Numerical analysis of elastic fields in a rectangular overlay on a perfectly rigid substrate, using mode-matching method

Abstract

The mode-matching method is applied to the numerical analysis of elastic fields in a rectangular overlay guide on a perfectly rigid substrate. In this new method, the truncated modal expansions, constructed by the linear combinations of the complete set of modal functions having the same wave number as the field being considered, are made to fit on the boundary conditions in the least-squares sense. These modal expansions and their partial derivatives are assured to converge uniformly to the true field and its and derivative, respectively, by increasing the truncation sizes. Therefore, precise discussions are expected not only on the dispersion relation but also on the particle velocity and the stress, the accurate calculation of which has been difficult so far. The numerical results agree well with those of Aalami by the finite-element method. The characteristic behaviours of the field distributions of each mode are made clear, with some degree of accuracy, for small truncation sizes. As a conclusion, it is confirmed that this new method is also useful for the numerical analysis of the mixed boundary-condition problem in the elastic field.