Comprehensive form of solution for Lamb’s dynamic problem expressed by Green’s functions

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 u zz and the radial displacement u rz can match Lamb’s previous results, and the solutions of the linear expansion source u rr and the linear torsional source u θθ 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.