Dynamic response of elliptical footings (Q1067871)

Dynamic response of an elliptical footing in frictionless contact with a homogeneous elastic half-space is considered. Both vertical and horizontal vibrations are treated. In the case of the vertical vibration, the mixed boundary value problem gives rise to a set of dual integral equations. For the horizontal vibration, we have a system of dual integral equations. The dual integral equations which are two dimensional in nature are reduced to two-dimensional Fredholm integral equations of the first kind. They are then recast in a suitable form after separating out the static solution. Successive low-frequency terms are then obtained by utilising the static solution. The series solutions up to \(\omega^ 2\), \(\omega\) being the frequency, are obtained, and analytical results for the dynamic compliances are obtained. In the limiting case of a circular footing, our results are in agreement with those of previous authors.