Study on the vibration transmission speed and damping characteristics of piano soundboard

Jinyi Chen
Key Laboratory of Bio-Based Material Science & Technology of Ministry of Education, Northeast Forestry University, Harbin 150040, China
Guanzheng Wan
Key Laboratory of Bio-Based Material Science & Technology of Ministry of Education, Northeast Forestry University, Harbin 150040, China
Lan He
Key Laboratory of Bio-Based Material Science & Technology of Ministry of Education, Northeast Forestry University, Harbin 150040, China
Jing Zhou
Key Laboratory of Bio-Based Material Science & Technology of Ministry of Education, Northeast Forestry University, Harbin 150040, China
Haotian Cui
Key Laboratory of Bio-Based Material Science & Technology of Ministry of Education, Northeast Forestry University, Harbin 150040, China
Zhenbo Liu
Key Laboratory of Bio-Based Material Science & Technology of Ministry of Education, Northeast Forestry University, Harbin 150040, China

Article ID: 4326

Keywords: four types of piano soundboards, wave velocity, damping ratio, different grain directions, frequency dependence

Abstract

The piano soundboard converts string vibrations into radiated sound, affecting tonal quality. However, the propagation and energy dissipation of vibration waves along different grain directions remain insufficiently studied. To study vibration wave propagation and dissipation in piano soundboards of different composite processes, four quarter-size soundboards (moisture content 7%–9%) were selected: one tone-wood soundboard (T) and three laminated boards (L90 with vertical core, L55 with inclined core, L180 with horizontal core). Free boundary conditions were simulated via elastic rope suspension; time-domain responses were recorded at 16 kHz sampling (2,048 points). The angle α between the line connecting the two accelerometers and the core layer direction (for T, grain direction defined as 0°) was varied from 0° (parallel) to 90° (perpendicular) in 15° steps. Wave velocity and damping ratios were extracted using gradient and envelope fitting methods. The results showed: T exhibited the highest wave velocity from 0° to 90°, decreasing with angle (R² = 0.985), and a maximum anisotropy ratio of 4.59; L90 was angle-insensitive with weak correlation (R²= 0.735); L55 showed a trend similar to T (R²= 0.990); the wave velocity of L180 generally decreased but rebounded at 30°. Broadband damping ratios were 0.002–0.007, with T averaging 0.0040 (maximum 0.0058), L90 the lowest (average 0.0035, maximum 0.0049), L55 the highest (average 0.0051, maximum 0.0065), and L180 averaging 0.0038 (maximum 0.0062). Narrowband analysis showed that the damping ratios of all soundboards decreased exponentially with increasing frequency. The results guide piano soundboard vibration, material selection, and processing.

Published

2026-07-23

How to Cite

Chen, J., Wan, G., He, L., Zhou, J., Cui, H., & Liu, Z. (2026). Study on the vibration transmission speed and damping characteristics of piano soundboard. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4326

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Vol. 60 No. 5 (2026): In Progress

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Bal BC, Bektaş İ. The effects of wood species, load direction, and adhesives on bending properties of laminated veneer lumber. BioResources. 2012; 7(3): 3104–3112. doi: 10.15376/biores.7.3.3104-3112

[2]Liu Z, Liu Y, Miao Y, et al. Relationship between vibration property of resonance board and subjective evaluation of piano acoustical quality. Scientia Silvae Sinicae. 2009; 45(4): 100–106. Available online: https://html.rhhz.net/linyekexue/html/090417.htm (in Chinese)

[3]Xu H, Xu G, Wang L, et al. Propagation behavior of acoustic wave in wood. Journal of Forestry Research. 2014; 25(3): 671–676. doi: 10.1007/s11676-014-0506-6

[4]Guo J, Fang S, Li M, et al. Anisotropic study of wave velocity and energy decay of stress wave propagation on wood surface. Wood Material Science & Engineering. 2025; 1–10. doi: 10.1080/17480272.2025.2589486

[5]Bader R, Plath N. Impact of Damping on Oscillation Patterns on the Plain Piano Soundboard. Acoustics. 2022; 4(4): 1013–1027. doi: 10.3390/acoustics4040062

