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Journal of Automation and Information Sciences
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ISSN Print: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v44.i8.50
pages 44-54

On Construction of Differential Model of Transversal Dynamic Displacements of 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 differential model, which determines three-dimensional field of transversal dynamic displacements of elastic layer of constant thickness by means of its surface loading, was constructed. Model is two-dimensional differential equation, which depends on degenerated coordinate. Special case of the model are classical and improved equations of dynamics of thin plates, obtained by other authors on the basis of different mechanical hypotheses.

REFERENCES

  1. Skopetskiy V.V., Stoyan V.A., Krivonos Yu.G., Mathematical modeling of direct and inverse problems of dynamics of systems with distributed parameters.

  2. Stoyan V.A., Mathematical modeling of linear, quasilinear and nonlinear dynamical systems.

  3. Timoshenko S.P., Course of theory of elasticity.

  4. Grigolyuk E.I., Selezov I.T., Mechanics of rigid deformable bodies. Vol. 5, Nonclassical theories of oscillations of rods, plates and shells.

  5. Lurie A.I., Spatial problems of elasticity theory.

  6. Stoyan V.A., On semi-three-dimensional equations of axisymmetric problem of elastodynamics of thick slabs.

  7. Petrashen G.I., To theory of oscillations of thin plates.

  8. Petrashen G.I., Molotkov L.A., On some problems of dynamical theory in the case of media, which contain thin layers.

  9. Selezov I.T., Investigation of transversal oscillations of plates.


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