CONCILIUM, Vol. 23, Nº 3, 2023 DOI: 10.53660/CLM-834-23B05 ISSN: 0010-5236 Energy spectral element method for longitudinal acoustic propagation in ducts Método dos elementos espectrais de energia para propagação acústica longitudinal em dutos Received: 2023-01-11 | Accepted: 2023-02-12 | Published: 2023-03-02 Elson Cesar Moraes ORCID: https://orcid.org/0000-0003-3717-5851 Mechanical Engineering Course, Federal University of Maranhão -UFMA, São Luís-MA, Brazil E-mail: elson.cm@ufma.br Vilson Souza Pereira ORCID: https://orcid.org/0000-0003-0814-0449 Mechanical Engineering Course, Federal University of Maranhão-UFMA, São Luís-MA, Brazil E-mail: vilson.sp@ufma.br José Maria Campos Dos Santos ORCID: https://orcid.org/0000-0002-3277-3492 Computational Mechanics Department, Faculty of Mechanical Engineer, State University of Campinas-UNICAMP, Campinas-SP, Brazil E-mail: zema@fem.unicamp.br 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). Keywords: Energy Flow Analysis; Waveguides; Energy Spectral Element Method; Acoustic Enclosure. RESUMO O comportamento do campo sonoro em um gabinete acústico é uma parte importante do projeto de cabines de passageiros de veículos de transporte, salas de concerto, salas de conferência e etc. Diferentes métodos de análise estão disponíveis e têm pontos fortes e fracos. Gabinetes submetidos a banda de baixa frequência e absorção desprezível nas paredes podem ser modelados por Análise Modal ou FEM. No entanto, à medida que a banda de frequência aumenta, ambos os métodos se tornam intensivos e a Análise Estatística de