Generalized Kelvin-Voigt Used in Soil Dynamics Study

The interpretation of dynamic test results is complex relative to the static case, because the mass, shape, and stiffness of the dynamic testing apparatus as well as the properties of the specimen must be considered. This interpretation is facilitated by representing the response of the material by a simplified model and by modeling the apparatus so that an analytical solution may be obtained for the specimen-apparatus system. The general steady state solution for the forced vibration of a cylindrical shaft of material represented by the generalized Kelvin-Voigt model is presented. This general solution can be used, together with the boundary conditions and properties of the various types of apparatus (i.e., apparatus involving the vibration of cylindrical specimens), to obtain the analytical solutions for these specimen-apparatus systems. An example of this procedure is given for a boundary value problem that is typical of some of the specimen-apparatus systems used in the past. The measured response for a cylindrical specimen of sand obtained with such an apparatus is compared with the computed results obtained from the analytical solution.