Numerical Analysis on Isotropic Elastic Waveguides by Mode-Matching Method - II. Particle Velocities and Dispersion Characteristics in Rods of Rectangular Cross Section

Abstract

The mode-matching method is applied for the precise numerical analysis of an isotropic elastic rod of rectangular cross sec- tion. In this method, the truncated modal expansions are matched to the boundary conditions in the sense of least squares, and convergence in the sequence of the modal expansions is assured. In the case of a rectangular rod, a complete set of modal functions for the expansions are concretely prepared, and the algorithm for numerical analysis is presented. Numerical results for the field distributions, whose analysis has been insufficient so far, are obtained together with the dispersion relations in the longitudinal, the torsional, the flexural, and the screw modes. Their accuracy is examined by the application of the extrapo- lation technique. As a consequence, dispersion relations are obtained with considerably high accuracy of 3-6 significant figures in every mode, and the field distributions with about 1-3 figures. In conclusion, it is confirmed that the mode-matching method is more precise and ef- fective for discussions on the homogeneous isotropic elastic waveguide.