To the Solving of the Nonstationary Spatial Lamb—Cerutti Problem

  • D. Prikazchikov
  • Yu. Protserov
  • N. VaysfeldEmail author
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)


The nonstationary Lamb-Cerutti problem was solved in the spatial statement for the elastic half-plane. Explicit formulae in the Laplace transform domain were derived. The solution was provided in detail for the case of steady state tangential and normal loads. Explicit formulae for the stresses and displacements of the half-space for both normal and tangent load were obtained.


Lamb-Cerutti problem Nonstationary Spatial Explicit form Integral transforms 



Support through the Erasmus + KA107 framework is gratefully acknowledge. The authors are also indebted to Prof J. Kaplunov for fruitful discussions.


  1. 1.
    Popov, G.Y., Vaisfeld, N.: On a new approach to the Lamb problem solution. Doklady Phys. 55(5), 246–251 (2010)CrossRefGoogle Scholar
  2. 2.
    Sretenskii, L.N.: In Problems of Continuum Mechanics, pp. 411–427. Akad. Nauk SSSR, Moscow (1961)Google Scholar
  3. 3.
    Kaplunov, J., Prikazchikov, D.: Asymptotic theory for Rayleigh and Rayleigh-type waves. Adv. Appl. Mech. 50, 1–106 (2017)CrossRefGoogle Scholar
  4. 4.
    Sonin, N.Y.: The Investigation of Cylindrical Functions and Special Polynomials (in Russian). Gostexizdat, Moscow (1954)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsKeele UniversityStaffordshireUK
  2. 2.Department of Mathematics, Physics and ITOdesa Mechnikov UniversityOdesaUkraine

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