Noise-absorbing properties of a homogeneous plate with arbitrary boundary conditions under the impact of a plane acoustic wave in acoustic medium

DOI: 10.34759/trd-2021-117-05


Lokteva N. A.1*, Ivanov S. I.2**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Russian Aircraft Corporation «MiG», 7, 1st Botkinsky passage, Moscow, 125284, Russia



The main purpose of the presented work consists in the displacements determining of the plate under the given boundary conditions. By reason of purely mathematical difficulties, such kind of problems consider, as a rule, a limited number of types of soundproof panels fixing, being reduced to the boundary conditions corresponding to the free bearing. Thus, obtaining techniques for solving the problems associated with interrelation of acoustic media and a plate is of significant scientific value. The approach used to solve problems with arbitrary boundary conditions is generally applicable to solving other problems, particularly, of the theory of plates and shells. It supposes a solution finding of a problem on sound absorbing properties of the homogeneous infinite plate. After this, strive for the fulfillment of boundary conditions in certain points of the infinite plate. The problem setting herewith is assumed related, where not only direct impact of the wave on the obstacle but also the acoustic media behavior prior to and after the noise absorbing obstacle are being accounted for. This formulation of the problem allows determining the noise level not only directly at the interface between the plate and the acoustic medium, but also at any distance from it.

The article presents the developed general approach to the solution of the problems with arbitrary boundary conditions for the plates. The problem of the plane harmonic wave interaction with the infinite homogeneous Kirchhoff-Love plate has been solved. The midline normal displacements were determined depending on the oncoming wave frequency. Influence functions for auxiliary forces, necessary to ensure the boundary conditions fulfillment in the specified points, were found for employing the method of compensating loads. The compensating forces values were determined based on the boundary conditions for rigid fixing of the plate edges. As an example, normal midline displacements, corresponding to the rigid fixing on the two edges and hinge attachment, were obtained based on superposition. The boundary conditions fulfillment in both cases was demonstrated. The sound absorption coefficient for a rigidly fixed plate has been determined.


Kirchhoff-Love plate, acoustic medium, harmonic wave, arbitrary boundary conditions, influence functions


  1. Denisov S.L., Medvedskii A.L. Trudy MAI, 2016, no. 91. URL:

  2. Paimushin V.N., Gazizullin R.K. Uchenye zapiski Kazanskogo universiteta. Seriya: fiziko-matematicheskie nauki, 2013, vol. 155, no. 3. pp. 126 – 141.

  3. Strett D.V. Teoriya zvuka (Theory of Sound), Moscow, Gostekhteorizdat, 1955, vol. 2, 474 p.

  4. Bobylev V.N., Moiseev V.A. Raschet zvukoizolyatsii odnosloinykh ograzhdayushchikh konstruktsii (Sound insulation computation of single-layer enclosing structures), Nizhnii Novgorod, NNGASU, 2000, 55 p.

  5. Zaborov V.I. Teoriya zvukoizolyatsii ograzhdayushchikh konstruktsii (The theory of enclosing structures soundproofing), Moscow, Stroiizdat, 1969, 185 p.

  6. Paimushin V.N., Gazizullin R.K. Uchenye zapiski Kazanskogo universiteta. Seriya: fiziko-matematicheskie nauki, 2020, vol. 162, no. 2, pp. 160 – 179. DOI: 10.26907/2541-7746.2020.2.160-179

  7. Paimushin V.N., Gazizullin R.K., Sharapov A.A. Uchenye zapiski Kazanskogo universiteta. Seriya: fiziko-matematicheskie nauki, 2015, vol. 157, no. 1, pp. 114 – 127.

  8. Beshenkov S.N., Goloskokov E.G., Ol'shanskii V.P. Akusticheskii zhurnal, 1974, vol. 20, no. 2, pp. 184 - 189.

  9. Kuznetsova E.L., Tarlakovskii D.V., Fedotenkov G.V., Medvedskii A.L. Trudy MAI. 2013, no. 71. URL:

  10. Bykova T.V., Mogilevich L.I., Popov V.S., Popova A.A., Chernenko A.V. Trudy MAI, 2018, no. 110. URL: DOI: 10.34759/trd-2020-110-6

  11. Paimushin V.N., Tarlakovskii D.V., Gazizullin R.K., Lukashevich A. Matematicheskie metody i fiziko-mekhanicheskie polya, 2014, vol. 57, no. 4, pp. 51 – 67.

  12. Firsanov V.V., Vo A.Kh., Chan N.D. Trudy MAI, 2019, no. 104. URL:

  13. Wilson G.P., Soroka W.W. Approximation to the Diffraction of Sound by a Circular Aperture in a Rigid Wall of Finite Thickness, Journal of the Acoustical Society of America, 1964, vol. 36, pp. 1023 – 1023. DOI:10.1121/1.1909325

  14. Kihlman T., Wilson G.P. Subway tunnel acoustics - influence of sound absorption treatment of tunnel walls, Engineering, 1976. URL:

  15. Kihlman Т.К., Nilsson A.C. The effects of some laboratory designs and. mounting conditions on reduction index measurements, Journal of Sound and Vibration, 1972, vol. 24, no. 3, pp. 349 – 364.

  16. Gorshkov A.G, Medvedskii A.L, Rabinskii L.N., Tarlakovskii D.V. Volny v sploshnykh sredakh (Waves in Continuous Media), Moscow, FIZMATLIT, 2004, 472 p.

  17. Igumnov L.A., Lokteva N.A., Paimushin V.N., Tarlakovskii D.V. Matematicheskie metody i fiziko-mekhanicheskie polya, 2013, vol. 56, no. 2, pp. 93 - 93.

  18. Ventsel' E.S., Dzhan-Temirov K.E., Trofimov A.M., Negol'sha E.V. Metod kompensiruyushchikh nagruzok v zadachakh teorii tonkikh plastinok i obolochek (Method of compensating loads in problems of the theory of thin plates and shells), Khar'kov, B.i., 1992, 93 p.

  19. Koreneva E.B. Mezhdunarodnyi zhurnal po raschetu grazhdanskikh i stroitel'nykh konstruktsii, 2018, vol. 14, no. 1, pp. 71 – 77. DOI: 10.22337/2587-9618-2018-14-1-71-77

  20. Nguen Ngok Khoa, Tarlakovskii D.V. Trudy MAI. 2012, no. 53, URL:

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