Transient response and multiple scattering of elastic waves by a linear array of regularly distributed cylindrical obstacles: Anti-plane S-wave analytical solution

Abstract

We study the multiple scattering of elastic waves by a finite linear array of regularly distributed cylindrical obstacles. The transient response of the system for incident anti–plane shear waves is given in detail. We present an extension of an original solution for rigid cylinders, developed by some of us in 1983. The solution is formally obtained for harmonic excitation and Fourier analysis provides the transient response. Material properties of the cylindrical inclusions are considered. A 2–D formulation is constructed by superposition of the incident field upon the waves diffracted by each obstacle. The solutions for each obstacle are constructed as expansions of cylindrical wave functions, after imposing continuity conditions for the displacements and tractions at the scatterers matrix interfaces with the aid of Graf's addition theorem. Thus, the total field can be referred to any cylindrical coordinates. The infinite system is approximated by a finite one and numerical results are obtained for different values of the parameters. Various cases of cavities and inclusions are studied. A double effect is produced by different filling materials, f. e. amplification at the incidence side and reductions at the far side, or vice versa. Synthetic seismograms and snapshots are computed to illustrate the complex features of wave propagation for this inhomogeneous model.