{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:59:04Z","timestamp":1790683144216,"version":"4.1.0"},"reference-count":28,"publisher":"Acoustical Society of America (ASA)","issue":"3","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>This paper proposes a hybrid matrix method (HMM) to predict the response of multilayered structures including poroelastic media. Hybrid matrices are a generalization of impedance and admittance matrices. It is shown that they are more convenient than the latter to deal with coupling between layers composed of media of different types. They are then a powerful tool to solve multilayered structure problems with any kind of interface. HMM is in addition designed to be stable thereby overcoming the major drawback of the transfer matrix method. The proposed method is also shown to be simpler and more efficient than a recursive method that was previously proposed. Various post-processing tools (finite-size effects, computation of dissipated powers) are also presented so as to illustrate its interest.<\/jats:p>","DOI":"10.1121\/10.0046650","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:21:49Z","timestamp":1790680909000},"page":"2641-2652","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid matrix method, a stable method for the prediction of multilayered structures including poroelastic media"],"prefix":"10.1121","volume":"160","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0534-000X","authenticated-orcid":false,"given":"Olivier","family":"Dazel","sequence":"first","affiliation":[{"name":"Laboratoire d'Acoustique de l'Universit\u00e9 du Mans (LAUM), UMR 6613, Institut d'Acoustique\u2013Graduate School (IA-GS), CNRS, Le Mans Universit\u00e9 ,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-7126-0550","authenticated-orcid":false,"given":"Bruno","family":"Brouard","sequence":"additional","affiliation":[{"name":"Laboratoire d'Acoustique de l'Universit\u00e9 du Mans (LAUM), UMR 6613, Institut d'Acoustique\u2013Graduate School (IA-GS), CNRS, Le Mans Universit\u00e9 ,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"2026092907214130900_c1","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1063\/1.1699629","article-title":"Transmission of elastic waves through a stratified solid medium","volume":"21","year":"1950","journal-title":"J. Appl. Phys."},{"key":"2026092907214130900_c2","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1785\/BSSA0430010017","article-title":"The dispersion of surface waves on multilayered media","volume":"43","year":"1953","journal-title":"Bull. Seismol. Soc. Am."},{"issue":"3","key":"2026092907214130900_c3","doi-asserted-by":"publisher","first-page":"1488","DOI":"10.1121\/1.408152","article-title":"Transfer matrix of multilayered absorbing and anisotropic media. Measurements and simulations of ultrasonic wave propagation through composite materials","volume":"94","year":"1993","journal-title":"J. Acoust. Soc. Am."},{"issue":"1","key":"2026092907214130900_c4","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1006\/jsvi.1995.0243","article-title":"A general method of modelling sound propagation in layered media","volume":"183","year":"1995","journal-title":"J. Sound Vib."},{"issue":"3","key":"2026092907214130900_c5","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1006\/jsvi.1996.0125","article-title":"Sound transmission through multi-panel structures lined with elastic porous materrials","volume":"191","year":"1996","journal-title":"J. Sound Vib."},{"issue":"16","key":"2026092907214130900_c6","doi-asserted-by":"publisher","first-page":"165102","DOI":"10.1063\/1.5108635","article-title":"Modeling and coupling of acoustical layered systems that consist of elements having different transfer matrix dimensions","volume":"126","year":"2019","journal-title":"J. Appl. Phys."},{"issue":"8","key":"2026092907214130900_c7","doi-asserted-by":"publisher","first-page":"084907","DOI":"10.1063\/1.4942443","article-title":"Acoustic analysis of anisotropic poroelastic multilayered systems","volume":"119","year":"2016","journal-title":"J. Appl. Phys."},{"issue":"1","key":"2026092907214130900_c8","doi-asserted-by":"publisher","first-page":"014906","DOI":"10.1063\/1.3159008","article-title":"Rayleigh waves in air saturated axisymmetrical soft porous media","volume":"106","year":"2009","journal-title":"J. Appl. Phys."},{"issue":"3","key":"2026092907214130900_c9","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1007\/s00419-024-02539-z","article-title":"TMM-based study on sound insulation characteristics of laminated cylindrical shell lined with porous materials","volume":"94","year":"2024","journal-title":"Arch. Appl. Mech."},{"key":"2026092907214130900_c10","doi-asserted-by":"publisher","first-page":"113852","DOI":"10.1016\/j.matdes.2025.113852","article-title":"Optimization of graded porous acoustic absorbers based on triply periodic minimal surfaces","volume":"253","year":"2025","journal-title":"Mater. Des."},{"issue":"4","key":"2026092907214130900_c11","doi-asserted-by":"publisher","first-page":"1931","DOI":"10.1121\/1.408707","article-title":"Delta operator technique to improve the Thomson\u2013Haskell-method stability for propagation in multilayered anisotropic absorbing plates","volume":"95","year":"1994","journal-title":"J. Acoust. Soc. Am."