Skip to main content
SpringerLink
Log in

Nonstationary dynamic problems of nonlinear viscoelasticity

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

Dynamic problems describing transient wave processes in linearly viscoelastic solids are considered for bounded domains of perturbation propagation and bounded creep of the material. The integral Laplace transform with respect to time is applied to the original problem, and several statements about the properties of Laplace transforms simplifying the construction of the original functions are stated. Relations establishing a correspondence between relaxation kernels that belong to various function classes but nevertheless affect the transient processes in a similar way are proposed. The results justifying these relations in a certain range of the input data are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. I. Shemyakin, “Propagation of Nonstationary Perturbations in a Viscoelastic Medium,” Dokl. Akad. Nauk SSSR 104(1), 34–37 (1955).

    MathSciNet  Google Scholar 

  2. M. Kh. Il’yasov, “Solutions of InhomogeneousWave Equations of Linear Viscoelasticity.” Dokl. Akad. Nauk AzSSR 36(12), 13–17 (1980).

    MathSciNet  MATH  Google Scholar 

  3. A. A. Lokshin and Yu. V. Suvorova, Mathematical Theory of Wave Propagation in Media with Memory (Izd-vo MGU, Moscow, 1982) [in Russian].

    MATH  Google Scholar 

  4. I. G. Filippov and O. A. Egorychev, Wave Processes in Linear Viscoelastic Media (Mashinostroenit, Moscow, 1983) [in Russian].

    Google Scholar 

  5. F. B. Badalov, Methods for Solving Integral and Integro-Differential Equations of Hereditary Viscoelasticity (Mekhnat, Tashkent, 1987) [in Russian].

    MATH  Google Scholar 

  6. V. I. Zheltkov, L. A. Tolokonnikov, and N. G. Khromova, “Transfer Functions in Viscoelastic Body Dynamics,” Dokl. Ross. Akad. Nauk 329(6), 718–719 (1993). [Dokl. Phys. (Engl. TRansl.) 38 (4), 149–150 (1993)].

    Google Scholar 

  7. S. A. Lychev, “CoupledDynamic ThermoviscoelasticityProblem,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 95–113 (2008) [Mech. Solids (Engl. Transl.) 43 (5), 769–784 (2008)].

    Google Scholar 

  8. D. S. Berry and S. C. Hunter, “The Propagation of Dynamic Stresses inVisco-Elastic Rods,” J. Mech. Phys. Solids 4(2), 72–95 (1956).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. O.W. Dillon, “Transient Stresses in Nonhomogeneous Viscoelastic (Maxwell) Materials,” J. Aerospace Sci. 29(3), 284–288 (1962).

    MathSciNet  MATH  Google Scholar 

  10. H. Kolsky, “StressWaves in Anelastic Solids,” J. Geophys. Res. 68(4), 1193–1194 (1963).

    Article  ADS  MATH  Google Scholar 

  11. B. D. Coleman, M. E. Gurtin, and I. R. Herrera, “Waves in Materials with Memory,” Arch. Ration. Mech. Anal. 19(1), 1–19; (4), 17–298 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  12. Lin Cong-mou and Yang Lin-de, “Analytic Solution on Propagating Law of Stress Wave from Explosion of Extended Charge in Linear Viscoelastic Medium,” J. Shandong Univ. Sci. Technol. Natur. Sci. 20(3), 1–3 (2001).

    Google Scholar 

  13. Yu. N. Rabotnov, Mechanics of Deformable Solids (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  14. S. G. Pshenichnov, “Analytic Solution of One-Dimensional Problems of Dynamics of Piecewise Homogeneous Viscoelastic Bodies,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1, 95–103 (1991) [Mech. Solids (Engl. Transl.)].

    Google Scholar 

  15. S. G. Pshenichnov, “To the Problem of Studies of Nonstationary Processes in Linearly Viscoelastic Bodies with Variable Poisson Ratio,” Izv. Tulsk. Gos. Univ. Ser. Mat. Mekh. Inf. 11(2), 116–126 (2005).

    Google Scholar 

  16. S. G. Pshenichnov and M. Yu. Stavrovskaya, “Axially Symmetric Problem of Dynamics for a Linearly Viscoelastic Hollow Cylinder of Finite Length,” Izv. Tulsk. Gos. Univ. Ser. Mat. Mekh. Inf. 12(2), 165–176 (2006).

    Google Scholar 

  17. S. G. Pshenichnov and M. Yu. Stavrovskaya, “Manifestation of Hereditary Properties of Materials in Nonstationary Dynamics of a Linearly Viscoelastic Cylinder of Finite Length,” Izv. Tulsk. Gos. Univ. Ser. Mat. Mekh. Inf. 13(2), 156–171 (2007).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119899, Russia

    S. G. Pshenichnov

Authors
  1. S. G. Pshenichnov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. G. Pshenichnov.

Additional information

Original Russian Text © S.G. Pshenichnov, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 1, pp. 83–95.

About this article

Cite this article

Pshenichnov, S.G. Nonstationary dynamic problems of nonlinear viscoelasticity. Mech. Solids 48, 68–78 (2013). https://doi.org/10.3103/S002565441301007X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S002565441301007X

Keywords

Search

Navigation