应用数学和力学(英文版)
應用數學和力學(英文版)
응용수학화역학(영문판)
APPLIED MATHEMATICS AND MECHANICS(ENGLISH EDITION)
2013年
12期
1543-1552
,共10页
丁伯阳%徐庭%陈军%欧阳明
丁伯暘%徐庭%陳軍%歐暘明
정백양%서정%진군%구양명
Lamb’s problem%Green’s function%comprehensive form of solution
By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld’s identity as well as Green’s functions of Stokes’ solution pertaining the conventional elastic dynamic equation, the results of Green’s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a semi-space, the authors obtain the solutions of Green’s function for Lamb’s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb’s previous results, and the solutions of the linear expansion source urr and the linear torsional source uθθ are also given in the paper. The authors reveal that Green’s function of Stokes’ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb’s problem for various situations. It may benefit the investigation of deepening and development of Lamb’s problems and solution for pertinent dynamic problems conveniently.