{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T15:11:00Z","timestamp":1775747460905,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,9]],"date-time":"2020-09-09T00:00:00Z","timestamp":1599609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["UIDB\/UIDP\/00134\/2020"],"award-info":[{"award-number":["UIDB\/UIDP\/00134\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["PTDC\/ECI-EGC\/31488\/2017"],"award-info":[{"award-number":["PTDC\/ECI-EGC\/31488\/2017"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["CEECIND\/04879\/2017"],"award-info":[{"award-number":["CEECIND\/04879\/2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JMSE"],"abstract":"<jats:p>The application of flexible horizontal porous structure has a significant impact on the design of breakwaters and wave energy absorption devices for coastal protection and wave energy extraction, respectively. This type of structure is more economical compared to a rigid type structure. Therefore, the hydroelastic response of the flexible porous structure can be investigated to widen the influence of structural deformations in design parameters. This paper presents a generalized expansion formula for the said problem based on Green\u2019s function in the water of finite depth (FD) and infinite depth (ID). The series form of the velocity potentials for the wave-maker problem is also derived using Green\u2019s second identity. The derived expansion formula is applied to a real physical problem and the analytical solution is obtained utilizing a matched eigenfunction expansion method under velocity potential decompositions. The convergence study of the series solution is checked. The present results and the published experimental datasets, as well as analysis, are compared. The effect of design parameters on the hydroelastic response of the submerged flexible porous plate is analyzed. It is observed that the analysis of the results will be useful for gaining insight into how to design a wave energy absorption device.<\/jats:p>","DOI":"10.3390\/jmse8090698","type":"journal-article","created":{"date-parts":[[2020,9,9]],"date-time":"2020-09-09T09:01:09Z","timestamp":1599642069000},"page":"698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Hydroelastic Response of a Flexible Submerged Porous Plate for Wave Energy Absorption"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2357-1765","authenticated-orcid":false,"given":"Sarat Chandra","family":"Mohapatra","sequence":"first","affiliation":[{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8570-4263","authenticated-orcid":false,"given":"C.","family":"Guedes Soares","sequence":"additional","affiliation":[{"name":"Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.oceaneng.2013.08.008","article-title":"Wave scattering by dual submerged horizontal porous plates","volume":"73","author":"Cho","year":"2013","journal-title":"Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101948","DOI":"10.1016\/j.apor.2019.101948","article-title":"Wave energy dissipation of a submerged horizontal flexible porous membrane under oblique wave interaction","volume":"94","author":"Guo","year":"2020","journal-title":"Appl. Ocean Res."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zheng, S., Meylan, M.H., Zhu, G., Greaves, D., and Iglesias, G. (2020). Hydroelastic interaction between water waves and an array of circular floating porous elastic plates. J. Fluid Mech.","DOI":"10.1017\/jfm.2020.508"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"102827","DOI":"10.1016\/j.jfluidstructs.2019.102827","article-title":"Wave scattering by a floating porous elastic plate of arbitrary shape: A semi\u2013analytical study","volume":"92","author":"Zheng","year":"2020","journal-title":"J. Fluids Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.apor.2018.06.002","article-title":"Surface gravity wave interaction with a submerged horizontal flexible porous plate","volume":"78","author":"Mohapatra","year":"2018","journal-title":"Appl. Ocean Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.apor.2018.12.007","article-title":"Interaction of uniform current with a circular cylinder submerged below an ice sheet","volume":"86","author":"Li","year":"2019","journal-title":"Appl. Ocean Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/S0029-8018(97)00037-1","article-title":"Wave reflection by a vertical wall with a horizontal submerged porous plate","volume":"25","author":"Wu","year":"1998","journal-title":"Ocean Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1061\/(ASCE)0733-9399(2000)126:10(1048)","article-title":"Short-wave and wave group scattering by submerged porous plate","volume":"126","author":"Neves","year":"2000","journal-title":"J. Eng. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.oceaneng.2012.01.001","article-title":"A new analytical solution for wave scattering by a submerged horizontal porous plate with finite thickness","volume":"42","author":"Liu","year":"2012","journal-title":"Ocean Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s10665-009-9355-2","article-title":"Asymptotic reflection of linear water waves by submerged horizontal porous plates","volume":"69","author":"Evans","year":"2011","journal-title":"J. Eng. