Shear wave dispersion analysis of incompressible waveguides

A suite of methodologies is presented to compute shear wave dispersion in incompressible waveguides encountered in biomedical imaging; plate, tube, and general prismatic waveguides, all immersed in an incompressible fluid, are considered in this effort. The developed approaches are based on semi-analytical finite element methods in the frequency domain with a specific focus on the complexities associated with the incompressibility of the solid media as well as the simplification facilitated by the incompressibility of the surrounding fluid. The proposed techniques use the traditional idea of selective reduced integration for the solid medium and the more recent idea of perfectly matched discrete layers for the surrounding fluid. Also, used is the recently developed complex-length finite element method for platelike structures. Several numerical examples are presented to illustrate the practicality and effectiveness of the developed techniques in computing shear wave dispersion in a variety of waveguides.