Vertical Vibrations of an Elastic Foundation with Arbitrary Embedment within a Transversely Isotropic, Layered Soil

This paper introduces a numerical model to investigate the vibratory response of elastic and rigid circular plates embedded in viscoelastic, transversely isotropic, three-dimensional layered media. In the present numerical scheme, the boundary-value problem corresponding to the case of time-harmonic concentrated and distributed axisymmetric vertical ring loads within a layered half-space is formulated according to an exact stiffness method. Its solution results in the required influence functions for the modeling of the present problem. The case of an embedded flexible plate is formulated in terms of a variational method. The deflection profile of the plate is written in terms of generalized coordinates combined with a polynomial approximation. These generalized coordinates are determined by the solution of the Lagrange's equation of motion, which involves the strain and kinetic energy of the flexible plate and energy due to contact tractions, as well as the potential energy due to the applied load. A set of Lagrange multipliers is incorporated into the equation of motion so that the boundary conditions at the plate edge are satisfied. The solution of the constrained Lagrangian function results in the deflection profile of the plate. The deflection profile of the embedded plate is shown for different governing parameters such as frequency and type of excitation and layering configuration of the surrounding medium. The present numerical scheme contributes to the study of dynamic response of buried foundations and anchors in non-homogeneous soils. (AU)