Torsion vibration of foundation in a functionally graded transversely isotropic, linearly elastic half-space

Abstract

The compliance function of a torsion excitation plays an important role in the response of dynamic excitation and is widely used in applied mechanics, foundation vibration and soil-structure interaction (SSI) problems. In this paper, an analytical and efficient method is presented to calculate the SSI coefficients of compliance function due to torsional oscillation of a rigid foundation in a transversely isotropic functionally graded (TIFG) half-space. Accordingly, the medium is considered linear elastic and the properties vary along the depth in exponential form to model the effect of elastic non-homogeneities. The problem is formulated by integrating the transformed components of traction acting on the foundation region which can be changed into a Fredholm integral equation. The results represent the impact of input frequency and material anisotropy on the SSI coefficients and shear stress variation. In addition, the distribution of angular shear stress over the foundation and the cut-off frequency is found explicitly. Also, the derived cut-off frequency of the present study characterizes whether wave propagation occurs in medium or not.

Keywords

• Compliance-stiffness torque function
• Functionally graded material (FGM)
• Analytical solution
• Rigid foundation