Finite difference method for dynamic response analysis of anchorage system

YAN Zhi-xin(言志信)^{1, 2}, DUAN Jian(段建)^{1, 2}, JIANG Ping(江平)^{1, 2}, LIU Zi-zhen(刘子振)^{1, 2, 3}, ZHAO Hong-liang(赵红亮)^{1, 2}, HUANG Wen-gui(黄文贵)^{1, 2}

(1. School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China;
2. Key Laboratory of Mechanics on Disaster and Environment in Western China of Ministry of Education of China
(Lanzhou University), Lanzhou 730000, China;
3. School of Civil Engineering and Architecture, Taizhou University, Taizhou 318000, China)

Abstract:Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect.

Key words:anchorage system; dynamic response; finite difference method; attenuation characteristic