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Journal of Automation and Information Sciences
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ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v45.i1.20
pages 16-29

On an Integral Model of the Transverse Dynamic Displacements of a Thick Elastic Layer

Vladimir Antonovich Stoyan
Kyiv National Taras Shevchenko University, Kyiv, Ukraine
Konstantin V. Dvirnychuk
Kiev National Taras Shevchenko University; Chernovtsy Yuriy Fedkovich National University, Chernovtsy

ABSTRACT

The problem of constructing the integral dependence of the function of spatially distributed transverse dynamic displacements of the points of a thick elastic layer caused by external dynamic loads on its limit surfaces is solved. The obtained results are compared with the solution of the problem of the axisymmetric dynamics of the considered layer, which is constructed by contour integration of the three-dimensional Lame equations.

REFERENCES

  1. Skopetsky V.V., Stoyan V.A., Krivonos Yu.G. , Mathematical modeling of direct and inverse problems of the dynamics of the systems with distributed parameters [in Ukrainian].

  2. Skopetsky V.V., Stoyan V.A., Zvaridchuk V.B. , Mathematical modeling of the dynamics of distributed space-time processes [in Ukrainian].

  3. Stoyan V.A. , Mathematical modeling of linear, quasilinear and nonlinear dynamical systems [in Ukrainian].

  4. Timoshenko S.P. , Course of elasticity theory [in Russian].

  5. Grigolyuk E.I., Selezov I.T. , Mechanics of rigid deformable bodies, Volume 5: Nonclassical theories of vibrations of rods, plates and shells [in Russian].

  6. Stoyan V.A., Dvirnichuk К.V. , On construction of differential model of transversal dynamic displacements of thick elastic layer.

  7. Stoyan V.A., Dvirnichuk K.V. , The construction of the integral equivalent of linear differential models [in Ukrainian].

  8. Petrashen G.I. , The theory of vibrations of thin plates.

  9. Petrashen G.I., Molotkov L.A. , Some problems of the dynamic theory in the case of media containing thin layers.


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