Resumo
Este estudo emprega simulação computacional com o objetivo de recriar virtualmente o campo acústico de ambientes internos. Pesquisas que almejam uma modelagem que corresponda de maneira acurada à realidade são indispensáveis para otimizar a análise do comportamento acústico desses espaços, visando à efetivação de um condicionamento acústico eficiente. Com o intuito de auxiliar profissionais no desenvolvimento de projetos de acústica de salas por meio de ferramentas computacionais de código aberto, esta pesquisa explora aspectos cruciais no momento de modelar a acústica de espaços reduzidos, como salas de estúdios de gravação ou home studios. Utilizou-se, neste trabalho, um dos métodos consagrados para simulação computacional desses ambientes, conhecido como Método de Elementos Finitos (MEF), para modelar o campo acústico em uma sala em escala reduzida. O processo envolveu múltiplas fases de ajuste do modelo computacional, fundamentadas em dados experimentais e considerando variáveis como temperatura, umidade, velocidade do som na fonte, difração ao redor de caixas acústicas e características dos materiais absorventes. Os principais resultados destacam o impacto das modificações no modelo, por meio da Função de Resposta em Frequência, da Curva de Decaimento de Energia e do Tempo de Reverberação. Conclui-se que tais informações são importantes para o desenvolvimento da modelagem e de projetos acústicos de salas mais acurados na faixa de frequência de baixa-média densidade modal.
Referências
ABNT. ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR ISO 3382-2. Acústica - Medição de parâmetros de acústica de salas - Parte 2: Tempo de reverberação em salas comuns. Rio de Janeiro: ABNT,19 p. 2017.
ARETZ, M. Specification of Realistic Boundary Conditions for the FE Simulation of Low Frequency Sound Fields in Recording Studios. Acta Acustica united with Acustica, v. 95, n. 5, p. 874–882, 1 sep. 2009. Available at: https://www.researchgate.net/publication/233542916_Specification_of_Realistic_Boundary_Conditions_for_the_FE_Simulation_of_Low_Frequency_Sound_Fields_in_Recording_Studios.
ARETZ, M.; VORLÄNDER, M. Efficient Modelling of Absorbing Boundaries in Room Acoustic FE Simulations. Acta Acustica united with Acustica, v. 96, n. 6, p. 1042–1050, 1 nov. 2010. Available at: https://www.researchgate.net/publication/233626667_Efficient_Modelling_of_Absorbing_Boundaries_in_Room_Acoustic_FE_Simulations
ARETZ, M.; VORLÄNDER, M. Combined wave and ray based room acoustic simulations of audio systems in car passenger compartments, Part II: Comparison of simulations and measurements. Applied Acoustics, v. 76, p. 52–65, feb. 2014. DOI: https://doi.org/10.1016/j.apacoust.2013.07.020.
ATALLA, N.; SGARD, F. Finite element and boundary methods in structural acoustics and vibration. Boca Raton: CRC Press, 2015. 470 p. DOI: https://doi.org/10.1201/b18366.
ATTENBOROUGH, K. Acoustical characteristics of porous materials acoustical of porous materialsphysics reports Physics Reports. v. 82, n. 3, p. 179-227, feb.1982. Available at: https://www.sciencedirect.com/science/article/abs/pii/0370157382901314.
BERZBORN, M.; BOMHARDT, R.; KLEIN, J.; VORLÄNDER, M. The ITA-Toolbox: An Open Source MATLAB Toolbox for Acoustic Measurements and Signal Processing. 2017. https://api.semanticscholar.org/CorpusID:65181335.
BILBAO, S.; AHRENS, J.; HAMILTON, B. Incorporating source directivity in wave-based virtual acoustics: Time-domain models and fitting to measured data. The Journal of the Acoustical Society of America, v. 146, n. 4, p. 2692–2703, oct. 2019. DOI: https://doi.org/10.1121/1.5130194.
BORREL-JENSEN, N.; ENGSIG-KARUP, A. P.; JEONG, C.-H. Physics-informed neural networks for one-dimensional sound field predictions with parameterized sources and impedance boundaries. JASA Express Letters, v. 1, n. 12, 1 dec. 2021. DOI: https://doi.org/10.1121/10.0009057.
