Wave propagation in a thinly two layered laminated medium with stress couples under initial stresses

Summary The present paper is an attempt to provide an approximate treatment based on Biots theory of incremental deformation to study the wave propagation in two thinly layered laminated medium under initial stresses. The cross-sectional distortion which plays an important role in the coupling of adherent layers is taken into account. The theory is derived in the context of plane strain deformation and the frequency equation for phase velocity of waves propagated has been obtained. It has been shown that under certain conditions when wave length becomes small compared to thickness of each layer, the wave approaches to Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface.

Notation and Nomenclature

For Medium—I M _i, L_i elastic coefficients - C _i bending moment - h _i thickness - P _i initial stress - _i fraction of the total thickness occupied by theith layer - b _i couple-stress coefficient For the equivalent anisotropic continuum H total thickness - M, L elastic coefficients - P average initial stress - s ₁₁ ⁽¹⁾ ,s ₂₂,s ₁₂ ⁽¹⁾ incremental stress components - u ₁,v ₁ displacement components alongx, y directions respectively - ₁ density - e _xx,e _yy,e _xy ⁽¹⁾ strain components with respect to rotated axes - w ₁ rotational component aboutz-axis - f ₁ x, f ₁ y components of incremental boundary forces per unit initial area For Medium-II N _j,Q _j elastic coefficients - D _j bending moment - K _j thickness - R _j initial stress - _j fraction of the total thickness occupied by thejth layer - g _j couple-stress coefficients For the equivalent anisotropic continuum K total thickness - N, Q elastic coefficients - R average initial stress - s ₁₁ ⁽²⁾ ,s ₂₂,s ₁₂ ⁽²⁾ incremental stress components - u ₂,v ₂ displacement components alongx, y directions respectively - ₂ density - e _xx, e_yy,e _xy ⁽²⁾ strain components with respect to rotated axes - w ₂ rotational component aboutz-axis - f ₂ x, f ₂ y components of incremental boundary forces per unit initial area With 5 Figures     

Fluxoid pinning by vanadium carbide precipitates in superconducting vanadium

Vanadium carbide precipitates were formed in pure, annealed vanadium foils by the introduction of carbon in the specimens. Thin, disk-shaped precipitates resulted with mean diameters in the range 100–2600 Å and with number densities from 3 × 10¹⁵ to 4 × 10¹⁷ particles/cm³. The macroscopic, pinning-force density for magnetic fluxoids was measured at temperatures from 2 to 5 K and for magnetic fields from 0 to H _c2(T). Peak pinning-force densities in the range of 3 × 10 to 3 × 10⁶ dyn/cm³ for T=0K were realized in the 30 specimens studied. The pinning force density was found to obey a scaling law for specimens meeting certain requirements with respect to precipitate particle size and number density. These requirements correlate with the temperature-dependent, superconducting coherence length (T). Many specimens obeyed the scaling law at temperatures T < T _c except near T _c, where (T) is large in comparison with the precipitate size.Part of this work was supported by the Applied Research Laboratory of The Pennsylvania State University, under contract with the U.S. Naval Sea Systems Command.     

The aging effect of the thermoelectric power of thin copper films

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$\text{S = S}{}_{\mathrm{<mtext>F</mtext>}}\text{(1?}\text{e}{}^{\mathrm{-\lambda t}}\text{)}$

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Approximating total citation counts from first author counts and from total papers

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An Inexpensive Digital Integrator for Gas Chromatography

SUMMARY

An inexpensive gas chromatographic integrator with digital readout is described. The device is precise to ±1 count and shows linear response to within ±2%. It is directly compatible with flame ionization detectors and is easily adapted to thermal conductivity detectors.     

Soft computing-based approaches to predict energy consumption and stability margin of six-legged robots moving on gradient terrains

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A DEM‐based parallel computing hydrodynamic and transport model

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Unconventional Field Dependence of Magnetoresistance of (TMTSF)2ClO4 Studied by 46-T Pulsed Magnetic Field System

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A multi-step linearization technique for a class of boundary value problems in non-linear mechanics

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Development of theoretical process maps to study the role of powder preheating in laser cladding

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