Journal of Mathematical Sciences

, Volume 203, Issue 2, pp 202–214 | Cite as

Elastic Half Plane Under the Action of Nonstationary Surface Kinematic Perturbations

  • V. A. Vestyak
  • A. R. Hachkevych
  • D. V. Tarlakovskii
  • R. F. Terletskii

A homogeneous isotropic elastic half plane with nonstationary normal displacements on the boundary is considered. With the use of the Laplace and Fourier integral transformations, we propose integral representations for displacements with kernels in the form of surface influence functions. The originals are computed by using an algorithm of joint inversion of these transformations based on the construction of analytic extensions of the transforms. The explicit form of the influence functions is obtained. Some examples of their evaluation are presented.


Half Plane Elastic Half Space Influence Function Joint Inversion Ukrainian National Academy 
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  1. 1.
    Ya. I. Burak, O. R. Hachkevych and R. F. Terletskyi, Thermal Mechanics of Multicomponent Bodies with Low Electroconductivity [in Ukrainian], Spolom, Lviv (2006), Vol. 1, in: Ya. I. Burak and R. M. Kushnir (Eds.), Modeling and Optimization in Thermomechanics of Electroconducting Inhomogeneous Bodies [in Ukrainian], Spolom, Lviv (2006–2011), Vol. 1–5.Google Scholar
  2. 2.
    V. A. Vestyak, A. S. Sadkov, and D. V. Tarlakovskii, “Propagation of unsteady bulk perturbations in an elastic half plane,” Mech. Solids, 46, No. 2, 266–274 (2011).CrossRefGoogle Scholar
  3. 3.
    V. A. Vestyak and D. V. Tarlakovskii, “Nonstationary waves in electromagnetoelastic bodies,” in: V. D. Kubenko, R. M. Kushnir, and D. V. Tarlakovskii (Eds.), Nonstationary Processes of Deformation of Structural Elements Caused by the Action of Fields of Various Physical Nature [in Ukrainian], Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv (2012), pp. 22–25.Google Scholar
  4. 4.
    O. R. Hachkevych, R. S. Musii, and D. V. Tarlakovskii, Thermal Mechanics of Nonferromagnetic Electroconducting Bodies under the Action of Impulsive Electromagnetic Fields with Modulated Amplitude [in Ukrainian], Spolom, Lviv (2011).Google Scholar
  5. 5.
    A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continua [in Russian], Fizmatlit, Moscow (2004).Google Scholar
  6. 6.
    A. G. Gorshkov and D. V. Tarlakovskii, Dynamic Contact Problems with Moving Boundaries [in Russian], Nauka, Moscow (1974).Google Scholar
  7. 7.
    E. L. Kuznetsova and D. V. Tarlakovskii, “Explicit form of the solution of the Lamb problem at any point of the half plane,” in: Proc. of the 12th Internat. Symp. “Dynamic and Technological Problems of the Mechanics of Structures and Continua” [in Russian], MAI, Moscow (2006), pp. 104–120.Google Scholar
  8. 8.
    L. I. Slepyan and Yu. S. Yakovlev, Integral Transformations in Nonstationary Problems of Mechanics [in Russian], Sudostroenie, Leningrad (1980).Google Scholar
  9. 9.
    He Tianhu, Tian Xiaogeng, and Shen Yapeng, “A generalized electromagneto-thermoelastic problem for an infinitely long solid cylinder,” Eur. J. Mech. A-Solid, 24, No 2, 349–359 (2005).CrossRefMATHGoogle Scholar
  10. 10.
    J. S. Kim and W. Soedel, “On the response of three-dimensional elastic bodies to distributed dynamic pressures. Part I: Half space,” J. Sound Vibrat., 126, No. 2, 279–295 (1988).CrossRefGoogle Scholar
  11. 11.
    J. S. Kim and W. Soedel, “On the response of three-dimensional elastic bodies to distributed dynamic pressures. Part II: Thick plate,” J. Sound Vibrat., 126, No. 2, 297–308 (1988).CrossRefGoogle Scholar
  12. 12.
    H. Lamb, “On the propagation of tremors over the surface on an elastic solid,” Phil. Trans. Roy. Soc. London. Ser. A, 203, 1–42 (1904).CrossRefGoogle Scholar
  13. 13.
    R. K. N. D. Rajapakse, Y. Chen, and T. Senjuntichai, “Electroelastic field of a piezoelectric annular finite cylinder,” Int. J. Solids Struct., 42, No. 11-12, 3487–3508 (2005).CrossRefMATHGoogle Scholar
  14. 14.
    M. Rakshit and B. Mukhopadhyay, “An electro-magneto-thermo-visco-elastic problem in an infinite medium with a cylindrical hole,” Int. J. Eng. Sci., 43, No. 11-12, 925–936 (2005).MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    M. Ziv, “A half space response to a finite surface source of an impulsive disturbance,” J. Acoust. Soc. Amer., 89, No. 4, 1556–1571 (1991).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • V. A. Vestyak
    • 1
  • A. R. Hachkevych
    • 2
  • D. V. Tarlakovskii
    • 1
  • R. F. Terletskii
    • 2
  1. 1.Moscow Aircraft Institute (National Research University)MoscowRussia
  2. 2.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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