Plate equations are used to determine dispersion curves for free waves in a layer and a supporting half space of different elastic properties. The approximate dispersion curves are compared with curves obtained by employing elasticity equations for the layer. For a relatively soft layer, agreement is good at small wave numbers. For a relatively stiff layer, good agreement is obtained over the whole range of wave numbers for which a free wave can exist. A comparison of the displacement distributions in plate and layer shows that the range of wave numbers for which the displacements are well matched is much smaller than the range for which good agreement in phase velocities is obtained. Finally, the dispersion curve for a plate on a Winkler foundation is compared with the corresponding curve for a plate in smooth contact with a semi-infinite continuum.

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