A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I. Theory and validation

The propagation of acoustic waves in waveguides with variable cross section is considered using multimodal decomposition. The approach adopted is to construct two infinite first‐order differential equations for the components of the pressure and the velocity projected over the normal modes. From these an infinite matricial Riccati equation is derived for the impedance matrix. These equations are ordinary differential equations that can be integrated after truncation at a sufficient number of modes and take into account the coupling between modes. The stiffness of the pressure‐velocity equations induced by the presence of evanescent modes is avoided by first calculating the impedance matrix along the guide. The method is checked using different examples where the solutions of the plane‐wave approximation or the finite element method are known. Results show the method provides simple and accurate means to obtain the acoustic field with correct boundary conditions in a nonuniform guide with no restriction on...