Skip to main content
SpringerLink
Log in

Dynamic deformation of glued beams

  • Published:
International Applied Mechanics Aims and scope

The dynamic deformation of two glued rectangular beams is studied. A problem formulation and problem-solving method are given. It is assumed that the structure moves in a vertical plane. The materials of the beams and adhesive interlayer (AI) are homogeneous and isotropic. The geometrical and mechanical characteristics of the beams are different. Assumptions on the stress–strain state of the beams and AI are formulated based on the theory of elasticity. The composite beam is decomposed into three beams. The virtual-displacement principle is formulated for each of them. The problem is solved by finding five functions defined on the beam axis. The formulated principles allow solving different problems of dynamic deformation of glued beams

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. N. A. deBruyne and R. Houwink (eds.), Adhesion and Adhesives, Elsevier, New York (1951).

    Google Scholar 

  2. Yu. P. Artyukhin, “Stresses in adhesive joints,” in: Research on the Theory of Plates and Shells [in Russian], Izd. Kazan. Univ., Kazan (1973), pp. 3–27.

  3. J. P. Jones and J. S. Whittier, “Dynamics of a flexibly bonded two-layered Timoshenko-type cylindrical shell,” AIAA J., 7, No. 2, 244–250 (1969).

    Article  MATH  ADS  Google Scholar 

  4. V. A. Yeremeyev and S. M. Kuzmenko, “Some static problems for elastic bodies with interphase boundaries,” Izv. VUZov, Sev.-Kavk. Region. Estest. Nauki, No. 3, 6–9 (2007).

  5. Ya. F. Kayuk and V. M. Seredenko, Mechanics of Interphase Interaction in Composite Materials [in Ukrainin], Nauk. Tovar. im. T. G. Shevchenka, Cherkasy (2005).

  6. I. F. Obraztsov, S. A. Lurie, P. A. Belov, D. B. Volkov-Bogorodskii, et al., “Fundamentals of interphase-layer theory,” Mekh. Komp. Mater. Konstr., 10, No. 4, 596–612 (2004).

    Google Scholar 

  7. R. G. Payton, “Dynamic bond stress in a composite structure subjected to a sudden pressure rise,” Trans. ASME, J. Appl. Mech., 32, No. 3, 643–650 (1965).

    MathSciNet  Google Scholar 

  8. V. G. Piskunov and A. O. Rasskazov, “Evolution of the theory of laminated plates and shells,” Int. App. Mech., 38, No. 2, 135–166 (2002).

    Article  Google Scholar 

  9. N. G. Ryabenkov, “Design of adhesively bonded joints for shells,” in: Research on the Theory of Plates and Shells [in Russian], Izd. Kazan. Univ., Kazan (1976), pp. 104–111.

  10. G. Epstein, Adhesive Bonding of Metals, Reinhold, New York (1954).

    Google Scholar 

  11. D. J. Allman, “A theory for elastic stresses adhesive bonded lap joints,” Quart. J. Mech. Appl. Math., 30, No. 4, 10–15 (1977).

    MathSciNet  Google Scholar 

  12. K. V. Avramov, C. Pierre, and N. V. Shyriaieva, “Nonlinear equations of flexural–flexural–torsinal oscillations of rotating beams with arbitrary cross-section,” Int. Appl. Mech., 44, No. 5, 582–589 (2008).

    Article  Google Scholar 

  13. R. M. Barker and F. Halt, “Analysis of bonded joints in vehicular structures,” AIAA J., 11, No. 12, 1650–1654 (1973).

    Article  ADS  Google Scholar 

  14. Chun Fei, Hu Gengkai, et al., “Influence of interface boundary on elastic properties of composites,” Acta Mater. Comp. Sin., 21, No. 1, 134–140 (2004).

    Google Scholar 

  15. F. Erdogan and M. Ratwani, “Stress distribution in bonded joints,” J. Comp. Mater., 5, No. 7, 378–393 (1971).

    Article  Google Scholar 

  16. Ya. F. Kayuk, “Stress state of flexible plates with a hole that are subject to bending,” Int. Appl. Mech., 43, No. 1, 85–100 (2007).

    Article  Google Scholar 

  17. Ya. F. Kayuk and M. K. Shekera, “On one dynamic problem for structurally inhomogeneous beams,” Int. Appl. Mech., 43, No. 11, 1256–1263 (2007).

    Article  Google Scholar 

  18. Ya. F. Kayuk, “Dynamic problems for layered shells of revolution with interfacial phenomena taken into account,” Int. Appl. Mech., 44, No. 7, 775–787 (2008).

    Article  MathSciNet  Google Scholar 

  19. W. J. Renton and J. R. Vinson, “Analysis of adhesively bonded joints between panels of composite materials,” J. Appl. Mech., No. 4, 101–106 (1977).

    Google Scholar 

  20. I. Sevostianov and M. Kachanow, “Effect of interphase layers: Applications to nanosize inclusion,” Int. J. Solids Struct., 44, No. 3–4, 1304–1315 (2007).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    Ya. F. Kayuk

Authors
  1. Ya. F. Kayuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya. F. Kayuk.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 46, No. 6, pp. 98–112, June 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kayuk, Y.F. Dynamic deformation of glued beams. Int Appl Mech 46, 696–708 (2010). https://doi.org/10.1007/s10778-010-0358-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-010-0358-5

Keywords

Search

Navigation