Effect of material damping on the impedance functions of an embedded circular foundation under vertical and horizontal excitation

Abstract

Machine foundations are generally affected by the vibratory shocks from different machines. The behavior of these foundations is influenced by the properties of underlying soil and the excitation frequency of the applied dynamic load. The influence of material damping on the dynamic impedance functions of a circular disk embedded in homogeneous elastic half space is analyzed using one-dimensional wave propagation in cones (cone model) and the results are presented in the form of dimensionless plots to observe the more realistic response of machine foundations. Three different types of material damping models viz., Hysteretic, Voigt and Kelvin model are introduced in the above elastic solutions using correspondence principle. The spring and damping coefficients of the embedded foundation are then computed in a wide range of frequency of excitation under vertical and horizontal mode of vibration varying the influencing parameters namely dimensionless frequency (a0), Poisson’s ratio (ν), embedment ratio (e/r0) and damping ratio (ξ). The outcomes from the present analysis suggest that the spring coefficient is nonlinearly affected by the dimensionless frequency and embedment ratio, for both the modes of vibration. The effect of material damping on spring coefficient is only significant for a0> 2, irrespective of the damping model used.