Frequency‐dependent response of a rigid disk on a transversely isotropic soil layer subjected to horizontal motion

Abstract

The transverse isotropy of soil induced by geological processes over a long period has attracted considerable attention, which can lead to significant differences in the origination, propagation and attenuation of the stand waves compared with purely isotropic soil. Considering that the circular geometry is most common in many engineering, an analytical investigation of the dynamic behavior of a rigid disk resting on the transversely isotropic soil layer overlying the rigid bedrock under forced horizontal displacements is presented in this paper. Firstly, the governing equations of soil motion are established based on the elasticity theory of cylindrical coordinate system. Secondly, a set of partial differential equations for this class of problems are decoupled to ordinary differential forms by virtue of complete potential functions, Fourier expansion method and Hankel transform technique. Furthermore, the displacements, strains and stresses formulation in term of the spatial domain under general boundary conditions are obtained with success. For validation, dynamic boundary value problems in the finite‐layered soil containing transversely isotropic materials are degenerated to the isotropic solution corresponding to elastic half‐space. After that, various examples are also included to investigate the influence of the elastic modulus ratio, shear modulus ratio and thickness of soil layer on the dynamic response of the system. The numerical results suggest that the soil anisotropy and soil layer thickness have a non‐neglectful effect on the horizontal dynamic vibration of the rigid disk.