Dispersion analysis of elastic waves in a layer interacting with a Winkler foundation

In this thesis, the dispersion of elastic waves in an elastic layer interacting with one and two-sided Winkler foundation is analyzed. For this purpose, dispersion relations are obtained for elastic layers interacting with the Winkler base on both one-sided and two-sided basis in accordance with the given boundary conditions, and polynomial approximations of the dispersion relations near the cut-off frequency are derived using the assumption of long wave-low frequency. The obtained approaches are compared with the conventional engineering formulation of a Kirchhoff plate resting on an elastic foundation. An explicit formula illustrating the veering of bending and extensional waves is presented as a one-sided foundation. Then, for the one-sided case, the equation of motion near the cut-off frequency for low-frequency bending motion is derived asymptotically, which is handled as a 3D-problem.