{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T11:11:09Z","timestamp":1759921869972,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T00:00:00Z","timestamp":1736812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper concerns the low-frequency symmetric (extensional) motions of a thin elastic layer submerged in a fluid. This problem is less investigated than that for antisymmetric motion corresponding to bending vibrations, partly because the classical theory for thin-plate extension is not oriented to model the transverse compression of the plate caused by the pressure of the fluid. It is also worth noting that, in contrast to a fluid-borne bending wave, the extensional wave radiates into the fluid, resulting in complex-valued terms in the associated dispersion relation. In this paper, we derive a refined asymptotic formulation for symmetric motion starting from the 2D plane strain problem regarding fluid\u2013structure interaction. The obtained results have the potential to be implemented for interpreting numerical and experimental data for a variety of modern engineering setups.<\/jats:p>","DOI":"10.3390\/sym17010119","type":"journal-article","created":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T03:29:43Z","timestamp":1736825383000},"page":"119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Low-Frequency Longitudinal Vibrations of a Fluid-Loaded Elastic Layer"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9709-6592","authenticated-orcid":false,"given":"Sheeru","family":"Shamsi","sequence":"first","affiliation":[{"name":"School of Computer Science and Mathematics, Keele University, Keele ST5 5BG, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9051-2103","authenticated-orcid":false,"given":"Ludmila","family":"Prikazchikova","sequence":"additional","affiliation":[{"name":"School of Computer Science and Mathematics, Keele University, Keele ST5 5BG, UK"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,14]]},"reference":[{"unstructured":"Rayleigh, J.W.S.B. (1896). The Theory of Sound, Macmillan.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Crighton, D.G., Dowling, A.P., Ffowcs-Williams, J., Heckl, M., Leppington, F., and Bartram, J.F. (1992). Modern Methods in Analytical Acoustics Lecture Notes, Springer.","key":"ref_2","DOI":"10.1007\/978-1-4471-0399-8"},{"unstructured":"Junger, M.C., and Feit, D. (1986). Sound, Structures, and Their Interaction, MIT Press.","key":"ref_3"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-460X(89)90983-8","article-title":"The 1988 Rayleigh medal lecture: Fluid loading\u2014The interaction between sound and vibration","volume":"133","author":"Crighton","year":"1989","journal-title":"J. Sound Vib."},{"unstructured":"Kaplunov, J.D., Kossovitch, L.Y., and Nolde, E. (1998). 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Solids"},{"key":"ref_9","first-page":"10812865241233737","article-title":"A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell","volume":"29","author":"Ege","year":"2024","journal-title":"Math. Mech. Solids"},{"key":"ref_10","first-page":"280","article-title":"Asymptotic formulae for the modal resonance of peripheral waves in the scattering of an obliquely incident plane acoustic wave by a cylindrical shell","volume":"80","author":"Kaplunov","year":"1994","journal-title":"Acta Acust. United Acust."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.jsv.2007.04.028","article-title":"Analysis of time harmonic wave propagation in an elastic layer under heavy fluid loading","volume":"305","author":"Sorokin","year":"2007","journal-title":"J. Sound Vib."},{"unstructured":"Achenbach, J. (2012). Wave Propagation in Elastic Solids, Elsevier.","key":"ref_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0165-2125(93)90001-V","article-title":"Plane vibrations and radiation of an elastic layer lying on a liquid half-space","volume":"17","author":"Kaplunov","year":"1993","journal-title":"Wave Motion"},{"doi-asserted-by":"crossref","unstructured":"Howe, M.S. (1998). Acoustics of Fluid-Structure Interactions, Cambridge University Press.","key":"ref_14","DOI":"10.1017\/CBO9780511662898"},{"doi-asserted-by":"crossref","unstructured":"Nakayama, Y. (2018). Introduction to Fluid Mechanics, Butterworth-Heinemann.","key":"ref_15","DOI":"10.1016\/B978-0-08-102437-9.00001-2"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/119\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:28:17Z","timestamp":1759919297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/119"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,14]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["sym17010119"],"URL":"https:\/\/doi.org\/10.3390\/sym17010119","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,1,14]]}}}