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

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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.

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References

  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. V. A. Stoyan, “Applying symbolic Lurie’s method in elastodynamics of thick plates,” DAN UkrRSR, Ser. A, No. 10, 927–931 (1972).

  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).

    MATH  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. I. Lurie, Spatial Problems of the Theory of Elasticity [in Russian], Gostekhizdat, Moscow (1955).

    Google Scholar 

  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).

  11. V. A. Stoyan, Mathematical Modeling of Linear, Quasilinear and Nonlinear Dynamic Systems [in Ukrainian], VPTs “Kyivs’kyi Universytet,” Kyiv (2011).

    Google Scholar 

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    V. A. Stoyan

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  1. V. A. Stoyan
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Correspondence to V. A. Stoyan.

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2018, pp. 68–77.

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Stoyan, V.A. Three-Dimensional Integral Mathematical Models of the Dynamics of Thick Elastic Plates. Cybern Syst Anal 54, 232–241 (2018). https://doi.org/10.1007/s10559-018-0024-1

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  • DOI: https://doi.org/10.1007/s10559-018-0024-1

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