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1

Transient vibrations of an elastic cylinder inserted in the elastic medium

Sulym H., Timar I., Turchyn I.

Acta Mechanica et Automatica

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2016

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Vol. 10, no. 2

133--136

EN

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.

2

Surface wave characteristics in a micropolar transversely isotropic halfspace underlying an inviscid liquid layer

Gupta R. R., Gupta R. R.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 1

49--60

EN

The present investigation deals with the propagation of waves in a micropolar transversely isotropic half space with an overlying inviscid fluid layer. Effects of fluid loading and anisotropy on the phase velocity, attenuation coefficient, specific loss and relative frequency shift. Finally, a numerical solution was carried out for aluminium epoxy material and the computer simulated results for the phase velocity, attenuation coefficient, specific loss and relative frequency shift are presented graphically. A particular case for the propagation of Rayleigh waves in a micropolar transversely isotropic half-space is deduced and dispersion curves are plotted for the same as functions of the wave number. An amplitude of displacements and microrotation together with the path of surface particles are also calculated for the propagation of Rayleigh waves in the latter case.

3

Effect of rotation on surface wave propagation in a elastic layer lying over a thermodiffusive elastic half-space having imperfect boundary

Kumar R., Chawla V.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 1

37-55

EN

The present investigation deals with the propagation of surface waves at an imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of generalized theory of thermoelastic diffusion. Lord and Shulman (L-S) theory in which thermal and thermo-mechanical relaxation time is governed by time constant and diffusion relaxation time is governed by other different time constants is selected for the study. The secular equation for surface waves in a compact form is derivied after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed at the free plane boundary and depicted graphically. Specific loss of energy is obtained and presented graphically. The effects of rotation are shown for phase velocity, attenuation coefficient and amplitudes of displacements, temperature change and concentration. Some special cases of interest are also deduced and compared with known results.