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     

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