{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:58Z","timestamp":1760241838316,"version":"build-2065373602"},"reference-count":6,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,9,22]],"date-time":"2018-09-22T00:00:00Z","timestamp":1537574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005357","name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","doi-asserted-by":"publisher","award":["APVV-14-0378"],"award-info":[{"award-number":["APVV-14-0378"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Slovak Grant Agency VEGA","award":["2\/0153\/16 and 1\/0078\/17"],"award-info":[{"award-number":["2\/0153\/16 and 1\/0078\/17"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced system.<\/jats:p>","DOI":"10.3390\/axioms7040069","type":"journal-article","created":{"date-parts":[[2018,9,24]],"date-time":"2018-09-24T10:38:49Z","timestamp":1537785529000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Periodically Forced Nonlinear Oscillatory Acoustic Vacuum"],"prefix":"10.3390","volume":"7","author":[{"given":"Makrina","family":"Agaoglou","sequence":"first","affiliation":[{"name":"Mathematical Institute of Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"},{"name":"Department of Mechanical Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7385-6737","authenticated-orcid":false,"given":"Michal","family":"Fe\u010dkan","sequence":"additional","affiliation":[{"name":"Mathematical Institute of Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"},{"name":"Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynsk\u00e1 dolina, 842 48 Bratislava, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1071-3077","authenticated-orcid":false,"given":"Michal","family":"Posp\u00ed\u0161il","sequence":"additional","affiliation":[{"name":"Mathematical Institute of Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"},{"name":"Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynsk\u00e1 dolina, 842 48 Bratislava, Slovakia"}]},{"given":"Vassilis M.","family":"Rothos","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3919-432X","authenticated-orcid":false,"given":"Alexander F.","family":"Vakakis","sequence":"additional","affiliation":[{"name":"Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1137\/140957949","article-title":"Nonlinear oscillatory acoustic vacuum","volume":"74","author":"Manevich","year":"2014","journal-title":"SIAM J. Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmps.2017.09.007","article-title":"Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane","volume":"110","author":"Zhang","year":"2018","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1137\/0518046","article-title":"Periodic orbits in slowly varying oscillators","volume":"18","author":"Wiggins","year":"1987","journal-title":"SIAM J. Math. Anal."},{"key":"ref_4","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2007). Table of Integrals, Series, and Products, Academic Press. [7th ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Fe\u010dkan, M. (2008). Topological Degree Approach to Bifurcation Problems, Springer.","DOI":"10.1007\/978-1-4020-8724-0"},{"key":"ref_6","unstructured":"Hale, J.K. (1980). Ordinary Differential Equations, Robert E. Krieger Publishing Company, Inc.. [2nd ed.]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/4\/69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:22:04Z","timestamp":1760196124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/4\/69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,22]]},"references-count":6,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["axioms7040069"],"URL":"https:\/\/doi.org\/10.3390\/axioms7040069","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2018,9,22]]}}}