequency Sound Absorption Owing to the Vibration of Lightweight Powder Using a 1D Beam Model
Abstract
:1. Introduction
2. Measurement Overview and Preliminary Investigation
2.1. Measurement Apparatus and Samples
2.2. Demonstration of Sound Absorption Due to Longitudinal Vibration
3. Theoretical Analysis
3.1. Transfer Matrix Method
3.2. Characteristic Impedance and Propagation Constants of Powder Layers
3.3. Characteristic Impedance and Propagation Constants of Nonwoven Fabrics
3.4. Characteristic Impedance and Propagation Constants of the Air Space
3.5. Cascade Connection of Four-Terminal Networks in Equivalent Circuits
3.6. SAC Calculation
3.7. Determination of the Loss Factor
4. Verification of the Transfer Matrix of the Powder Layer
4.1. Comparison of the Experimental and Theoretical Values of the SAC in the Powder Layer Alone
4.2. Comparison of Experimental and Theoretical Values for the SAC with a Back Air Space
4.3. Powders to Which This Method Can Be Applied
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
SAC | Sound absorption coefficient |
SAM | Sound-absorbing materials |
5-DOF | Five degrees of freedom |
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Bulk Density ρ [g/cm3] | First Peak Frequency [Hz] | Feret Diameter [μm] | |
---|---|---|---|
Granulated silica (Featherfield Co., Ltd., Hiroshima, Japan) | 0.0568 | 550 | 43 |
Hollow plastic beads A (Expancel® 920DE40d30) (Japan Fillite Co., Ltd., Osaka, Japan) | 0.0298 | 1100 | 42 |
Hollow plastic beads B (matsumoto micro sphere® F–80DE) (Matsumoto Yushi-Seiyaku Co., Ltd., Osaka, Japan) | 0.0139 | 1837.5 | 110 |
Hollow glass beads (Hobbico, Inc., Champaign, IL, USA) | 0.0800 | 950 | 29 |
Calcium-carbonate-coated hollow plastic beads A (EMC–40(B)) (Japan Fillite Co., Ltd., Osaka, Japan) | 0.082 | 850 | 53 |
Calcium-carbonate-coated hollow plastic beads B (EMC–80(B)) (Japan Fillite Co., Ltd., Osaka, Japan) | 0.0707 | 1012.5 | 70 |
Calcium-carbonate-coated hollow plastic beads C (EMC–120()) (Japan Fillite Co., Ltd., Osaka, Japan) | 0.0628 | 1137.5 | 120 |
Experimental Value of the Absorption Coefficient at First Peak Frequency | |||
---|---|---|---|
Granulated silica | 0.991 | 0.176 | 0.257 |
Hollow plastic beads A (Expancel® 920DE40d30) | 0.989 | 0.164 | 0.250 |
Hollow plastic beads B (Matsumoto micro sphere® F–80DE) | 1.000 | 0.262 | |
Hollow glass beads | 0.808 | 0.034 | 0.224 |
Calcium-carbonate-coated hollow plastic beads A (EMC–40(B)) | 0.996 | 0.083 | 0.107 |
Calcium-carbonate-coated hollow plastic beads B (EMC–80(B)) | 0.988 | 0.074 | 0.115 |
Calcium-carbonate-coated hollow plastic beads C (EMC–120(α)) | 0.919 | 0.051 | 0.166 |
(Experimental) [Hz] | (Theoretical) [Hz] | Percent Error [%] | |
---|---|---|---|
Granulated silica | 550 | 555 | 0.90 |
Hollow plastic beads A (Expancel® 920DE40d30) | 1100 | 1107.5 | 0.68 |
Hollow plastic beads B (Matsumoto micro sphere® F–80DE) | 1837.5 | 1852.5 | 0.81 |
Hollow glass beads | 950 | 955 | 0.52 |
Calcium-carbonate-coated hollow plastic beads A (EMC–40(B)) | 850 | 850 | 0.00 |
Calcium-carbonate-coated hollow plastic beads B (EMC–80(B)) | 1012.5 | 1012.5 | 0.00 |
Calcium-carbonate-coated hollow plastic beads C (EMC–120(α)) | 1137.5 | 1142.5 | 0.44 |
(Experimental) [Hz] | (Theoretical) [Hz] | Percent Error [%] | |
---|---|---|---|
Granulated silica | 375 | 330 | 12.0 |
Hollow plastic beads A (Expancel® 920DE40d30) | 512.5 | 502.5 | 1.95 |
Hollow plastic beads B (Matsumoto micro sphere® F–80DE) | 775 | 755 | 2.58 |
Hollow glass beads | 387.5 | 320 | 17.4 |
Calcium-carbonate-coated hollow plastic beads A (EMC–40(B)) | 362.5 | 312.5 | 13.8 |
Calcium-carbonate-coated hollow plastic beads B (EMC–80(B)) | 387.5 | 340 | 12.3 |
Calcium-carbonate-coated hollow plastic beads C (EMC–120(α)) | 400 | 365 | 8.75 |
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Sakamoto, S.; Kawakami, Y.; Soeta, H.; Kubo, Y. Theoretical Analysis of Low-Frequency Sound Absorption Owing to the Vibration of Lightweight Powder Using a 1D Beam Model. Materials 2025, 18, 2611. https://doi.org/10.3390/ma18112611
Sakamoto S, Kawakami Y, Soeta H, Kubo Y. Theoretical Analysis of Low-Frequency Sound Absorption Owing to the Vibration of Lightweight Powder Using a 1D Beam Model. Materials. 2025; 18(11):2611. https://doi.org/10.3390/ma18112611
Chicago/Turabian StyleSakamoto, Shuichi, Yuya Kawakami, Hiroaki Soeta, and Yosuke Kubo. 2025. "Theoretical Analysis of Low-Frequency Sound Absorption Owing to the Vibration of Lightweight Powder Using a 1D Beam Model" Materials 18, no. 11: 2611. https://doi.org/10.3390/ma18112611
APA StyleSakamoto, S., Kawakami, Y., Soeta, H., & Kubo, Y. (2025). Theoretical Analysis of Low-Frequency Sound Absorption Owing to the Vibration of Lightweight Powder Using a 1D Beam Model. Materials, 18(11), 2611. https://doi.org/10.3390/ma18112611