Vertical vibration of a circular footing on a linear-wave-velocity half-space

An exact treatment is presented for the problem of a rigid surface foundation vibrating vertically on an elastic half-space with a linear wave velocity profile. By means of a displacement-potential representation and integral transforms, the dynamic problem is formulated as a set of dual integral equations which are reducible to a Fredholm integral equation of the second kind. Numerical results are presented to illustrate the effects of the in situ inhomogeneity on the static and dynamic foundation responses. Characteristic features of the inhomogeneous half-space problem, such as the presence of local maxima in the dynamic foundation compliance functions and the existence of cut-off frequencies, are demonstrated.