Open Access

ARTICLE

A Green's Function for Variable Density Elastodynamics under Plane Strain Conditions by Hormander's Method

George D. Manolis¹, Stavros Pavlou²

1 Aristotle University of Thessaloniki, Greece
2 University of Patras, Greece

Computer Modeling in Engineering & Sciences 2002, 3(3), 399-416. https://doi.org/10.3970/cmes.2002.003.399

Abstract

A free-space Green's function for problems involving time-harmonic elastic waves in variable density materials under plane strain conditions is developed herein by means of Hormander's method in the context of matrix algebra formalism. The challenge when solving problems involving inhomogenous media is that the coefficients appearing in the governing equations of motion are position-dependent. Furthermore, an additional difficulty stems from the fact that these governing equations are vectorial, which implies that coordinate transformation techniques that have been successful with scalar waves can no longer be used. Thus, the present work aims at establishing the necessary background that will allow for construction of Green's functions for a general class of inhomogeneous media that is not necessarily restricted to the variable density case. These functions, besides being useful in their own right, are also important within the context of boundary integral formulations, where they appear as kernels in the underlying integral equations. Finally, a numerical example serves to illustrate the proposed methodology and to quantify the influence of a variable density profile on the propagation of elastic waves.

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