Numerical analysis on elastic waveguides with elliptical cross-section by mode-matching method

A mode-matching method is applied to accurate numerical analysis of the elastic waveguide with elliptical cross-section. This method is based on the Rayleigh expansion theorem and on the boundarymatching procedure in the sense of least-squares, and guarantees the uniform convergence of the solutions represented by modal expansions in an arbitrarily shaped cross-section. By this method, the dispersion relations of the waveguide in the case of large ellipticity, the precise analysis of which has been difficult so far, are obtained with extremely high accuracy. Moreover, the field distributions of the particle velocity (deformations of the cross-section) are also made clear for each mode. The degree of accuracy of such results is examined in detail, compared to those of the collocation method. In conclusion, it may be said that the mode-matching method is also a more effective and accurate method for numerical analysis of the elastic field in the waveguide with any other cross-section as well as the elliptical or rectangular ones, compared with the other methods.