Application of Integral Transform Method to Calculate Impedance Functions

Abstract

To solve vibration problems of structure founded on the soil, the dynamic behavior of the soil needs to be understood and an accurate dynamic stiffness model of the soil has to be developed. Frequency dependent dynamic stiffness matrix of the massless, flexible soil-structure interface can be calculated analytically or numerically, depending on the complexity of the problem, using Boundary Element Method [1] or Thin Layer Method [3]. In this paper the impedance functions of a stiff rectangular foundation laying on a half-space are determined with the help of the Integral Transform Method (ITM) [4]. The Integral Transform Method is an efficient method to calculate wave propagation in an elastic homogeneous, or layered half-space. By the use of the decomposition of Helmholtz, the Lamé’s equations of elastodynamics are converted to a system of decoupled partial differential wave equations in space-time domain. With the help of a threefold Fourier Transform in the wave number-frequency domain wave equations can be transformed into a system of three decoupled ordinary differential equations which can be solved in the transformed domain. The results in the original domain can be finally obtained by an Inverse Fourier Transform. Using ITM method the dynamic stiffness of flexible foundation are determinate first. After that the impedance functions of the stiff foundation are obtained using kinematic transformation matrix. The obtained results are compared with impedance functions from literature.