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2364","DOI":"10.1016\/j.oceaneng.2007.05.002","article-title":"Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate","volume":"34","author":"Liu","year":"2007","journal-title":"Ocean Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s10665-010-9406-8","article-title":"An alternate analytical solution for water-wave motion over a submerged horizontal porous plate","volume":"69","author":"Liu","year":"2011","journal-title":"J. Eng. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.oceaneng.2012.12.044","article-title":"Transmission of oblique incident waves by a submerged horizontal porous plate","volume":"61","author":"Cho","year":"2013","journal-title":"Ocean Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s42241-018-0053-2","article-title":"Surface gravity wave interaction with submerged horizontal flexible structures","volume":"30","author":"Mohapatra","year":"2018","journal-title":"J. Hydrodyn. Ser. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.ijengsci.2006.01.001","article-title":"Oblique wave scattering by a circular cylinder submerged beneath an ice-cover","volume":"44","author":"Das","year":"2006","journal-title":"Int. J. Eng. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1017\/jfm.2015.582","article-title":"Radiation of waves by a cylinder submerged in water with ice floe or polynya","volume":"784","author":"Sturova","year":"2015","journal-title":"J. Fluid Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1134\/S002189441506019X","article-title":"Oscillations of a cylindrical body submerged in a fluid with ice cover","volume":"56","author":"Tkacheva","year":"2015","journal-title":"J. Appl. Mech. Tech. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107027","DOI":"10.1016\/j.oceaneng.2020.107027","article-title":"Review of developments in porous membranes and net-type structures for breakwaters and fish cages","volume":"200","author":"Guo","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0378-3839(96)00019-1","article-title":"3-D non-breaking regular wave interaction with submerged breakwaters","volume":"28","author":"Losada","year":"1996","journal-title":"Coast. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0378-3839(96)00020-8","article-title":"Interaction of non-breaking directional random waves with submerged breakwaters","volume":"28","author":"Losada","year":"1996","journal-title":"Coast. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0378-3839(97)00011-2","article-title":"Harmonic generation past a submerged porous step","volume":"31","author":"Losada","year":"1997","journal-title":"Coast. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1016\/j.oceaneng.2008.08.003","article-title":"Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate","volume":"35","author":"Liu","year":"2008","journal-title":"Ocean Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0022112008001845","article-title":"Wave absorbing system using inclined perforated plates","volume":"608","author":"Cho","year":"2008","journal-title":"J. Fluid Mech."},{"key":"ref_24","unstructured":"Yueh, C.Y., and Chuang, S.H. (2009, January 21\u201326). Wave scattering by a submerged porous plate wave absorber. Proceedings of the 19th International Offshore and Polar Engineering Conference, Osaka, Japan."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.coastaleng.2013.04.003","article-title":"Wave reflection and transmission by porous breakwaters: A new analytical solution","volume":"78","author":"Liu","year":"2013","journal-title":"Coast. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1080\/03091929.2014.937806","article-title":"Oblique wave diffraction by a flexible floating structure in th epresence of a submerged flexible structure","volume":"108","author":"Mohapatra","year":"2014","journal-title":"Geophys. Astrophys. Fluid Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.jfluidstructs.2012.07.005","article-title":"Effect of compression on wave diffraction by a floating elastic plate","volume":"36","author":"Mohapatra","year":"2013","journal-title":"J. Fluids Struct."},{"key":"ref_28","unstructured":"Guedes Soares, C., and Santos, T.A. (2016). Effect of submerged horizontal flexible membrane on moored floating elastic plate. Maritime Technology and Engineering 3, Taylor & Francis Group."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.apor.2018.10.009","article-title":"Interaction of ocean waves with floating and submerged horizontal flexible structures in three-dimensions","volume":"83","author":"Mohapatra","year":"2019","journal-title":"Appl. Ocean Res."}],"container-title":["Journal of Marine Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-1312\/8\/9\/698\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:08:16Z","timestamp":1760177296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-1312\/8\/9\/698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,9]]},"references-count":29,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["jmse8090698"],"URL":"https:\/\/doi.org\/10.3390\/jmse8090698","relation":{},"ISSN":["2077-1312"],"issn-type":[{"value":"2077-1312","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,9]]}}}