[6]Yang Y. Research on GRNN Prediction Model for Acoustic Quality of Yueqin Based on Wood Vibration Characteristics. Forest Engineering. 2024; 40(4): 160–167. Available online: https://cjournal.hep.com.cn/1006-8023/CN/10.7525/j.issn.1006-8023.2024.04.017 (in Chinese)

[7]Sanabria SJ, Furrer R, Neuenschwander J, et al. Analytical modeling, finite-difference simulation and experimental validation of air-coupled ultrasound beam refraction and damping through timber laminates, with application to non-destructive testing. Ultrasonics. 2015; 63: 65–85. doi: 10.1016/j.ultras.2015.06.013

[8]Brémaud I, Gril J. Moisture content dependence of anisotropic vibrational properties of wood at quasi equilibrium: analytical review and multi-trajectories experiments. Holzforschung. 2021; 75(4): 313–327. doi: 10.1515/hf-2020-0028

[9]Faktorová D, Stanciu MD, Krbata M, et al. Analysis of the Anisotropy of Sound Propagation Velocity in Thin Wooden Plates Using Lamb Waves. Polymers. 2024; 16(6): 753. doi: 10.3390/polym16060753

[10]Vallely S, Schoenwald S. Higher-order modal parameter estimation and verification of cross-laminated timber plates for structural-acoustic analyses. Acta Acustica. 2024; 8: 52. doi: 10.1051/aacus/2024043

[11]Nkibeu JB, Makomra V, Sali M, et al. Damping properties of some tropical wood species determined by free transverse vibration method. Wood Material Science & Engineering. 2025; 20(6): 1189–1195. doi: 10.1080/17480272.2024.2388213

[12]Liu Y, Zhao G. Wood Science, 2nd ed. China Forestry Publishing House; 2012.

[13]Song R, Li Y, Han S, et al. Mechanism by Which Heat Treatment Influences the Acoustic Vibration Characteristics of Bamboo. Materials. 2025; 18(23): 5335. doi: 10.3390/ma18235335

[14]Cai B, Bo L, Campbell A, et al. Noncontact pulsed laser-scanning laser Doppler vibrometer (PL-SLDV) phased array imaging for damage detection in composites. Ultrasonics. 2026; 157: 107787. doi: 10.1016/j.ultras.2025.107787

[15]Shi J, Yin S, Huang W, et al. Application of vibrational methods in wood performance testing: A short review. BioResources. 2025; 20(2). doi: 10.15376/biores.20.2.Shi

[16]Urgela S. Grading of wooden plates for musical instrument making by means of holographic interferometry. Optical Engineering. 1998; 37(7): 2108. doi: 10.1117/1.601702

[17]Zhang C, Luo J, Xu W, et al. Comparison of two kinds of sound velocity measurement methods of spruce timber used for piano. Journal of Forestry Engineering. 2010; 24(3): 56–59. (in Chinese)

[18]Stanciu MD, Nastac SM, Chen CW, et al. Exploring the Dynamic Properties of Tropical and Temperate Wood Species for Musical Instruments. Applied Sciences. 2025; 15(22): 11926. doi: 10.3390/app152211926

[19]Kouroussis G, Fekih LB, Descamps T. Using experimental modal analysis to assess the behaviour of timber elements. Mechanics & Industry. 2017; 18(7): 704. doi: 10.1051/meca/2017042

[20]Ege K, Boutillon X, Rébillat M. Vibroacoustics of the piano soundboard: (Non)linearity and modal properties in the low- and mid-frequency ranges. Journal of Sound and Vibration. 2013; 332(5): 1288–1305. doi: 10.1016/j.jsv.2012.10.012

[21]Zhao K, Yang Y, Luo Y. Broadband Love Wave Phase Velocity Maps Based on Modified Double‐Beamforming of Ambient Noise Cross‐Correlations. Journal of Geophysical Research: Solid Earth. 2024; 129(3). doi: 10.1029/2023JB026871

[22]Li M, Wang M, Ding R, et al. Study of acoustic emission propagation characteristics and energy attenuation of surface transverse wave and internal longitudinal wave of wood. Wood Science and Technology. 2021; 55(6): 1619–1637. doi: 10.1007/s00226-021-01329-y

