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Time-domain Method for Free Field in Layered Half Space under P-SV Waves of Oblique Incidence

ZHAO Mi1,DU Xiu-li1,LIU Jing-bo2,HAN Qiang1(1.The Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education,Beijing University of Technology, Beijing 100124,China;2.Department of Civil Engineering,Tsinghua University,Beijing 100084,China)  
A 1D finite element method in time domain has been proposed by Liu and Wang for calculating the in-plane free wave field in elastic layered half space under the plane P and SV waves of oblique incidence(Engineering Mechanics,2007,24(7): 16-22(in Chinese) and Acta Mechanica Sinica,2007,23: 673-680).The viscous artificial boundary condition is used in this method to approximately model the radiation damping of underlying bedrock half space.This leads to the 1D finite element method with low accuracy.An artificial boundary condition is proposed in this paper,which can exactly model the radiation damping of bedrock half space.Due to that the outgoing waves in bedrock are the plane P and SV waves with known propagation directions,using the constitutive relation between stress and displacement in elastic media,the impedance boundary condition between stress and velocity on artificial boundary is developed.The 1D finite element method is further improved by using the new artificial boundary condition to replace the viscous boundary condition.Numerical examples indicate that the improved 1D finite element method has the higher accuracy than the original method,and the solution using the improved method is identical very well with the theoretical solution.
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