Lamb waves in a fluid-solid bilayer
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Leaky-Lamb waves (LLW) have been used extensively for nondestructive testing of homogeneous as well as composite materials. One of the limitations of some of the LLW modes is that they suffer from rapid spatial decay due to leakage of energy into water. Therefore, many interesting features of the theory cannot be observed experimentally. This provides the motivation for the present work: by their very nature, harmonic guided waves do not suffer any geometrical attenuation. Consider a fluid-solid bilayer of infinite extent with the x3 axis perpendicular to the layer; the fluid is assumed to be nonviscous and isotropic (i.e. with one independent elastic constant) and the solid is assumed to be elastic and isotropic (i.e. with two independent elastic constants). Consider a plane wave propagating in the x1-direction with the particle motion confined to the x1-x3 plane and plane strain conditions in the x2-direction. There are six boundary conditions: zero normal and shear stresses at the traction-free boundaries, zero shear stress and continuity of normal displacements and normal stresses at the interface. The dispersion equation is obtained by setting the determinant of the resulting six-by-six matrix to zero. Numerical results in the form of phase velocity, group velocity, and mode shapes are presented for the case of a water/aluminum bilayer. Several interesting features are observed and discussed.
