{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:06:39Z","timestamp":1753880799875,"version":"3.41.2"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2018\/29\/B\/ST8\/02207"],"award-info":[{"award-number":["2018\/29\/B\/ST8\/02207"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p> These studies focus on the forced vibrations of rectangular plates incorporating oscillating inclusions uniformly distributed in the carrier elastic medium. Plate\u2019s equations of motion consist of the Lam\u00e9 equation for a carrier material and the equation for oscillators representing the inclusions. The oscillators are acted upon by the nonlinear friction force, described by Coulomb\u2019s modified law, and a cubically nonlinear elastic force. The simply supported forced plate is considered. Using the Galerkin approximation, the problem of plate vibrations is reduced to the study of a system of ODEs. According to numerical and qualitative analyses, the application of harmonic forcing causes the appearance of periodic, quasiperiodic, and chaotic regimes in the system. In particular, the analytical expression is derived for the periodic regimes of the forcing frequency. The scenarios of vibration\u2019s development is identified at the variation of forcing amplitude. The quasiperiodic and chaotic modes are studied by means of Poincar\u00e9 section technique, and Fourier and Lyapunov spectra analyses. The statistical properties of the sequences of temporal intervals between maxima of system\u2019s solutions are considered in more detail. The sequence extracted from the chaotic trajectory is shown to possess long-term correlations and approximately obeys the Weibull distribution. <\/jats:p>","DOI":"10.1142\/s0218127422500158","type":"journal-article","created":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T10:36:43Z","timestamp":1645612603000},"source":"Crossref","is-referenced-by-count":3,"title":["Nonlinear Forced Vibrations of Plates with Oscillating Inclusions"],"prefix":"10.1142","volume":"32","author":[{"given":"A.","family":"Gawlik","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, AGH University of Science and Technology, Mickiewicz Avenue 30, Krakow 30-059, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"Vladimirov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, AGH University of Science and Technology, Mickiewicz Avenue 30, Krakow 30-059, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4944-2646","authenticated-orcid":false,"given":"S.","family":"Skurativskyi","sequence":"additional","affiliation":[{"name":"Subbotin Institute of Geophysics, National Academy of Sciences of Ukraine, Palladin Avenue 32, Kyiv 03142, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Klepka","sequence":"additional","affiliation":[{"name":"Department of Robotics and Mechatronics, AGH University of Science and Technology, Mickiewicz Avenue 30, Krakow 30-059, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,2,22]]},"reference":[{"key":"S0218127422500158BIB001","first-page":"113","volume":"23","author":"Andrianov I.","year":"1987","journal-title":"Prikladnaia Mekhanika"},{"key":"S0218127422500158BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2017.02.007"},{"key":"S0218127422500158BIB003","doi-asserted-by":"publisher","DOI":"10.1115\/1.2048687"},{"volume-title":"Mathematical Modeling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields","year":"2021","author":"Awrejcewicz J.","key":"S0218127422500158BIB004"},{"key":"S0218127422500158BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2020.106734"},{"volume-title":"Order Within Chaos","year":"1991","author":"Berg\u00e9 P.","key":"S0218127422500158BIB006"},{"key":"S0218127422500158BIB007","doi-asserted-by":"publisher","DOI":"10.1134\/S1560354711010060"},{"key":"S0218127422500158BIB008","doi-asserted-by":"publisher","DOI":"10.1002\/9783527626359.ch4"},{"key":"S0218127422500158BIB009","doi-asserted-by":"publisher","DOI":"10.1121\/1.1642619"},{"key":"S0218127422500158BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-460X(02)00921-5"},{"volume-title":"Self-Organization in Nonlocal Non-Equilibrium Media","year":"2011","author":"Danylenko V.","key":"S0218127422500158BIB011"},{"key":"S0218127422500158BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2016.04.010"},{"key":"S0218127422500158BIB013","first-page":"425","volume":"6","author":"Danylenko V.","year":"2017","journal-title":"Discont. 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