Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 232–241 | Cite as

Three-Dimensional Integral Mathematical Models of the Dynamics of Thick Elastic Plates

Article
First Online:
Received:

Abstract

The complex of problems related to constructing three-dimensional field of elastic dynamic displacements of flat elastic plate with arbitrary boundary-edge surface is solved. It is assumed that boundary condition of the plate is given in terms of powerful perturbation factors or displacement vector function. Problems solutions are based on classical Lame equations of spatial theory of elasticity under root-mean-square consistency of the solution with corresponding external-dynamic observations of the plate. The accuracy of such consistency is estimated. The uniqueness conditions for the solution of the considered problems are formulated.

Keywords

spatially distributed dynamic systems spatial problems of elasticity theory pseudoinversion thick elastic plates 
This is a preview of subscription content, log in to check access

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. N. Nemish and Yu. I. Khoma, “Stress-deformation state of thick shells and plates. Three-dimensional theory (Review),” Intern. Applied Mech., Vol. 27, No. 11, 1035–1055 (1991).Google Scholar
  2. 2.
    V. A. Stoyan, “Applying symbolic Lurie’s method in elastodynamics of thick plates,” DAN UkrRSR, Ser. A, No. 10, 927–931 (1972).Google Scholar
  3. 3.
    V. A. Stoyan, “An algorithm for constructing nonclassical differential equations of elastodynamics applicable to thick plates,” Intern. Applied Mech., Vol. 12, No. 7, 668–672 (1976).MATHGoogle Scholar
  4. 4.
    V. A. Stoyan and K. V. Dvirnychuk, “On construction of differential model of transversal dynamic displacements of thick elastic layer,” J. Autom. Inform. Sci., Vol. 44, No. 8, 44–54 (2012).CrossRefGoogle Scholar
  5. 5.
    V. A. Stoyan and K. V. Dvirnychuk, “On an integral model of transversal dynamic displacements of a thick elastic layer,” J. Autom. Inform. Sci., Vol. 45, No. 1, 16–29 (2013).CrossRefMATHGoogle Scholar
  6. 6.
    V. A. Stoyan and K. V. Dvirnychuk, “Mathematical modeling of three-dimensional fields of transverse dynamic displacements of thick elastic plates,” Cybern. Syst. Analysis, Vol. 49, No. 6, 852–864 (2013).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    V. A. Stoyan and K. V. Dvirnychuk, “Mathematical modeling of the control of dynamics of thick elastic plates. I. Control under continuous desired state,” Cybern. Syst. Analysis, Vol. 50, No. 3, 394–409 (2014).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    V. A. Stoyan and K. V. Dvirnychuk, “Mathematical modeling of the control of dynamics of thick elastic plates. II. Control under discrete desired state,” Cybern. Syst. Analysis, Vol. 51, No. 2, 261–275 (2015).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    A. I. Lurie, Spatial Problems of the Theory of Elasticity [in Russian], Gostekhizdat, Moscow (1955).Google Scholar
  10. 10.
    V. A. Stoyan and K. V. Dvirnychuk, “Constructing the integral equivalent of linear differential models,” Dopov. Nac. Akad. Nauk Ukrainy, No. 9, 36–43 (2012).Google Scholar
  11. 11.
    V. A. Stoyan, Mathematical Modeling of Linear, Quasilinear and Nonlinear Dynamic Systems [in Ukrainian], VPTs “Kyivs’kyi Universytet,” Kyiv (2011).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

Personalised recommendations