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Wave propagation in swelling porous elastic layer

Kumar R., Taneja D., Kumar K.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 2

379-398

EN

The present investigation deals with the propagation of straight and circularly crested Lamb waves in a swelling porous elastic layer subjected to stress free boundary. A Helmholtz decomposition technique has been used to simplify the mathematical model. The secular equations for different mechanical situations are obtained. Numerical computations are performed to compute the symmetric and skew-symmetric phase velocity and attenuation coefficient in Swelling Porous (SP) and without Swelling Porous (elastic) (WSP) media. At short wavelength limits, the secular equations for symmetric and skew-symmetric waves in the stress free swelling porous and without swelling porous elastic layer reduce to the Rayleigh surface wave frequency equation. The amplitudes of displacements and stresses are obtained and are presented graphically. Some special cases have been deduced from the present investigation. The present study has immense applications to geophysical problems and structure problems.

2

Rayleigh-Lamb waves in micropolar thermoelastic plate coated with inviscid fluid

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 3

709-729

EN

The propagation of Rayleigh-Lamb waves in a micropolar generalized thermoelastic plate coated with an inviscid fluid is investigated in the context of Lord and Shulman (L-S), Green and Lindsay (G-L) and Chandrasekhariah and Tzou (C-T) theories of thermoelasticity. The secular equations for the symmetric and skew-symmetric mode propagation are derived. The regions and short wavelength waves of secular equations are also discussed. At short wavelength limits, the secular equations reduce to the Rayleigh surface wave frequency equation. Finally, the numerical solution is carried out for a magnesium crystal composite material plate coated with water layers. The dispersion curves, attenuation coefficients and amplitudes of stresses and temperature distribution for symmetric and skew-symmetric wave modes are computed analytically and presented graphically. This work could be useful in underwater acoustics. The present study has immense applications to defence science, mainly in geophysical problems, such as water-covered or oil-covered layers in the earth's crust.

3

Axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 1

211-237

EN

The propagation of axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of the conventional coupled thermoelasticity (CT) and Lord and Shulman (L-S) theories of thermoelasticity. The generalized theory of elasticity developed by Lord and Shulman is employed by assuming the mechanical behaviour as dynamic to study the problem. Mathematical modeling of the problem of obtaining dispersion curves for microstretch isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using the variable separable method to obtain the secular equations in isolated mathematical conditions for the plates with a stress free thermally insulated and isothermal boundary surface. The secular equations for both the symmetric and skew-symmetric wave mode propagation have been obtained. Thin plate results have also been deduced. These vibration modes are found to be dispersive and dissipated in character. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to the Rayleigh surface wave frequency equation. The dispersion curves, attenuation coefficients and amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically for the Lord and Shulman theory of elasticity. The theoretical and numerical computations are found to be in close aggrement.

4

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.

5

Propagatlon of Rayleigh-Lamb waves in thermomicrostretch elastic plates

Pathania D. S., Sharma J. N., Kumar R.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 4

1147-1163

EN

The propagation of waves in a thermo-microstretch elastic plate subjected to stress free isothermal and thermally insulated conditions is investigated in the context of the conventional coupled thermoelasticity (CT), Lord-Shulman (LS), and Green-Lindsay (GL) theories of thermoelasticity. The secular equations for the thermomicrostretch elastic plate in a closed form and isolated mathematical conditions for the symmetric and skewsymmetric wave mode propagation in completely separate terms are derived. The secular equations for the thermo-microstretch elastic plate, coupled thermoelastic, micropolar elastic, thermoelastic and elastic plates have been deduced as particular cases from the secular equations derived. At short wave length limits, the secular equations for the symmetric and skew symmetric waves in stresses free, thermally insulated and isothermal, thermo-microstretch elastic plate reduce to the Rayleigh surface wave's frequency equation. Finally, in order to illustrate the analytical development, the numerical solution is carried out for aluminum-epoxy composite material. The symmetric and skew symmetric wave modes are computed numerically and presented graphically. The theory and numerical computations are found to be in close agreement.