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1

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.

2

Wave propagation at the imperfect boundary between transversely isotropic thermoelastic diffusive half-space and an isotropic elastic layer

Kumar R., Chawla V.

Journal of Technical Physics

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2009

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Vol. 50, no 2

121-146

EN

The present investigation is devoted to a study of the surface wave propagation at imperfect boundary between a homogenous, transversely isotropic thermoelastic diffusive half-space and an isotropic elastic layer of finite thickness. The secular equation for surface waves in compact form is derived 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 numerically at the free plane boundary. Specific loss of energy is obtained and depicted graphically. Special cases of interest are also deduced and compared with known results.

3

Analysis of wave motion in transversely isotropic generalized thermoelastic diffusive plate

Kumar R., Kansal T.

Journal of Technical Physics

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2009

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Vol. 50, no 1

17-40

EN

The present investigation deals with the propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, thin elastic plate of finite width, in the context of generalized theory of thermoelastic diffusion. Lord and Shulman(L-S) theory, in which thermal and thermo-mechanical relaxation is governed by a time constant and diffusion relaxation is governed by other different time constant, is selected for the study. According to the characteristic equation, three quasi-longitudinal waves, namely: quasi-elastodiffusive(QED-mode), quasi-massdiffusive(QMD-mode) and quasi-thermodiffusive(QTD-mode), can propagate in addition to quasi-transverse waves(QSV-mode), and the purely quasi-transverse motion(QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew-symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew-symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation, are presented graphically in order to illustrate and compare the analytical results. Some special cases of frequency equation are also deduced from the present investigation.

4

Analysis of wave motion in micropolar plate possessing cubic symmetry

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 2

403-414

EN

The present paper concentrates at studying the analysis of wave motion in a homogenous isotropic micropolar plate possessing cubic symmetry. The upper and lower surfaces of the plate are subjected to stress free conditions. The frequency equations for symmetric and skewsymmetric wave modes of propagation are derived. The amplitudes of displacement components and microrotation are also computed and presented graphically during the symmetric and skewsymmetric motion of the plate. Finally, in order to illustrate and verify the analytical developments, numerical solution of frequency equation corresponding to stress free micropolar cubic crystal plate is carried out for magnesium crystal material and represented graphically. The results of phase velocity, displacements and microrotation have been compared for micropolar cubic crystal plate and micropolar elastic plate and illustrated graphically.

5

Analysis of free vibrations for Rayleigh lamb waves in a micropolar viscoelastic plate

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 2

383-397

EN

The propagation of free vibrations in a homogeneous isotropic micropolar viscoelastic plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. The regions of secular equations are obtained and special cases such as Lame modes, thin plate results and short wavelength waves are also discussed. At short wavelength limit, the secular equations for symmetric and skew symmetric waves in a stress free plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of normal force stress, tangential force stress and tangential couple stress are obtained and depicted graphically. Finally, numerical solution is carried out for magnesium crystal composite material plate.