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This article, however, presents the results of a study investigating a bimorph magnetostrictive-aluminium beam vibrating in a non-homogeneous bias field. By comparing results obtained under different operating conditions of the system, the combined effect of the non-linear beam stress and the non-homogeneous external magnetic field on the dynamics of the Villari phenomenon is determined. The preliminary results prove that the application of non-linear magnetic fields to the magnetostrictive devices ensures the extension of energy harvesting bandwidth of these devices and can be used to improve their control possibilities. A study of time series and hysteresis loops provides more detailed information about the non-linear magnetization and dynamics of the system.<\/jats:p>","DOI":"10.1177\/0959651818813221","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T06:08:27Z","timestamp":1543385307000},"page":"431-440","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-linear dynamics of the Villari effect in the presence of a non-homogeneous magnetic field"],"prefix":"10.1177","volume":"233","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9631-9785","authenticated-orcid":false,"given":"Andrzej","family":"Rysak","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering, Lublin University of Technology, Lublin, Poland"}]},{"given":"Magdalena","family":"Gregorczyk","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Lublin University of Technology, Lublin, Poland"}]}],"member":"179","published-online":{"date-parts":[[2018,11,28]]},"reference":[{"key":"bibr1-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-87396-6"},{"key":"bibr2-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/0304-8853(86)90066-1"},{"key":"bibr3-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3868-4"},{"issue":"1","key":"bibr4-0959651818813221","first-page":"27","volume":"28","author":"Jiles DC","year":"1992","journal-title":"J Magn Magn Mater"},{"key":"bibr5-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1109\/20.846217"},{"key":"bibr6-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1063\/1.344708"},{"key":"bibr7-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7949(03)00016-6"},{"key":"bibr8-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1088\/0964-1726\/17\/4\/045009"},{"key":"bibr9-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1088\/0960-1317\/22\/9\/094009"},{"key":"bibr10-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1177\/1045389X12436729"},{"key":"bibr11-0959651818813221","first-page":"493","volume-title":"Dynamical systems: theory and applications","author":"Rysak A"},{"key":"bibr12-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1063\/1.372521"},{"key":"bibr13-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2008.10.014"},{"key":"bibr14-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1243\/0954406042690489"},{"key":"bibr15-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/j.sna.2015.10.007"},{"key":"bibr16-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2012.10.029"},{"key":"bibr17-0959651818813221","volume-title":"Nonlinear oscillations","author":"Nayfeh AH","year":"2008"},{"key":"bibr18-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-018-4124-2"},{"key":"bibr19-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2018.01.024"},{"key":"bibr20-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/S0041-624X(99)00061-X"},{"key":"bibr21-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/S0921-4534(01)01198-4"},{"key":"bibr22-0959651818813221","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-8853(01)00199-8"}],"container-title":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651818813221","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0959651818813221","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651818813221","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:37:34Z","timestamp":1777675054000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0959651818813221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,28]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["10.1177\/0959651818813221"],"URL":"https:\/\/doi.org\/10.1177\/0959651818813221","relation":{},"ISSN":["0959-6518","2041-3041"],"issn-type":[{"value":"0959-6518","type":"print"},{"value":"2041-3041","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,28]]}}}