Wave Propagation around Thin Structures using the MFS

This paper presents a strategy for using the Method of Fundamental Solutions (MFS) to model the propagation of elastic waves around thin structures, like empty cracks or thin rigid screens, located in a homogeneous elastic medium. The authors make use of a simple approach for modeling these propagation conditions using the MFS together with decomposition of the domain into distinct regions. This approach makes it possible to avoid the undetermined system of equations that arises from imposing boundary conditions at both sides of a thin structure. The numerical implementation of the MFS is performed in the frequency domain, making use of the Fundamental Solutions defined by Tadeu and Kausel (2000) for the propagation of elastic waves generated by a 2.5D load located in an unbounded domain. Using this formulation, it is then possible to model 3D structures which have a constant cross-section in the z direction. This calculation is performed by decomposing the 3D response into a sequence of 2D responses computed for different wave-numbers along z. The first part of the paper describes the formulation of the method in detail, also presenting the Fundamental Solutions used. Then, the method is verified by comparing its results against those given by a frequency domain formulation of the Traction Boundary Element Method (TBEM). \newline A final section of the paper presents a sample application which illustrates the applicability of the method to study the wave propagation around a thin rigid screen, embedded in a fluid medium. For this case, time domain responses are computed and presented in the form of snapshots.