Archives of Acoustics, 47, 4, pp. 539-546, 2022

Correction of Evanescent Wave Influence on the Flexural Wave Velocity and Wavelength Estimation Based on a Mode Shape Function

Academy of Technical and Art Applied Studies

Belgrade University

Miomir MIJIĆ
Belgrade University

Edinburgh Napier University
United Kingdom

The aim of this research is to use a simple acoustic method of a very near field recording, which enables measurement and display of oscillation modes, to estimate the velocity of flexural waves, based on the wavelengths of standing waves measured on the sample. The paper analyses cases of 1D geometry, flexural waves that occur on a beam excited by an impulse. Measurements were conducted on two different samples: steel and a wooden beam of the same length. Due to the appearance of evanescent waves at the boundary regions, the distance between the nodes of standing waves that occur deviates from half the wavelength, which can be compensated using a correction factor. Cases of fixed and free boundary conditions were analysed. By quantifying how much the boundary conditions change the mode shape function, it can be predicted how the mode of oscillation changes if the boundary conditions change, which can also find application in musical acoustics and sound radiation analysis.
Keywords: mode shape function; flexural wave velocity; very near field
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


ASTM E1875-13 (2013), Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance, ASTM International, doi: 10.1520/E1875-13.

ASTM E1876-15 (2015), Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Impulse Excitation of Vibration, ASTM International, doi: 10.1520/E1876-21.

Bissinger G., Oliver D. (2007), 3-D laser vibrometry on legendary old Italian violins, Sound and Vibration, 3(7): 10–14.

Brancheriau L. (2014), An alternative solution for the determination of elastic parameters in free–free flexural vibration of a Timoshenko beam,Wood Science and Technology, 48: 1269–1279, doi: 10.1007/s00226-014-0672-x.

Chladni E.F.F. (1787), Discoveries on the theory of sound, [in German: Entdeckungen über die Theorie des Klanges], Leipzig: bey Weidmanns Erben und Reich, doi: 10.3931/e-rara-4235.

de Bree H.-E., Svetovoy V., Raangs R., Visser R. (2004), The very near field, theory, simulations and measurements of sound pressure and particle velocity in the very near field, [in:] Proceedings of the 11th International Congress on Sound and Vibration, pp. 1–8.

Diligent O., Lowe M.J.S., Le Clézio E., Castaings M., Hosten B. (2003), Prediction and measurement of evanescent Lamb modes at the free end of a plate when the fundamental antisymmetric mode A0 is incident, The Journal of the Acoustical Society of America, 113(6): 3032–3042, doi: 10.1121/1.1568758.

Fahy F. (1985), Sound and Structural Vibration, Radiation, Transmission and Response, Academic Press Inc., New York.

Gough C. (2007), The violin: Chladni patterns, plates, shells and sounds, The European Physical Journal Special Topics, 145: 77–101, doi: 10.1140/epjst/e2007-00149-0.

Gough C. (2016), Violin acoustics, Acoustics Today, 12(2): 22–30.

Graff K.F. (1975), Wave Motion in Elastic Solids, Ohio State University Press.

Gren P., Tatar K., Granström J., Molin N.-E., Jansson E. V. (2006), Laser vibrometry measurements of vibration and sound fields of a bowed violin, Measurement Science and Technology, 17(4): 635–644, doi: 10.1088/0957-0233/17/4/005.

Jansson E., Molin N.-E., Sundin H. (1970), Resonances of a violin body studied by hologram interferometry and acoustical methods, Physica Scripta, 2(6): 243–256, doi: 10.1088/0031-8949/2/6/002.

Kalkert C., Kayser J. (2010), Laser Doppler Velocimetry, Biophysics Laboratory, University of California, San Diego.

Keele D.E. (1974), Low-frequency loudspeaker assessment by nearfield sound-pressure measurement, Journal of the Audio Engineering Society, 22(3): 154–162.

Meirovitch L. (1986), Elements of Vibration Analysis, McGraw-Hill College.

Pantelic F., Mijic M., Šumarac Pavlovic D., Ridley-Ellis D., Dudeš D. (2020), Analysis of a wooden specimen’s mechanical properties through acoustic measurements in the very near field, The Journal of the Acoustical Society of America, 147(4): EL320-EL325, doi: 10.1121/10.0001030.

Pantelic F., Prezelj J. (2014), Hair tension influence on the vibroacoustic properties of the double bass bow, The Journal of the Acoustical Society of America, 136(4): EL288–EL294, doi: 10.1121/1.4896408.

Pantelic F., Ridley-Ellis D., Mijic M., Šumarac Pavlovic D. (2017), Monitoring changes in wood properties using Very Near Field sound pressure scanning, [in:] 4th Annual Conference COST FP1302 WoodMusICK, Brussels, Belgium.

Prezelj J., Lipar P., Belšak A., Cudina M. (2013), On acoustic very near field measurements, Mechanical Systems and Signal Processing, 40(1): 194–207, doi: 10.1016/j.ymssp.2013.05.008.

Rayleigh J.W.S. (1945), The Theory of Sound, Vol. I–II, Dover Publications, New York.

Ryden N., Lowe M.J.S (2004), Guided wave propagation in three-layer pavement structures, The Journal of the Acoustical Society of America, 116(5): 2902–2913, doi: 10.1121/1.18082231.

Takiuti B.E., Manconi E., Brennan M.J., Lopes Jr. V. (2020), Wave scattering from discontinuities related to corrosion-like damage in one-dimensional waveguides, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42: 521, doi: 10.1007/s40430-020-02574-1.

Timoshenko S.P. (1921), On the correction for shear of the differential equation for transverse vibrations of prismatic bars, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(245): 744–746, doi: 10.1080/14786442108636264.

Woodhouse J. (2014), The acoustics of the violin: a review, Reports on Progress in Physics, 77(11): 115901.

DOI: 10.24425/aoa.2022.142017