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1

Study of circular crested waves in a micropolar porous medium possessing cubic symmetry

Kumar R., Panchal M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2011

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Vol. 59, nr 1

103-110

EN

The paper is concerned with the propagation of circular crested Lamb waves in a homogeneous micpropolar porous medium possessing cubic symmetry. The frequency equations, connecting the phase velocity with wave number and other material parameters, for symmetric as well as antisymmetric modes of wave propagation are derived. The amplitudes of displacement components, microrotation and volume fraction field are computed numerically. The numerical results obtained have been illustrated graphically to understand the behavior of phase velocity and attenuation coefficient versus wave number of a wave.

2

One-dimensional elongation of a cubic crystal

Wesołowski Z.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2004

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Vol. 52, nr 2

91-97

EN

Large elongation in one definite direction of a crystal of cubic symmetry is considered. The equations of second order elasticity theory are applied. In this approximation three constants of the second order and six constants of the third order characterize the crystal. The stress is a function of the elongation direction. The elongation directions for which the stress reaches an extreme value have been analyzed.

3

Elastodynamics of time harmonic sources in a thermally conducing cubic crystal

Kumar R., Rani L.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

637-650

EN

The disturbance due to a time harmonic mechanical, horizontal or vertical and thermal source in a homogeneous, thermally conducting cubic crystal, elastic half-plane is investigated by applying the Fourier transform. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to compare the results for different theories of generalized thermoelasticity for insulated boundary and temperature gradient boundary.

4

On resonances of nonlinear elastic waves in a cubic crystal

Domański W., Jabłoński T.

Archives of Mechanics

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2001

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Vol. 53, nr 2

91-104

EN

Using the method of weakly nonlinear geometric optics, we obtain asymptotic transport evolution equations for high-frequency, small amplitude nonlinear elastic waves in a cubic crystal. Both geometrical and physical nonlinearities are included in our model. We expand strain energy up to the third order terms with respect to the strain matrix components. The nonlinear resonant asymptotic equations obtained are of integro-differential type. The coefficients of these equations are called resonant interaction coefficients (RIC). They determine whether and between which waves the nonlinear resonant interactions occur. We have calculated all the RIC in the explicit analytical form for three different crystalline directions of a one-dimensional wave motion. Comparison of the results shows that the direction of propagation influences the resonant interactions in an essential way. Moreover, our analytical formulas for RIC can be used to determine the material constants of a crystal.