Effects of Damping and Dynamic Soil Mass on Footing Vibration

Effects of different kinds of damping and dynamic soil mass on horizontal and vertical footing vibration, e.g. dynamic stiffness and footing mass, have been analyzed. Total damping should include material damping and geometrical damping. Material damping tends to reduce the dynamic stiffness of the footing. Dynamic soil mass and the effect of footing mass with respect to the geometrical damping have been considered in the vibration analyses. Expressions for total mass, total damping and total dynamic stiffness of the system for horizontal and vertical vibration have been presented in this paper for use in these analyses. The differential equation for evaluation of these effects and some important circular frequencies for horizontal vibration of a rigid footing on an elastic half space are discussed. The newly presented expressions for total mass, total damping and total dynamic stiffness could be used to calculate whether permanent displacement or resonant frequency and the maximum amplitude of vibration will occur.