Skip to main content
SpringerLink
Log in

Planar Flexural Vibrations and Dissipative Heating of Laminated Rectangular Plates

  • Published:
International Applied Mechanics Aims and scope

Abstract

The coupled thermomechanical dynamic behavior of a heterogeneous solid is investigated by an example of laminated inelastic rectangular plates subjected to forced vibration and dissipative heating. The problem is solved in two formulations: complete and approximate. The complete formulation uses generalized flow theory to describe the inelastic properties of the material. The approximate formulation employs a model based on the idea of complex moduli. Special distributions of the field variables and amplitude–frequency responses of the rectangular plate are analyzed. The effect of the loading level on the mode shape and stress distribution is studied as well. A good agreement between the results obtained in the complete and approximate formulations is pointed out.

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. Ya. A. Zhuk, I. K. Senchenkov, V. I. Kozlov, and G. A. Tabieva, “Axisymmetric dynamic problem of coupled thermoviscoplasticity,” Int. Appl. Mech., 37, No. 10, 1311–1317 (2001).

    Google Scholar 

  2. Ya. A. Zhuk, I. K. Senchenkov, O. P. Chervinko, and G. A. Tabieva, “The complex-moduli solution of an axisymmetric dynamic problem of coupled thermoviscoplasticity under harmonic loading,” Int. Appl. Mech., 37, No. 12, 1585–1593 (2001).

    Google Scholar 

  3. Ya. A. Zhuk, I. K. Senchenkov, O. P. Chervinko, and G. A. Tabieva, “Axisymmetric vibrations and dissipative heating of a laminated viscoplastic disk,” Int. Appl. Mech., 38, No. 1, 95–102 (2002).

    Google Scholar 

  4. V. A. Pal'mov, Vibrations of Elastoplastic Bodies [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  5. I. K. Senchenkov and Ya. A. Zhuk, “Thermodynamic analysis of one thermoviscoplastic deformation model,” Prikl. Mekh., 33, No. 2, 41–48 (1997).

    Google Scholar 

  6. I. K. Senchenkov and Ya. A. Zhuk, “Scleronomous model of cyclic deformation of viscoplastic bodies under harmonic deformation,” Dop. NAN Ukrainy, No.12, 83–89 (1996).

    Google Scholar 

  7. I. K. Senchenkov, Ya. A. Zhuk, G. A. Tabieva, and O. P. Chervinko, “Simplified models of the thermoviscoplastic behavior of bodies under harmonic loading,” Prikl. Mekh., 33, No. 9, 24–33 (1997).

    Google Scholar 

  8. I. K. Senchenkov, V. I. Kozlov, and G. A. Tabieva, “Numerical simulation of a plane thermoviscoplastic state of bodies including phase transformations,” Prikl. Mekh., 32, No. 12, 72–79 (1996).

    Google Scholar 

  9. V. N. Poturaev (ed.), V. I. Dyrda, V. G. Karnaukhov et al., Thermomechanics of Elastomer Structural Elements under Cyclic Loading [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  10. T. Chiba and H. Kobayashi, “Response characteristics of piping systems supported by viscoelastic and elastoplastic dampers,” J. Press. Vessel Technol., No. 1, 34–39 (1990).

    Google Scholar 

  11. K. S. Chan, U. S. Lindholm, S. R. Bodner, and K. P. Walker, “High-temperature inelastic deformation under uniaxial loading: theory and experiment,” J. Eng. Mater. Technol., No. 4, 345–354 (1989).

    Google Scholar 

  12. S. Aizawa, T. Kanizawa, and M. Higasino, “Case studies of smart materials for civil structures,” Smart Mat. Struct., 7, 617–626 (1998).

    Google Scholar 

  13. S. R. Bodner and Y. Partom, “Constitutive equations for elastoviscoplastic strain hardening material,” Trans. ASME, J. Appl. Mech., 42, 385–389 (1975).

    Google Scholar 

  14. H. D. Bui (ed.), A. Ehrlacher, and Q. S. Nguyen (ed.), “Thermomechanical coupling in fracture mechanics,” in: Thermomechanical Couplings in Solids, Elsevier (1987), pp. 327–342.

  15. K. Shiba, S. Mase, Y. Yabe, and K. Tamura, “Active/passive vibration control systems for tall buildings,” Smart Mat. Struct., 7, 588–598 (1998).

    Google Scholar 

  16. Ya. A. Zhuk and I. K. Senchenkov, “The coupled thermomechanical behavior of a three-layer viscoplastic beam under harmonic loading,” Int. Appl. Mech., 36, No. 2, 271–279 (2000).

    Google Scholar 

  17. Ya. A. Zhuk and I. K. Senchenkov, “The concentration of stresses and strains in a notched cylinder of a viscoplastic material under harmonic loading,” Int. Appl. Mech., 35, No. 2, 120–127 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    Ya. A. Zhuk, O. P. Chervinko & G. A. Tabieva

Authors
  1. Ya. A. Zhuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. P. Chervinko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. A. Tabieva
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhuk, Y.A., Chervinko, O.P. & Tabieva, G.A. Planar Flexural Vibrations and Dissipative Heating of Laminated Rectangular Plates. International Applied Mechanics 38, 837–844 (2002). https://doi.org/10.1023/A:1020889526497

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020889526497

Keywords

Search

Navigation