Nonstationary Dynamic Problems for Elastic and Viscoelastic Piecewise Homogeneous Bodies

  • Pshenichnov SergeyEmail author
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)


The problems of transient wave processes in linearly viscoelastic piecewise homogeneous bodies with small deformations, boundedness of the disturbances propagation region, and creep boundedness of the material of homogeneous components of the bodies are considered The issues related to the construction of solutions of such problems by the method of the integral Laplace transform with respect to time and subsequent reversal are touched upon. The statements about the properties of the Laplace transform simplifying the construction of the originals are formulated. The case when all homogeneous components of the body are linearly elastic is considered.


Dynamics of viscoelastic bodies Piecewise homogeneous bodies Wave processes 



The reported study was funded by Russian Foundation for Basic Research, according to the research projects No. 19-08-00438 a, 18-08-00471 a.


  1. 1.
    Sabodash, P.F.: Propagation of longitudinal viscoelastic waves in a three-layer medium. Polym. Mech. 7(1), 124–128 (1971). [in Russian]CrossRefGoogle Scholar
  2. 2.
    Kozlov, V.I., Kucher, N.K.: Dynamic behavior of multilayer cylindrical structures with transient loads. Strength Mater. 12(5), 639–648 (1980). [in Russian]CrossRefGoogle Scholar
  3. 3.
    Nuriev, B.R.: Impact on a viscoelastic layered composite. Izv. Akad. Nauk AzSSR. Ser. Fiz-Tekh. Mat. Nauk 4, 35–41 (1985). (in Russian)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Songnan, L., Ping, G.: Dynamic response of layered viscoelastic half-space and its application to dynamic foundation problems. Hubnan Daxue Xuebao J. Hunan Univ. 20(1), 57–64 (1993)Google Scholar
  5. 5.
    Lokshin, A.A.: The head wave at the boundary of two hereditary-elastic half-spaces. The case of a linear source. J. Appl. Math. Mech. 58(1), 171–176 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hyung Suk Lee: Viscowave—a new solution for viscoelastic wave propagation of layered structures subjected to an impact load. Int. J. Pavement Eng. 15(6), 542–557 (2014)CrossRefGoogle Scholar
  7. 7.
    Hashemi, S.H., Khaniki, H.B.: Dynamic behavior of multi-layered viscoelastic nanobeam system embedded in a viscoelastic medium with a moving nanoparticle. J. Mech. 33(5), 559–575 (2017)CrossRefGoogle Scholar
  8. 8.
    Korovaytseva, E.A., Pshenichnov, S.G.: The study of transient wave propagation in linearly visco-elastic bodies subject to the continuous heterogeneity of the material. Prob. Strength Plast. 78(3), 262–270 (2016). [in Russian]CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

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