BRANDÃO, E.; MAREZE, P. H.; LENZI, A.; SILVA, A. R. Impedance measurement of non-locally reactive samples and the influence of the assumption of local reaction. The Journal of the Acoustical Society of America, v. 133, n. 5, p. 2722–2731, 1 may. 2013. DOI: https://doi.org/10.1121/1.4799015.
BRANDÃO, E.; SANTOS, E. S. O.; MELO, V. S. G.; TENENBAUM, R. A.; MAREZE, P. H. On the performance investigation of distinct algorithms for room acoustics simulation. Applied Acoustics, v. 187, p. 108484, feb. 2022. DOI: https://doi.org/10.1016/j.apacoust.2021.108484.
BRANDÃO, E.; FONSECA, W. D.; MAREZE, P. H. An algorithmic approach to electroacoustical analogies. The Journal of the Acoustical Society of America, v.152, n. 1, p. 667-678, jul. 2022. DOI: https://doi.org/10.1121/10.0012886.
BRANDÃO, E.; MORGADO, G.; FONSECA, W. D. A ray tracing engine integrated with Blender and with uncertainty estimation: Description and initial results. Building Acoustics, v. 28, n. 2, p. 99–118, 20 jun. 2021. DOI: https://doi.org/10.1177/1351010X20964758.
COPETTI, G.; MAREZE, P. H.; DRESCH. F.; MARGHETI. S.; GOMES. A. B.; MONTEIRO. M. S. C.; FONSECA, W. D. BRANDÃO. E.; SPECHT. L. P. Modelagem em elementos finitos do campo acústico de um pneu sobre camadas porosas asfálticas. In: ENCONTRO DA SOCIEDADE BRASILEIRA DE ACÚSTICA, 28., 2018. Proceedings [...]. Santa Maria: Universidade Federal de Santa Maria, 2018. Disponível em: https://proceedings.science/sobrac/trabalhos/modelagem-em-elementos-finitos-do-campo-acustico-de-um-pneu-sobre-camadas-porosa?lang=pt-br; Acesso em: 06 Mar. 2025.
COX, T. J.; D’ANTONIO, P. Acoustic absorbers and diffusers: theory, design and application. 3. ed. London: Taylor & Francis, 2017.
DRAGONETTI, R.; ROMANO, R. A. Considerations on the sound absorption of non-locally reacting porous layers. Applied Acoustics, v. 87, p. 46–56, jan. 2015. DOI: https://doi.org/10.1016/j.apacoust.2014.06.011.
DATSCH, S.; MAREZE, P; FONSECA, W. D’A. Estudo de erros de medição da resistividade de materiais de absorção: simulação computacional e método experimental. In: CONGRESSO IBEROAMERICANO DE ACÚSTICA, 12., 2022. Anais [...]. Florianópolis, 2022. Available at: https://www.researchgate.net/publication/364660887. Acesso em: 6 mar. 2025.
FONSECA, W. D'A.; BRANDÃO, E.; MAREZE, P. H.; MELO, V. S. G.; TENENBAUM, R. A.; SANTOS, C.; PAIXÃO, D. Acoustical Engineering: A Complete Academic Undergraduate Program in Brazil. The Journal of The Acoustical Society of America, [S.L.], v. 152, n. 2, p. 1180–1191, 1 aug. 2022. DOI: http://doi.org/10.1121/10.0013570.
FONSECA, W. D'A. EAC 1019 - Psicoacústica (2023-2). Curso de Engenharia Acústica, Santa Maria, Universidade Federal de Santa Maria, 2023. Notas de aula.
GUMEROV, N. A.; DURAISWAMI, R. Fast multipole accelerated boundary element methods for room acoustics. The Journal of the Acoustical Society of America, v. 150, n. 3, p. 1707–1720, 1 set. 2021. DOI: https://doi.org/10.1121/10.0006102.
GUNNARSDÓTTIR, K.; JEONG, C.-H.; MARBJERG, G. Acoustic behavior of porous ceiling absorbers based on local and extended reaction. The Journal of the Acoustical Society of America, v. 137, n. 1, p. 509–512, 1 jan. 2015. DOI: https://doi.org/10.1121/1.4904541.
