{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T05:41:02Z","timestamp":1771306862447,"version":"3.50.1"},"reference-count":95,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T00:00:00Z","timestamp":1735257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2021-1350"],"award-info":[{"award-number":["075-15-2021-1350"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["15.SIN.21.0004"],"award-info":[{"award-number":["15.SIN.21.0004"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The solution of the non-linear F\u00f6ppl\u2013von K\u00e1rm\u00e1n equations for square plates in the form of expansion over a system of eigenfunctions, generated by a linear self-adjoint operator, is obtained. The coefficients of the expansion are determined via the reduction method from the infinite-dimensional system of cubic equations. This allows the proposed solution to be considered as a non-linear generalization of the classical Galerkin approach. The novelty of the study is in the strict formulation of the auxiliary boundary problem, which makes it possible to take into account a rigid fixation against any displacements along the boundary. To verify the proposed solution, it is compared with experimental data. The latter is obtained by the holographic interferometry of small deflection increments superimposed on the large deflection caused by initial pressure. Experiment and theory show a good agreement.<\/jats:p>","DOI":"10.3390\/sym17010032","type":"journal-article","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T09:13:32Z","timestamp":1735290812000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Galerkin-Type Solution of the F\u00f6ppl\u2013von K\u00e1rm\u00e1n Equations for Square Plates"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7590-1389","authenticated-orcid":false,"given":"Sergey","family":"Lychev","sequence":"first","affiliation":[{"name":"Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6892-7740","authenticated-orcid":false,"given":"Alexander","family":"Digilov","sequence":"additional","affiliation":[{"name":"Ishlinsky Institute for Problems in Mechanics RAS, 119526 Moscow, Russia"}]},{"given":"Nikolay","family":"Djuzhev","sequence":"additional","affiliation":[{"name":"MEMSEC R&D Center, National Research University of Electronic Technology (MIET), 124498 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"key":"ref_1","unstructured":"F\u00f6ppl, A. 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