Energy spectral element method for longitudinal acoustic propagation in ducts

Abstract

Sound field behavior in an acoustic enclosure is an important part of the design of transportation vehicle passenger cabin, concert halls, conference rooms, and etc. Different analysis methods are available and have strengths and weaknesses. Low frequency band envelopes and negligible absorption in the walls can be modeled by Modal Analysis or Finite Element Method. However, as the frequency band increases, both methods become computationally intensive and Statistical Energy Analysis or the Sabine model can be an efficient approach. However, these methods do not take into account any spatial variation within the enclosure. The Energy Flow Analysis (EFA) solution for acoustic enclosures can be done analytically. In this paper, the Energy Spectral Element Method (ESEM) is formulated and applied to predict the spatial distribution of energy flux and density of acoustic ducts at high frequencies. ESEM is a matrix methodology based on EFA to solve acoustic and structural vibration problems. In this work, numerical models involving simple and coupled one-dimensional acoustic ducts are generated by ESEM, and the results are compared with energy densities calculated from the pressure fields predicted by the Spectral Element Method (SEM).