HAK, C. C. J. M.; WENMAEKERS, R. H. C.; VAN LUXEMBURG, L. C. J. Measuring Room Impulse Responses: Impact of the Decay Range on Derived Room Acoustic Parameters. Acta Acustica united with Acustica, v. 98, n. 6, p. 907–915, 1 nov. 2012. Available at: https://www.researchgate.net/publication/263749388_Measuring_Room_Impulse_Responses_Impact_of_the_Decay_Range_on_Derived_Room_Acoustic_Parameters.
HAMILTON, B.; BILBAO, S. FDTD Methods for 3-D Room Acoustics Simulation with High-Order Accuracy in Space and Time. IEEE/ACM Transactions on Audio, Speech, and Language Processing, v. 25, n. 11, p. 2112–2124, nov. 2017. DOI: https://doi.org/10.1109/TASLP.2017.2744799 .
HARGREAVES, J. A.; RENDELL, L. R.; LAM, Y. W. A framework for auralization of boundary element method simulations including source and receiver directivity. The Journal of the Acoustical Society of America, v. 145, n. 4, p. 2625–2637, 1 apr. 2019. DOI: https://doi.org/10.1121/1.5096171.
HODGSON, M.; WAREING, A. Comparisons of predicted steady-state levels in rooms with extended- and local-reaction bounding surfaces. Journal of Sound and Vibration, v. 309, n. 1–2, p. 167–177, 8 jan. 2008. DOI: https://doi.org/10.1016/j.jsv.2007.06.069
HORNIKX, M.; KRIJNEN, T.; VAN HARTEN, L. openPSTD: The open source pseudospectral time-domain method for acoustic propagation. Computer Physics Communications, v. 203, p. 298–308, jun. 2016. DOI : https://doi.org/10.1016/j.cpc.2016.02.029
JEONG, C. H. Guideline for adopting the local reaction assumption for porous absorbers in terms of random incidence absorption coefficients. Acta Acustica united with Acustica, v. 97, n. 5, p. 779–790, sep. 2011. DOI: https://doi.org/10.3813/AAA.918458
JEONG, C.-H.; MARBJERG, G.; BRUNSKOG, J. Uncertainty of input data for room acoustic simulations. BNAM Baltic-Nordic Acoustic Meeting. Stockholm, Sweden, jun. 2016.
KEMERICH, B. Aprimorando a simulação computacional em acústica de salas: Uma investigação detalhada sobre absorvedores em modelos numéricos. Trabalho de Conclusão de Curso (Engenharia Acústica) – Universidade Federal de Santa Maria, Santa Maria, 2024.
KLEINER, M.; TICHY, J. Acoustics of small rooms. London:Taylor & Francis, 2014. https://doi.org/10.1201/b16866
Mareze, P.; Pereira, M.; Godinho, L.; Mendes, P. Study of analytical and numerical models for diffuse field sound absorption prediction according to the porous panel dimensions. INTER-NOISE and NOISE-CON Congress and Conference Proceedings (Institute of Noise Control Engineering, 2019), Vol. 259, pp. 6941–6953. Available at: https://www.researchgate.net/publication/333918419_Study_of_analytical_and_numerical_models_for_diffuse_field_sound_absorption_prediction_according_to_the_porous_panel_dimensions/references
MIKI, Y. Acoustical properties of porous materials-Modifications of Delany-Bazley models. Journal of the Acoustical Society of Japan (E), v. 11, n. 1, p. 11-19, 1990. DOI: https://doi.org/10.1250/ast.11.19
OKUZONO, T.; MOHAMED, M. S.; SAKAGAMI, K. Potential of Room Acoustic Solver with Plane-Wave Enriched Finite Element Method. Applied Sciences, v. 10, n. 6, p. 1969, 13 mar. 2020. DOI: https://doi.org/10.3390/app10061969
OKUZONO, T.; YOSHIDA, T. High potential of small-room acoustic modeling with 3D time-domain finite element method. Frontiers in Built Environment, v. 8, 2 dec. 2022. DOI: https://doi.org/10.3389/fbuil.2022.1006365
PIND, F.; JEONG, C.H.; ENGSIG-KARUP, A.; HESTHAVEN, J.; STROMANN, J. Time-domain room acoustic simulations with extended-reacting porous absorbers using the discontinuous Galerkin method. The Journal of the Acoustical Society of America, v. 148, n. 5, p. 2851–2863, 1 nov. 2020. DOI: https://doi.org/10.1121/10.0002448
SAARELMA, J.; SAVIOJA, L.; BOTTS, J. Finite-difference time-domain solver for room acoustics using graphics processing units. Dissertação (Mestrado em Tecnologia de Mídia). Aalto University – School of Electrical Engineering, Helsinki, 2013.
