Vibration of viscoelastic foundations

Simple approximate solutions are presented for the steady-state response of a massless, rigid disk, which is supported at the surface of a linear viscoelastic halfspace and is excited by a harmonically varying horizontal or vertical force, or by a harmonically varying moment about an axis in the plane of the disk. The halfspace is idealized either as a standard Voigt solid or as a constant hysteretic solid. The solution for the massless disk is then applied to the analysis of foundations with mass, and for each mode of excitation, comprehensive numerical data are presented to illustrate the effects of viscoelastic action on the response of both the massless disk and of foundations with mass It is shown that the principal effects of material damping are to increase the damping capacity of the foundation and to reduce its ‘natural’ frequency. In the mathematically equivalent representation of the elastically supported massless disk as a spring-dashpot combination without mass, it is shown that the effective stiffness of the spring may become negative over significant ranges of the exciting frequency, and that it is preferable to model the disk-halfspace system as an oscillator with mass, taking its spring constant equal to the static stiffness of the original system.