Wave propagation in connected waveguides of varying cross-section

Abstract

The spectral element method is extended to problems involving arbitrary non-uniform waveguides by introducing an approximate tapered element. The depth of the cross-section is assumed to vary linearly, thus allowing an arbitrary variation to be modelled as a collection of piece-wise linear segments. The frequency dependent stiffness relation is established using the displacement fields of the uniform deep waveguide (both longitudinal and transverse) as the Ritz functions. The element is verified by comparison with a 2-D finite element solution.