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2 Acta Mechanica et Automatica

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Transient Plane Waves in Multilayered Half-Space

100%

Turchyn I. , Turchyn O.

tom Vol. 7, no. 1

53-57

Considered the dynamic problem of the theory of elasticity for multilayered half-space. Boundary surface of inhomogeneous half-space loaded with normal load, and the boundaries of separation layers are in conditions of ideal mechanical contact. The formulation involves non-classical separation of equations of motion using two functions with a particular mechanical meaning volumetric expansion and function of acceleration of the shift. In terms of these functions obtained two wave equation, written boundary conditions and the conditions of ideal mechanical contact of layers. Using the Laguerre and Fourier integral transformations was obtained the solution of the formulated problem. The results of the calculation of the stress-strain state in the half-space with a coating for a local impact loading are presented.

Transient vibrations of an elastic cylinder inserted in the elastic medium

80%

Sulym H. , Timar I. , Turchyn I.

Acta Mechanica et Automatica

2016

tom Vol. 10, no. 2

133--136

Using method of Laguerre polynomials we have obtained the solution of the dynamic problem of the theory of elasticity for elastic cylinder inserted into massive body modeled as a space. The source of non-stationary processes in composite is high intensity force load of the inner surface of the cylinder. On the surface separation of materials of space and cylinder the conditions of ideal mechanical contact are satisfied. The solution is obtained as series of Laguerre polynomials, which coefficients are found from recurrent relations. The results of numerical analysis of transient stress-strain state in elastic space with cylindrical insertion might be used for the technological process of hydraulic fracturing during shale gas extraction.