Generalized characteristic method of elastodynamics
A generalized characteristic method is developed to solve two-dimensional time-domain elastodynamic problems. It can be seen as the two-dimensional development of the method of characteristics analogous to d'Alembert's solution for one-dimensional problems. Using the solutions of two-dimensional elastodynamics problems in the complete \((x, y, t)\) space, the real characteristic surfaces are extended to the complex domains in which they are called generalized characteristics. Employing the expressions for stress components along the generalized characteristics, the initial-boundary value problems of elastodynamics can be reduced to a set of algebraic equations whose solutions are first order derivatives of the displacement components. The method leads directly to the reflection coefficients of elastic waves, whose fronts can be of arbitrary convex shape. The full plane Green's function is then found as the solution of a boundary value problem. The generalized characteristics are used directly to analyse the regions of reflected and head waves. The reflection coefficients and the full plane Green's function can be applied to the solution of Lamb's problem for a buried source. The solution yields particular compact expressions for the surface displacement and for subspace displacements induced by a surface force. Some numerical results are given for the displacement histories of receivers near and far from the source in the half-plane. The method can also be used in problems for transversely isotropic media and in problems of electromagnetic radiation.
scientific article; zbMATH DE number 612086