{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T05:29:42Z","timestamp":1780464582693,"version":"3.54.1"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,4]],"date-time":"2017-05-04T00:00:00Z","timestamp":1493856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The acoustic performance of the ducted Helmholtz resonator (HR) system is analyzed theoretically and numerically. The periodic HR array could provide a wider noise attenuation band due to the coupling of the Bragg reflection and the HR\u2019s resonance. However, the transmission loss achieved by a periodic HR array is mainly dependent on the number of HRs, which restricted by the available space in the longitudinal direction of the duct. The full distance along the longitudinal direction of the duct for HR\u2019s installation is sometimes unavailable in practical applications. Only several pieces of the duct may be available for the installation. It is therefore that this paper concentrates on the acoustic performance of a HR array consisting of several periodic parts. The transfer matrix method and the Bragg theory are used to investigate wave propagation in the duct. The theoretical prediction results show good agreement with the Finite Element Method (FEM) simulation results. The present study provides a practical way in noise control application of ventilation ductwork system by utilizing the advantage of periodicity with the limitation of available completed installation length for HRs.<\/jats:p>","DOI":"10.3390\/s17051029","type":"journal-article","created":{"date-parts":[[2017,5,4]],"date-time":"2017-05-04T11:44:18Z","timestamp":1493898258000},"page":"1029","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Noise Attenuation Performance of a Helmholtz Resonator Array Consist of Several Periodic Parts"],"prefix":"10.3390","volume":"17","author":[{"given":"Dizi","family":"Wu","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Architecture and Art, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9510-2071","authenticated-orcid":false,"given":"Cheuk","family":"Mak","sequence":"additional","affiliation":[{"name":"Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenzhi","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.buildenv.2017.02.006","article-title":"Life cycle assessment for three ventilation methods","volume":"116","author":"Fong","year":"2017","journal-title":"Build. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.enbuild.2016.05.055","article-title":"Ventilation of air-conditioned residential buildings: A case study in Hong Kong","volume":"127","author":"Ai","year":"2016","journal-title":"Energy Build."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3756","DOI":"10.1121\/1.3127129","article-title":"Flow noise from spoilers in ducts","volume":"125","author":"Mak","year":"2009","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.buildenv.2015.03.017","article-title":"Recent advances in building acoustics: An overview of prediction methods and their applications","volume":"91","author":"Mak","year":"2015","journal-title":"Build. Environ."},{"key":"ref_5","unstructured":"Fry, A. (1987). Noise Control in Building Services, Pergamon Press. [1st ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1121\/1.1907235","article-title":"On the theory and design of acoustic resonators","volume":"25","author":"Ingard","year":"1953","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.apacoust.2016.08.020","article-title":"An extended neck versus a spiral neck of the Helmholtz resonator","volume":"115","author":"Cai","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0022-460X(73)80234-2","article-title":"Theory of a generalized Helmholtz resonator","volume":"26","author":"Tang","year":"1973","journal-title":"J. Sound Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2360","DOI":"10.1121\/1.428622","article-title":"Circular asymmetric Helmholtz resonator","volume":"107","author":"Selamet","year":"2000","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1121\/1.410196","article-title":"Time harmonic acoustic Bloch wave propagation in periodic waveguides. Part I. Theory","volume":"96","author":"Bradley","year":"1994","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1854","DOI":"10.1121\/1.410197","article-title":"Time harmonic acoustic Bloch wave propagation in periodic waveguides. Part II. Experiment","volume":"96","author":"Bradley","year":"1994","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.1121\/1.2036222","article-title":"Silencer design by using array resonators for low-freqeuncy band noise reduction","volume":"118","author":"Seo","year":"2005","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"EL316","DOI":"10.1121\/1.3691826","article-title":"Acoustic performance of a duct loaded with identical resonators","volume":"131","author":"Wang","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"EL471","DOI":"10.1121\/1.4968530","article-title":"Noise control zone for a periodic ducted Helmholtz resonator system","volume":"140","author":"Cai","year":"2016","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.apacoust.2017.02.006","article-title":"Noise attenuation performance improvement by adding Helmholtz resonator on the periodic ducted Helmholtz resonator system","volume":"112","author":"Cai","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1007\/s12206-016-0119-4","article-title":"Transmission loss of a silencer using resonator arrays at high sound pressure level","volume":"30","author":"Seo","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.wavemoti.2015.02.005","article-title":"Generation of acoustic solitary waves in a lattice of Helmholtz resonators","volume":"56","author":"Richoux","year":"2015","journal-title":"J. Wave Motion"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1006\/jsvi.1995.0620","article-title":"Wave transmission through one-dimensional near periodic structures: Optimum and random disorder","volume":"188","author":"Langley","year":"1995","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1006\/jsvi.1995.0529","article-title":"Theoretical, computational and experimental investigation of Helmholtz resonators with fixed volume: Lumped versus distributed analysis","volume":"187","author":"Selamet","year":"1995","journal-title":"J. Sound Vib."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1121\/1.413185","article-title":"Four-pole parameters of a duct with low Mach number flow","volume":"98","author":"Ji","year":"1995","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_21","unstructured":"Munjal, M.L. (1987). Acoustic of Ducts and Mufflers, John Wiley & Sons. [1st ed.]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1121\/1.3132706","article-title":"A study of coupled flexural-longitudinal wave motion in a periodic dual-beam structure with transverse connection","volume":"126","author":"Yun","year":"2009","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1446","DOI":"10.1121\/1.412085","article-title":"Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators","volume":"97","author":"Sugimoto","year":"1995","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1121\/1.2164987","article-title":"A review of finite-element methods for time-harmonic acoustics","volume":"119","author":"Thompson","year":"2006","journal-title":"J. Acoust. Soc. Am."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/5\/1029\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:34:36Z","timestamp":1760207676000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/5\/1029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,4]]},"references-count":24,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,5]]}},"alternative-id":["s17051029"],"URL":"https:\/\/doi.org\/10.3390\/s17051029","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,4]]}}}