Eigenproperties of massive rigid body on elastic half-space

This paper examines the eigenvalues and eigenvectors of a massive rigid square block bonded to an elastic medium. Uncoupled vertical and coupled sliding-rocking modes of vibration are considered. The supporting medium is modeled as an elastic homogeneous or layered, inertial or massless half-space. For a geometricaliy damped system, the eigenvalues are complex-valued, while they are purely imaginary in an undamped system. Numerical results are presented to illustrate the effects of inertial interaction. The data is computed by a procedure that takes into account the mixed boundary conditions at the surface of the half-space.