[23]Bahmani H, Mostafaei H, Mostofinejad D. Review of Energy Dissipation Mechanisms in Concrete: Role of Advanced Materials, Mix Design, and Curing Conditions. Sustainability. 2025; 17(15): 6723. doi: 10.3390/su17156723

[24]Hu Z, Wang X, Zheng G. Free Vibration Identification of the Geometrically Nonlinear Isolator with Elastic Rings by Using Hilbert Transform. In: Nonlinear Dynamics, Volume 1. Springer International Publishing; 2017. pp. 69–76. doi: 10.1007/978-3-319-54404-5_7

[25]Thomson WT. Theory of Vibration with Applications, 4th ed. CRC Press; 1993. doi: 10.1201/9780203718841

[26]Xu Z, Tao Y, Hernandez L. Novel Methods for the Computation of Small-Strain Damping Ratios of Soils from Cyclic Torsional Shear and Free-Vibration Decay Testing. Geotechnics. 2021; 1(2): 330–346. doi: 10.3390/geotechnics1020016

[27]Merhar M. Identification of Damping of Spruce Wood (Picea abies) under Various Levels of Moisture Content Using Time-Scale Decomposition. Polymers. 2024; 16(10): 1313. doi: 10.3390/polym16101313

[28]Wavelet Packets: Decomposing the Details. Available online: https://ww2.mathworks.cn/help/wavelet/ug/wavelet-packets-decomposing-the-details.html (accessed on 25 April 2026).

[29]Horbelt N, Dunlop JWC, Bertinetti L, et al. Effects of moisture and cellulose fibril angle on the tensile properties of native single Norway spruce wood fibres. Wood Science and Technology. 2021; 55(5): 1305–1318. doi: 10.1007/s00226-021-01315-4

[30]He L, Liang Y, Zhang L, et al. Measurement and Analysis of the Vibration Responses of Piano Soundboards with Different Structures. Materials. 2024; 17(5): 1004. doi: 10.3390/ma17051004

[31]Tan C, Huang B, Liu D, et al. Effect of Mimic Vegetation with Different Stiffness on Regular Wave Propagation and Turbulence. Water. 2019; 11(1): 109. doi: 10.3390/w11010109

[32]Gupta S, Haq M, Cvetkovic K, et al. Numerical Far-Field Investigation into Guided Waves Interaction at Weak Interfaces in Hybrid Composites. Journal of Composites Science. 2025; 9(8): 387. doi: 10.3390/jcs9080387

[33]Wang L, Rokhlin SI. Ultrasonic wave interaction with multidirectional composites: Modeling and experiment. The Journal of the Acoustical Society of America. 2003; 114(5): 2582–2595. doi: 10.1121/1.1616920

[34]Ye J, Sun Y. Sound Radiation Characteristics Analysis of Laminates Based on Sound Radiation Modal Method. Noise and Vibration Control, 2023; 43(3): 27–33. Available online: https://nvc.sjtu.edu.cn/CN/abstract/abstract3466.shtml (in Chinese)

[35]Shan S, Zhang Y, Song Y, et al. Cumulative second harmonic Lamb wave generation and propagation in composite laminates: an insight into the influence of material anisotropy and damping. e-Journal of Nondestructive Testing. 2024; 29(7). doi: 10.58286/29758

[36]Feng H, Li L. Review of damping composite materials and structures involving self-healing constituents. Frontiers of Mechanical Engineering. 2025; 20(2): 15. doi: 10.1007/s11465-025-0833-7

[37]Al-Dulaijan SU, Youzera H, Meftah SA, et al. Nonlinear Damping and Vibration Assessment of Sandwich Beam with Composite Faces and Viscoelastic Core Layer. International Journal of Structural Stability and Dynamics. 2024; 24(08): 2450083. doi: 10.1142/S0219455424500834

[38]Li Z, Chu S, Zhang Y, et al. Transforming interface properties of wood laminate composites functionalized by adhesive penetration. Composites Part B: Engineering. 2023; 263: 110859. doi: 10.1016/j.compositesb.2023.110859

[39]Chełmecki J, Szeptyński P, Jasińska D, et al. Analyzing the Vibration Response of Adhesively Bonded Composite Cantilevers. Materials. 2024; 18(1): 93. doi: 10.3390/ma18010093

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Study on the vibration transmission speed and damping characteristics of piano soundboard

Abstract

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