3D dynamic response of a multi-layered transversely isotropic half-space subjected to a moving point load along a horizontal straight line with constant speed

Abstract

Please cite this article as: Zhenning BA , Jianwen Liang , Vincent W. Lee , Hang Ji , 3D dynamic response of a multi-layered transversely isotropic half-space subjected to a moving point load along a horizontal straight line with constant speed, Abstract: The steady-state dynamic response of a multi-layered transversely isotropic (TI) half-space generated by a point load moving along a horizontal straight line with constant speed is investigated in this paper. To solve this problem, the direct stiffness method combined with the inverse Fourier transform is employed. First, the dynamic equilibrium equations for the TI medium are solved in the frequency and wavenumber domains and the exact three-dimensional (3D) dynamic stiffness matrix for the layered TI half-space is established. Then, the solution in the frequency and wavenumber domains is obtained through the direct stiffness method. Finally, the dynamic response in the time and space domains is obtained using the double inverse Fourier transform with respect to the frequency and one horizontal wavenumber. The accuracy of the method is verified through comparisons with the results for the limiting isotropic case (de Barros and Luco, 1994) as well as the results for the non-moving 3D point load being applied in a multi-layered TI half-space (Khojasteh et al., 2011). Numerical results for both the uniform TI half-space and multi-layered TI half-space are presented, and the effects of the moving speed and especially the material anisotropy on the dynamic response are analyzed. Numerical results show that the dynamic response in a TI medium can be significantly different from that in an isotropic medium, and material anisotropy is very important for the accurate assessment of the dynamic response due to a point load moving in a TI half-space.

Analytical/Numerical Solutions to the Problem of the Dynamic Response of an Elastic Plate on a Continuously Non-Homogeneous Cross-Anisotropic Viscoelastic Soil to a Moving Load

“…For the second verification, the problem of a load moving on the surface of a homogeneous cross-anisotropic half-space medium is solved by the proposed method and compared with the solution of Ba et al [27]. Thus, assuming the same values with Ba et al [27], i.e., E=5 GPa, =2E, v= =0.25, , =0.3 and =2000 kg/ , one can obtain the normalized vertical displacement = at a depth z=10 m as a function of the normalized load speed = as shown in Fig. 3b.…”

“…2) Works associated with elastic beams or plates on a homogeneous or layered, isotropic half-space under point or distributed, constant or time harmonic loads moving with constants speed, e.g., [23][24][25][26]. 3) Works associated with or without plates on a homogeneous or layered, transversely isotropic (or cross-anisotropic) elastic half-spaces under point or distributed, constant or time harmonic loads moving with constant speed, e.g., [27][28]. 4) Works associated with homogeneous, transversely isotropic (or cross-anisotropic) elastic half-spaces under dynamic but stationary loads, e.g.…”

Elastodynamic Solutions of a Finite Soil Layer under Interior Distributed Actions

“…Mechanical behaviors of soils under dynamic loads, such as traffic loads, construction operations, machinery vibrations, and earthquakes, are of fundamental importance in pavement engineering, geotechnical, and seismic engineering [1][2][3]. By treating soil materials as single-phase elastic or viscoelastic media, their dynamic responses to external loads have been studied extensively in classical treatments [4][5][6].…”

Moving load response of an axially loaded Timoshenko beam on a multilayered transversely isotropic half‐space comprising different media

“…Nevertheless, the problem of a dynamic load applied directly to a TI or anisotropic foundation has been extensively investigated in recent years. [36][37][38][39][40][41][42][43][44] The subsoils were modeled as solely one type of TI medium in these works, namely, as a TI elastic or poroelastic half-space. However, the distribution of the groundwater in the foundation is very complicated, which results in the complexities of the water content and saturation of different soils.…”

“…Researches on the dynamic response of a beam coupled with a TI half‐space are quite limited according to the above literature review. Nevertheless, the problem of a dynamic load applied directly to a TI or anisotropic foundation has been extensively investigated in recent years 36–44 . The subsoils were modeled as solely one type of TI medium in these works, namely, as a TI elastic or poroelastic half‐space.…”