José Efraín Rodríguez-Sánchez

Numerical Formulation to Study Fluid-Solid Interfaces Excited by Elastic Waves

In this paper, the scattering of elastic waves in a fluid-solid interface is researched. The Indirect Boundary Element Method (IBEM) was used to study this wave propagation phenomenon in a 2D fluid-solid model. The source, represented by a Hankel´s function of the second kind, is always applied in the fluid. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. The approach presented is usually called IBEM as the sources’ strengths should be obtained as an intermediate step. This indirect formulation can give a deep physical insight to the analyst on the generated diffracted waves, because it is closer to the physical reality and can be regarded as a realization of Huygens’ Principle, which mathematically is fully equivalent to the classical Somigliana’s representation theorem. In order to gauge accuracy, the method was tested by comparing it to an analytical solution. A near interface pulse generates scattered waves that can be registered by sensors located in the fluid. Results are presented in time domain, where several aspects related to the different wave types that emerge from this kind of problems are pointed out.

Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation

In the present communication, scattering of elastic waves in fluid-layered solid interfaces is studied. The indirect boundary element method is used to deal with this wave propagation phenomenon in 2D fluid-layered solid models. The source is represented by Hankel’s function of second kind and this is always applied in the fluid. Our method is an approximate boundary integral technique which is based upon an integral representation for scattered elastic waves using single-layer boundary sources. This approach is typically called indirect because the sources’ strengths are calculated as an intermediate step. In addition, this formulation is regarded as a realization of Huygens’ principle. The results are presented in frequency and time domains. Various aspects related to the different wave types that emerge from this kind of problems are emphasized. A near interface pulse generates changes in the pressure field and can be registered by receivers located in the fluid. In order to show the accuracy of our method, we validated the results with those obtained by the discrete wave number applied to a fluid-solid interface joining two half-spaces, one fluid and the other an elastic solid.

Coupled Response for Rigid Foundations

A matrix formulation to determine the coupled response of rigid foundations where soil properties are modeled by springs and dashpots is presented. Location and orientation of springs and dashpots can be arbitrary, thus a general solution is determined. The response is given in terms of translational and rotational displacements considering coupled effects. Physics of the problem presented here has been extensively studied and a broad range of useful formulae to determine springs and dashpots properties for soil-structure interaction is available. These published formulae for springs and dashpots properties are an input to the approach presented. Thus, the novelty of this approach is a matrix manipulation that leads to a simple expression allowing coupling all degrees of freedom even when springs and dashpots are not orthogonally oriented. For validation purposes, finite element solutions are compared with the approach presented.