Free vibration of a soil pile system subjected to static axial loading

The lateral free vibration behavior of a typical pile embedded in a uniform soil is presented. The pile was modeled by elements having a continuous distribution of stiffness and mass along its length and the soil resistance was assumed to be of the linear Winkler type. The Wittrick-Williams algorithm was used to solve the non-linear eigenvalue problem of the soil pile system that developed from treating the problem as a system with an infinite number of degrees of freedom. The continuous formulation used in the free vibration problem enabled us to consider the weight of the superstructure acting at the top of the pile to be a lumped mass that influences the mass of the system as is done conventionally. The axial static loading due to the weight of the superstructure, which when included affects the formulation of the dynamic stiffness matrix of the system was also considered. The effects of the weight on the superstructure, pile boundary conditions, and the soil modulus, on the frequency of the lateral free vibration problem were determined from a parametric study undertaken.