},{"issue":"8","key":"2026092907214130900_c12","doi-asserted-by":"publisher","first-page":"083506","DOI":"10.1063\/1.4790629","article-title":"A stable method to model the acoustic response of multilayered structures","volume":"113","year":"2013","journal-title":"J. Appl. Phys."},{"key":"2026092907214130900_c13","doi-asserted-by":"publisher","first-page":"117898","DOI":"10.1016\/j.jsv.2023.117898","article-title":"A general and stable approach to modeling and coupling multilayered acoustical systems with various types of layers","volume":"567","year":"2023","journal-title":"J. Sound Vib."},{"issue":"6","key":"2026092907214130900_c14","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/S0041-624X(01)00082-8","article-title":"Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media","volume":"39","year":"2001","journal-title":"Ultrasonics"},{"issue":"4","key":"2026092907214130900_c15","doi-asserted-by":"publisher","first-page":"2208","DOI":"10.1063\/1.355324","article-title":"Acoustic propagation in anisotropic periodically multilayered media: A method to solve numerical instabilities","volume":"74","year":"1993","journal-title":"J. Appl. Phys."},{"issue":"4","key":"2026092907214130900_c16","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1109\/58.393096","article-title":"Matrix techniques for modeling ultrasonic waves in multilayered media","volume":"42","year":"1995","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"issue":"6","key":"2026092907214130900_c17","doi-asserted-by":"publisher","first-page":"3990","DOI":"10.1121\/10.0036809","article-title":"An efficient and stable approach for modeling wave propagation through poro-elastic layers within multilayered acoustical systems under normal incidence","volume":"157","year":"2025","journal-title":"J. Acoust. Soc. Am."},{"issue":"2","key":"2026092907214130900_c18","doi-asserted-by":"publisher","first-page":"922","DOI":"10.4271\/2023-01-1052","article-title":"A transfer-matrix-based approach to predicting acoustic properties of a layered system in a general, efficient, and stable way","volume":"06","year":"2023","journal-title":"SAE Int. J. Adv. Curr. Prac. Mobility"},{"key":"2026092907214130900_c19","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.apacoust.2015.08.012","article-title":"Acoustic attenuation analysis of network systems by using impedance matrix method","volume":"101","year":"2016","journal-title":"Appl. Acoust."},{"issue":"3","key":"2026092907214130900_c20","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1121\/1.1391249","article-title":"Sound propagation in rigid bends: A multimodal approach","volume":"110","year":"2001","journal-title":"J. Acoust. Soc. Am."},{"issue":"2164","key":"2026092907214130900_c21","doi-asserted-by":"publisher","first-page":"20130448","DOI":"10.1098\/rspa.2013.0448","article-title":"Improved multimodal admittance method in varying cross section waveguides","volume":"470","year":"2014","journal-title":"Proc. R. Soc. A: Math. Phys. Eng. Sci."},{"issue":"2068","key":"2026092907214130900_c22","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1098\/rspa.2005.1612","article-title":"Lamb wave propagation in elastic waveguides with variable thickness","volume":"462","year":"2006","journal-title":"Proc. R Soc. A"},{"issue":"6","key":"2026092907214130900_c23","doi-asserted-by":"publisher","first-page":"3509","DOI":"10.1121\/1.2734482","article-title":"An alternative Biot's displacement formulation for porous materials","volume":"121","year":"2007","journal-title":"J. Acoust. Soc. Am"},{"key":"2026092907214130900_c24","volume-title":"Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials","year":"2009"},{"issue":"5","key":"2026092907214130900_c25","doi-asserted-by":"publisher","first-page":"3418","DOI":"10.1121\/10.0001210","article-title":"Effect of casing on sound absorption characteristics of fine spherical granular material","volume":"147","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"key":"2026092907214130900_c26","unstructured":"Matelys Research Lab, \u201cAlphacell\u201d (2026), https:\/\/alphacell.matelys.com (Last viewed 16\/09\/2026)."},{"issue":"10","key":"2026092907214130900_c27","doi-asserted-by":"publisher","first-page":"1192","DOI":"10.1016\/j.apacoust.2006.06.010","article-title":"A review of analytical methods, based on the wave approach, to compute partitions transmission loss","volume":"68","year":"2007","journal-title":"Appl. Acoust."},{"issue":"4","key":"2026092907214130900_c28","doi-asserted-by":"publisher","first-page":"2054","DOI":"10.1121\/1.2874520","article-title":"Expressions of dissipated powers and stored energies in poroelastic media modeled by {u,U} and {u,P} formulations","volume":"123","year":"2008","journal-title":"J. Acoust. Soc. Am."}],"container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/160\/3\/2641\/21155273\/2641_1_10.0046650.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/160\/3\/2641\/21155273\/2641_1_10.0046650.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:21:51Z","timestamp":1790680911000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/160\/3\/2641\/3405528\/Hybrid-matrix-method-a-stable-method-for-the"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,1]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9,1]]}},"URL":"https:\/\/doi.org\/10.1121\/10.0046650","relation":{},"ISSN":["1520-8524"],"issn-type":[{"value":"1520-8524","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,9]]},"published":{"date-parts":[[2026,9,1]]}}}