The Wave Field of a Layer with a Cylindrical Cavity

  • Anna FesenkoEmail author
  • Nataly Vaysfel’d
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)


The wave field of an infinite elastic layer weakened by a cylindrical cavity is constructed in this paper. The ideal contact conditions are given on the upper and bottom faces of the layer. The normal dynamic tensile load is applied to a cylindrical cavity’s surface at the initial moment of time. The Laplace and finite sin- and cos- Fourier integral transformations are applied successively directly to axisymmetric equations of motion and to the boundary conditions, on the contrary to the traditional approaches, when integral transformations are applied to solutions’ representation through harmonic and biharmonic functions. This operation leads to a one-dimensional vector inhomogeneous boundary value problem with respect to unknown transformations of displacements. The problem is solved using matrix differential calculus. The field of initial displacements is derived after application of inverse integral transformations. The normal stress on the faces of the elastic layer are constructed and investigated depending on the mechanical and dynamic parameters.


Elastic layer Dynamic load Cylindrical cavity Integral transformation 


  1. 1.
    Popov, G.Y.: An exact solution of the elasticity theory problem for an infinite layer weakened by a cylindric cavity. Dokladu RUN, 451(5), 1–4 (2013)Google Scholar
  2. 2.
    Menshykov, O., Menshykova, M., Vaysfeld, N.: Exact analytical solution for a pie-shaped wedge thick plate under oscillating load. Acta Mech. 228(12), 4435–4450 (2017). Scholar
  3. 3.
    Malitz, P.Y., Privarnikov, A.K.: The application of weber-type transformations to the solution of elasticity problems for layered media with a cylindrical hole. J. Voprosu prochnosty i plastichnossty 56–64 (1971)Google Scholar
  4. 4.
    Arutunyan, N.H., Abramyan, B.L.: Some axisymmetric problems for a half-space and an elastic layer with a vertical cylindrical notch. J. Izv. AN Arm. SSR. Mekhanica 22(3), 3–13 (1969)Google Scholar
  5. 5.
    Jain, N.K., Mittal, N.D.: Finite element analysis for stress concentration and deflection in isotopic, orthotropic and laminated composite plates with central circular hole under transverse static load. Mater. Sci. Eng. 498, 115–124 (2008)CrossRefGoogle Scholar
  6. 6.
    Zheng, Y., Chang-Boo, K., Chongdu, C., Hyeon Gyu, B.: The concentration of stress and strain in finite thickness elastic plate containing a circular hole. Int. J. of Solids Struct. 45(3–4), 713–731 (2008)zbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Physics and Information TechnologiesOdessa I.I. Mechnikov National UniversityOdessaUkraine

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