Skip to main content
Log in

Vibrations of Circular Composite Plates on an Elastic Foundation Under the Action of Local Loads

  • Published:
Mechanics of Composite Materials Aims and scope

The axisymmetric vibrations of an elastic circular composite plate on an elastic foundation under the action of sudden local loads are studied. To describe the kinematics of the plate, asymmetric across its thickness, the hypothesis of broken normal is assumed. The reaction of the foundation is described based on the Winkler model. The filler is lightweight. Analytical solutions of initial boundary-value problems aree found, and their numerical analysis in the cases of circular and annular loads is carried out.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. V. Z. Vlasov and N. N. Leontjev, Beams, Plates, and Shells on an Elastic Foundation [in Russian], Gos. Izd. Fiz. Mat. Liter., Moscow (1960).

    Google Scholar 

  2. V. V. Bolotin and J. N. Novichkov, Mechanics of Multilayered Structures [in Russian], Mashinostroyenie, Moscow (1980).

    Google Scholar 

  3. A. G. Gorshkov, E. I. Starovoitov, and A. V. YarovaYa, Mechanics of Layered Viscoelastoplastic Structural Members [in Russian], Fiz. Mat. Lit., Moscow (2005).

    Google Scholar 

  4. E. I. Starovoitov and F. B. Nagiyev, Foundations of the Theory of Elasticity, Plasticity and Viscoelasticity, Apple Academic Press, Toronto, New Jersey (2012).

    Google Scholar 

  5. V. K. Prisyazhnyuk and V. G. Piskunov, “Model of composite shallow shells and plates for solving problems of statics, dynamics and contact interaction,” Mech. Compos. Mater., 23, No. 6, 719-727 (1987).

    Article  Google Scholar 

  6. E. I. Starovoytov, D. V.Leonenko, and M. Suleyman, “Deformation of a composite plate on an elastic foundation by local loads,” Mech. Compos. Mater., 43, No. 1, 75-84 (2007).

    Article  Google Scholar 

  7. E. I. Starovoytov, E. P. Dorovskaya, and S. A. Starovoytov, “Cylindrical bending of an elastic rectangular sandwich plate on a deformable foundation,” Mech. Compos. Mater., 46, No. 1, 57-68 (2010).

    Article  Google Scholar 

  8. E. I. Starovoytov and D. V. Leonenko, “Thermoelastic bending of a ring three-layer plate on an elastic foundation,” Prikl. Mekh., 44, No. 9, 94-103 (2008).

    Google Scholar 

  9. E. I. Starovoitov, A. V. Yarovaya, and D. V. Leonenko, Local and Impulse Loadings of Three-Layer Structural Members, BelGUT, Gomel (2003).

    Google Scholar 

  10. N. A. Abrosimov, “Numerical study of the axysimmentric deformations of composite shells of revolution under shock loads,” Mech. Compos. Mater., 23, No. 4, 447-453 (1987).

    Article  Google Scholar 

  11. D. V. Leonenko and E. I. Starovoitov, “Thermal impact on a circular sandwich plate on an elastic foundation,” Mech. of Solids, 47, No. 1, 111-118 (2012).

    Article  Google Scholar 

  12. E. I. Starovoitov and D. V. Leonenko, “Impact of thermal and ionizing radiation on a circular sandwich plate on an elastic foundation,” Int. Appl. Mech., 47, No. 5, 580-589 (2011).

    Article  Google Scholar 

  13. A. G. Gorshkov, Amar Abdul Karim Salman, D. V. Tarlakovskii, and G. V. Fedotenkov, “Impact by deformable cylindrical body on an elastic semispace,” Izvestiya RAN. Mekhanika Tverd. Tela, No. 3, 82 (2004).

  14. V. A. Vestyak, V. A. Lemeshev, and D. V. Tarlakovskii, “One-dimensional nonstationary waves in an electromagnetoelastic semispace or a layer,” Dokl. Akad. Nauk, 426, No. 6, 747-749 (2009).

    Google Scholar 

  15. A. G. Gorshkov, D. V. Tarlakovskii, and A. M. Shukurov, “Nonstationary oscillations of an elastic medium bounded by two eccentric spherical surfaces,” Prikl. Mat. Mekh., 58, No. 2, 85 (1994).

    Google Scholar 

  16. E. I. Starovoitov, D. V. Leonenko, D. V., Tarlakovsky, “Resonance vibrations of circular composite plates on an elastic foundation,” Mech. Compos. Mater., 51, No. 5, 561-570 (2015).

    Article  Google Scholar 

  17. H. Bateman and A. Erdélyi, Higher Transcendental Functions, McGraw-Hill Book Company, New York (1953).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. I. Starovoitov.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 52, No. 5, pp. 943-954, September-October, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Starovoitov, E.I., Leonenko, D.V. Vibrations of Circular Composite Plates on an Elastic Foundation Under the Action of Local Loads. Mech Compos Mater 52, 665–672 (2016). https://doi.org/10.1007/s11029-016-9615-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-016-9615-y

Keywords

Navigation