Analysis of Sound Propagation Across Acoustic Ducts With Discontinuities Using a High Precision Finite Element Method

Abstract

A high-precision numerical method is presented to model acoustic wave propagation along a duct with discontinuities. The discontinuous duct can be divided into homogeneous and inhomogeneous substructures. The inhomogeneous substructures are purely discretized by the conventional finite element method, while only cross-sectional areas need to be discretized for homogeneous substructures. The Legendre transformation is then used to transform the semi-discretized problem from the Lagrangian system into the Hamiltonian system. A Riccati equation-based high precision integration method is taken to perform the integral along the longitudinal direction, i.e., the homogeneous direction, to generate stiffness matrices of substructures. The final system stiffness matrix is obtained by assembling stiffness matrices of homogeneous substructures with stiffness matrices of inhomogeneous substructures. Numerical examples are provided to validate the proposed method, and these examples have shown high efficiency and accuracy compared with the conventional finite element method.