Analysis of finite periodic waveguides for elastic waves using finite‐element method

A solution based on a finite‐element method is proposed for calculation of the reflection and transmission characteristics of a finite periodic waveguide for elastic waves. Although finite‐element methods have already been applied to the discontinuity problem in an acoustic waveguide, it has not been possible due to excessive computation time and memory requirement to apply directly the finite‐element method to many discontinuities such as a periodic acoustic waveguide. In this paper, formulations have been undertaken with the substructure which is a related technology of the finite‐element method. Hence, the finite‐element method can be applied directly to all the discontinuities. As a result, in the finite periodic waveguides for acoustic waves, the mutual interaction of the surface wave and the bulk wave can be taken into account over all the discontinuities. The present method has been applied to a groove‐type grating reflector and the validity and effectiveness of the method has been confirmed by comparison with experimental results. An analysis has also been carried out for the positive and negative reflection‐type reflector proposed recently in which the grooves and ridges are combined. It has been confirmed numerically that this reflector has a larger reflection coefficient and smaller bulk wave conversion loss than the conventional reflector.