A research and modeling of wave processes at the scattering of nonlinear acoustic waves on cylindrical bodies

  • Iftikhar B. Abbasov Southern Federal University, Rostov-on-Don, Russia
Keywords: acoustic waves, cylindrical bodies, nonlinear interaction, scattering diagram, scattering


The article is devoted to the study of the scattering of nonlinear acoustic waves on cylindrical bodies. There was made a review of publications on the scattering of acoustic waves by inhomogeneities of the medium in the form of cylindrical bodies and shells. There were noted features of the small parameter method application in nonlinear acoustics. A three-dimensional model of the geometry of the problem in cylindrical coordinates was presented, nonlinear wave processes occurring between the falling plane and scattered cylindrical waves were described. The inhomogeneous wave equation is solved by the method of successive approximations of series expansion in a small parameter. An asymptotic expression for the acoustic pressure of a difference-frequency wave was obtained. A program for calculating scattering diagrams has been developed, and an algorithm for its operation is given. The acoustic pressure scattering diagram of a differential frequency wave on a rigid cylinder and its three-dimensional model are presented. The radius of convergence of the used method of expansion in a small parameter is determined.


Download data is not yet available.


Abbasov, I. B. (Ed.). (2016). Hyrdoacoustic Ocean Exploration: Theories and Experimental Application. John Wiley & Sons.

Abbasov, I. B., & Zagrai, N. P. (2019). Wave Problems of Scattering on Cylindrical Bodies. In 2019 Radiation and Scattering of Electromagnetic Waves (RSEMW) (pp. 228-231). IEEE. https://doi.org/10.1109/RSEMW.2019.8792694

Abbasov, I. B., & Zagrai, N. P. (2017). The problems of wave scattering by spheroidal bodies. In 2017 Radiation and Scattering of Electromagnetic Waves (RSEMW) (pp. 84-86). IEEE. https://doi.org/10.1109/RSEMW.2017.8103571

Andronov, I. V., & Lavrov, Y. A. (2015). Scattering by an elliptic cylinder with a strongly elongated cross section. Acoustical Physics, 61(4), 383-387. https://doi.org/10.1134/S1063771015040016

Dean III, L. W. (1962). Interactions between sound waves. The Journal of the Acoustical Society of America, 34(8), 1039-1044. https://doi.org/10.1121/1.1918241

Desjouy, C., Ollivier, S., Marsden, O., Karzova, M., & Blanc-Benon, P. (2016). Irregular reflection of weak acoustic shock pulses on rigid boundaries: Schlieren experiments and direct numerical simulation based on a Navier-Stokes solver. Physics of Fluids, 28(2), 027102. https://doi.org/10.1063/1.4940987

Dmitriev, K. V. (2018). Scattering of an Acoustic Field by Refraction–Density Inhomogeneities with a Small Wave Size and Solution of the Problem of Direct Scattering in an Inhomogeneous Medium. Acoustical Physics, 64(2), 131-143. https://doi.org/10.1134/S1063771018020033

Dos Santos, S., Lints, M., Poirot, N., & Salupere, A. (2015). Optimized excitation for nonlinear wave propagation in complex media: From biomedical acoustic imaging to nondestructive testing of cultural heritage. The Journal of the Acoustical Society of America, 138(3), 1796-1796. https://doi.org/10.1121/1.4933698

Duck, F. A. (2002). Nonlinear acoustics in diagnostic ultrasound. Ultrasound in medicine & biology, 28(1), 1-18. https://doi.org/10.1016/S0301-5629(01)00463-X

Dwight, G. B. (1983). Tablitsy integralov i drugie matematicheskie formuly [Tables of Integrals and Other Mathematical Formulas].

Gurbatov, S. N., Gryaznova, I. Y., & Ivashchenko, E. N. (2016). Study of acoustic wave backscattering by discrete inhomogeneities of different sizes. Acoustical Physics, 62(2), 202-206. https://doi.org/10.1134/S106377101602007X

Kleshchev, A. A. (2011). Scattering of low-frequency pulsed sound signals from elastic cylindrical shells. Acoustical Physics, 57(3), 375. https://doi.org/10.1134/S1063771011020102

Korn, G. A., & Korn, T. M. (2000). Mathematical handbook for scientists and engineers: definitions, theorems, and formulas for reference and review. Courier Corporation.

Larin, N. V., & Tolokonnikov, L. A. (2015). The scattering of a plane sound wave by an elastic cylinder with a discrete-layered covering. Journal of Applied Mathematics and Mechanics, 79(2), 164-169. https://doi.org/10.1016/j.jappmathmech.2015.07.007

Mitri, F. G. (2016). Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves. Ultrasonics, 66, 27-33. https://doi.org/10.1016/j.ultras.2015.12.003

Novikov, B. K., Rudenko, O. V., Timoshenko, V. I., & Breazeale, M. A. (1988). Nonlinear Underwater Acoustics by BK Novikov, OV Rudenko, and VI Timoshenko. https://doi.org/10.1121/1.396924

Ostashev, V. E., & Wilson, D. K. (2015). Acoustics in moving inhomogeneous media. CRC Press.

Partridge, C., & Smith, E. R. (1995). Acoustic scattering from bodies: Range of validity of the deformed cylinder method. The Journal of the Acoustical Society of America, 97(2), 784-795. https://doi.org/10.1121/1.412943

Rosa-Santos, P., Taveira-Pinto, F., Teixeira, L., & Ribeiro, J. (2015). CECO wave energy converter: Experimental proof of concept. Journal of Renewable and Sustainable Energy, 7(6), 061704. https://doi.org/10.1063/1.4938179

Skudrzyk, Eugen. The foundations of acoustics: basic mathematics and basic acoustics. Springer Science & Business Media, 2012.

How to Cite
Abbasov, I. (2019). A research and modeling of wave processes at the scattering of nonlinear acoustic waves on cylindrical bodies. International Research Journal of Engineering, IT & Scientific Research, 5(5), 32-44. https://doi.org/10.21744/irjeis.v5n5.779