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Sci.","Applied Sciences"],"abstract":"<jats:p>This study presents a comprehensive analysis of the efficiency of periodic metamaterials in attenuating acoustic noise within the audible frequency range of 20 Hz to 20 kHz, in both in-plane (i.e., through the periodicity) and out-of-plane (i.e., through the thickness) directions. This dual assessment is pivotal for understanding the utility of these periodic metamaterials as multi-directional acoustic filters. The present study utilized previously optimized unit cells to construct unidimensional and planar periodic metamaterials, designated as: Optimal Basic-Periodic, Optimal Semi-Periodic, Optimal Tapered-Diverging, and Optimal Tapered-Converging. These unit cells exhibited bandgaps encompassing at least 90% of the audible frequency spectrum. To assess performance, multiple numerical simulations under insertion conditions were conducted, demonstrating that the insertion of metamaterials effectively attenuates at least 54.52 dB of the noise levels within the audible frequency range as sound traverses through both the periodicity and thickness directions, specifically within ranges aligning with bandgaps. Subsequently, a small prototype was fabricated via additive manufacturing, and preliminary experimental validation of through-thickness attenuation was conducted. The measurements showed that the small prototype attenuated within the bandgap ranges and resulted in a 23.74 dB reduction within the audible frequency range.<\/jats:p>","DOI":"10.3390\/app16199654","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T12:09:25Z","timestamp":1790683765000},"page":"9654","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bandgap-Rich Unidimensional and Planar Periodic Metamaterials for Multi-Directional Acoustic Filtering"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-3737-9215","authenticated-orcid":false,"given":"Mohamed","family":"Shendy","sequence":"first","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0853-996X","authenticated-orcid":false,"given":"Nima","family":"Maftoon","sequence":"additional","affiliation":[{"name":"Department of Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Armaghan","family":"Salehian","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.3233\/OER-2007-7301","article-title":"Effects of Noise and Music on Human and Task Performance: A Systematic Review","volume":"7","author":"Dalton","year":"2007","journal-title":"Occup. 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