{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:48:28Z","timestamp":1765039708436,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Ministry of Economy and Innovation (MINECO) and the European Union FEDER","award":["PID2019-109175GB-C22","UIDB\/04029\/2020","LA\/P\/0112\/2020"],"award-info":[{"award-number":["PID2019-109175GB-C22","UIDB\/04029\/2020","LA\/P\/0112\/2020"]}]},{"name":"FCT\/MCTES through national funds (PIDDAC) under the R&amp;D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE)","award":["PID2019-109175GB-C22","UIDB\/04029\/2020","LA\/P\/0112\/2020"],"award-info":[{"award-number":["PID2019-109175GB-C22","UIDB\/04029\/2020","LA\/P\/0112\/2020"]}]},{"name":"Associate Laboratory Advanced Production and Intelligent Systems ARISE","award":["PID2019-109175GB-C22","UIDB\/04029\/2020","LA\/P\/0112\/2020"],"award-info":[{"award-number":["PID2019-109175GB-C22","UIDB\/04029\/2020","LA\/P\/0112\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>Extracting the microscopic parameters of a porous material is a complex task, and attempts have been made to develop models that can simulate their characteristics, gathering the least amount of information possible. As a case in point, tests to evaluate macroscopic behaviors such as tortuosity, which depends directly on the microscopic fluid velocities, are highly susceptible to generate errors if the precision of the measurement devices is not correct, and the same goes for the other parameters. For this reason, in this paper, a sound propagation model in porous materials with a rigid frame is presented based on a local theory, which tries to simplify, even more, the way to obtain the basic characteristics of porous materials, such as their absorption coefficient at normal and random incidence, and their normal surface impedance. The proposed linearized equivalent fluid model presents four phenomenological coefficients, which characterize acoustic propagation trough the material. Their values are obtained from the material thickness and a measurement in an impedance tube following the ISO 10534 standard. Thus, what is only required is the measured absorption coefficient, either on one third or one octave bands, to fully represent the acoustic behavior in the finite different in time domain (FDTD) method. The model has been simulated with FDTD in porous and fibrous kernels, and the results show a strong agreement with the laboratory measurements and with the analytical results calculated with well-established semi-phenomenological models.<\/jats:p>","DOI":"10.3390\/app14031222","type":"journal-article","created":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T08:44:08Z","timestamp":1706777048000},"page":"1222","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Equivalent Acoustic Material for Air-Filled Porous Absorption Simulations in Finite Different Time Domain Methods: Design and Comparison"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0446-7439","authenticated-orcid":false,"given":"P. C.","family":"Iglesias","sequence":"first","affiliation":[{"name":"Instituto de Investigaci\u00f3n para la Gesti\u00f3n Integrada de Zonas Costeras, Universitat Polit\u00e8cnica de Val\u00e8ncia, Campus de Gand\u00eda, C. Paranimf, 1, 46730 Gandia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2989-375X","authenticated-orcid":false,"given":"L.","family":"Godinho","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Civil, Universidade de Coimbra, ISISE, ARISE, R. Luis Reis dos Santos 290, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5507-7799","authenticated-orcid":false,"given":"J.","family":"Redondo","sequence":"additional","affiliation":[{"name":"Instituto de Investigaci\u00f3n para la Gesti\u00f3n Integrada de Zonas Costeras, Universitat Polit\u00e8cnica de Val\u00e8ncia, Campus de Gand\u00eda, C. Paranimf, 1, 46730 Gandia, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0370-1573(82)90131-4","article-title":"Acoustical characteristics of porous materials","volume":"82","author":"Attenborough","year":"1982","journal-title":"Phys. Rep."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1121\/1.1908239","article-title":"Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range","volume":"28","author":"Biot","year":"1956","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1121\/1.1908241","article-title":"Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range","volume":"28","author":"Biot","year":"1956","journal-title":"J. Acoust. Soc. 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