Calculation of reflection and transmission coefficients of joints using a hybrid finite element/wave and finite element approach

Often structures comprise waveguides connected by joints. The knowledge of the reflection and transmission properties of these joints is important for many applications. This paper presents a hybrid approach, combining a finite element (FE) and a wave and finite element (WFE) model, for calculating the reflection and transmission coefficients of a joint. First, the joint is modelled using standard FE. Then, the waveguide is modelled using the WFE method, where the FE model of a small segment of the waveguide, whose cross-section could be arbitrarily complex, is post-processed to yield the wave properties of the whole waveguide. The two models are coupled to find the reflection and transmission matrices of the joint. This hybrid approach allows for developing a model of the structure where the basis functions are the waves travelling through the structure's various waveguides. Numerical examples are presented.