Dynamic Properties of Thin-Walled Structures Under Changing Pressure Conditions in the Contact Fluid

  • M. A. Sumbatyan
  • Evgeny N. Barkanov
  • A. E. TarasovEmail author
Part of the Engineering Materials book series (ENG.MAT.)


We propose an analytical algorithm to study harmonic oscillation of a rectangular elastic plate in an incompressible fluid, with varying pressure conditions. Application of the two-dimensional Fourier transform leads to a two-dimensional integral equation with a two-dimensional integral as a kernel. The solution of the basic integral equation is represented as a series by the Chebyshev orthogonal polynomials. The problem is reduced to an infinite system of one-dimensional integral equations. The asymptotic approach allows us to solve each equation of the system independently. The solution of the integral equation leads to an ordinary differential equation of the fourth order for the function of the plate vibrations. The obtained solution determines the form of the oscillation. The results are given on example of the aluminum plate oscillations for a number of frequencies by varying air pressure density. The results are compared with experimental data.


Harmonic oscillation Air damping Incompressible fluid Elastic plate Integral equation 


  1. 1.
    M. Wesolowski, E. Barkanov, Air damping influence on dynamic parameters of laminated composite plates. Measurement 85, 239 (2016)CrossRefGoogle Scholar
  2. 2.
    M.A. Sumbatyan, A. Scalia, Equations of Mathematical Diffraction Theory (CRC Press, Boca Raton, 2004)Google Scholar
  3. 3.
    A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, Integrals and Series (Gordon and Breach Science Publishers, Amsterdam, 1986), pp. 1–3Google Scholar
  4. 4.
    A. Pompei, A. Rigano, M.A. Sumbatyan, Contact problem for a rectangular punch on the porous elastic half-space. J. Elasticity 76, 1 (2004)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • M. A. Sumbatyan
    • 1
  • Evgeny N. Barkanov
    • 2
  • A. E. Tarasov
    • 1
    Email author
  1. 1.I.I. Vorovich Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia
  2. 2.Riga Technical UniversityRigaLatvia

Personalised recommendations