SAVIOJA, L.; SVENSSON, U. P. Overview of geometrical room acoustic modeling techniques. The Journal of the Acoustical Society of America, v. 138, n. 2, p. 708–730, 1 aug. 2015. DOI: https://doi.org/10.1121/1.4926438
SCHROEDER, M. R. Integrated-impulse method measuring sound decay without using impulses. The Journal of the Acoustical Society of America, v. 66, n. 2, p. 497–500, 1 aug. 1979. https://doi.org/10.1121/1.383103
SCHROEDER, M. R. The ‘“Schroeder frequency”’ revisited. The Journal of the Acoustical Society of America, v. 99, n. 5, p. 3240–3241, 1 may. 1996. DOI: https://doi.org/10.1121/1.414868
SHIN, K.; HAMMOND, J. K. Fundamentals of Signal Processing: for Sound and Vibration Engineers. 1. ed. New Jersey, Wiley, 2008. 416p.
SOARES, M.; BRANDÃO, E.; TENEMBAUM, R.; MAREZE, P. Low-frequency room acoustical simulation of a small room with BEM and complex-valued surface impedances. Applied Acoustics, v. 188, p. 108570, jan. 2022. DOI: https://doi.org/10.1016/j.apacoust.2021.108570.
SOUZA, G. Análise do coeficiente de espalhamento em uma minicâmara reverberante. Trabalho de Conclusão de Curso (Engenharia Acústica) – Universidade Federal de Santa Maria, Santa Maria, 2018.
TOMIKU, R.; OTSURU, T. Sound fields analysis in an irregular-shaped reverberation room by finite element method. Journal of Architecture and Planning (Transactions of AIJ), v. 67, n. 551, p. 9–15, 2002. DOI: https://doi.org/10.3130/aija.67.9_1
VORLÄNDER, M. Computer simulations in room acoustics: Concepts and uncertainties. The Journal of the Acoustical Society of America, v. 133, n. 3, p. 1203–1213, 1 mar. 2013. DOI: https://doi.org/10.1121/1.4788978
YASUDA, Y.; UENO, S.; KADOTA, M.; SEKINE, H. Applicability of locally reacting boundary conditions to porous material layer backed by rigid wall: Wave-based numerical study in non-diffuse sound field with unevenly distributed sound absorbing surfaces. Applied Acoustics, v. 113, p. 45–57, dec. 2016. DOI: https://doi.org/10.1016/j.apacoust.2016.06.006
YASUDA, Y.; SAITO, K.; SEKINE, H. Effects of the convergence tolerance of iterative methods used in the boundary element method on the calculation results of sound fields in rooms. Applied Acoustics, v. 157, p. 106997, jan. 2020. DOI: https://doi.org/10.1016/j.apacoust.2019.08.003
YASUDA, Y.; UENO, S.; SEKINE, H. A note on applicability of locally-reacting boundary conditions for Delany-Bazley type porous material layer backed by rigid wall. Acoustical Science and Technology, v. 36, n. 5, p. 459–462, 2015. DOI: https://doi.org/10.1250/ast.36.459
YATABE, K.; SUGAHARA, A. Convex-optimization-based post-processing for computing room impulse response by frequency-domain FEM. Applied Acoustics, v. 199, p. 108988, oct. 2022. DOI: https://doi.org/10.1016/j.apacoust.2022.108988

Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Copyright (c) 2025 PARC: Pesquisa em Arquitetura e Construção