{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T22:38:44Z","timestamp":1773873524540,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:00:00Z","timestamp":1669248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Brazilian agencies CAPES","award":["306525\/2015-1"],"award-info":[{"award-number":["306525\/2015-1"]}]},{"name":"Brazilian agencies CAPES","award":["307371\/2017-4"],"award-info":[{"award-number":["307371\/2017-4"]}]},{"name":"Brazilian agencies CAPES","award":["DIALOG 0019\/DLG\/2019\/10"],"award-info":[{"award-number":["DIALOG 0019\/DLG\/2019\/10"]}]},{"name":"Brazilian Council for Scientific and Technological Development, CNPq","award":["306525\/2015-1"],"award-info":[{"award-number":["306525\/2015-1"]}]},{"name":"Brazilian Council for Scientific and Technological Development, CNPq","award":["307371\/2017-4"],"award-info":[{"award-number":["307371\/2017-4"]}]},{"name":"Brazilian Council for Scientific and Technological Development, CNPq","award":["DIALOG 0019\/DLG\/2019\/10"],"award-info":[{"award-number":["DIALOG 0019\/DLG\/2019\/10"]}]},{"name":"program of the Ministry of Science and Higher Education","award":["306525\/2015-1"],"award-info":[{"award-number":["306525\/2015-1"]}]},{"name":"program of the Ministry of Science and Higher Education","award":["307371\/2017-4"],"award-info":[{"award-number":["307371\/2017-4"]}]},{"name":"program of the Ministry of Science and Higher Education","award":["DIALOG 0019\/DLG\/2019\/10"],"award-info":[{"award-number":["DIALOG 0019\/DLG\/2019\/10"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we analyzed the nonlinear fractional dynamics in the equations of motion of a bar coupled to support under the effect of a potential described by two equally spaced magnetic poles. We also considered Bouc\u2013Wen damping in the equations of motion. For external force vibrations, we considered an equation of a non-ideal motor based on the parameters that related the interaction between the oscillation and the excitation source. With such considerations, we explored the influence of the fractional derivative operator parameter on the average power generated by the device and the dynamic behavior to determine the chaotic and periodic regions. We use Bifurcation Diagrams, Test 0\u20131, Phase Portrait, and Poincar\u00e9 Maps. As a conclusion, we established a set of parameters for the fractional differential equations to obtain higher average powers and the periodicity windows that corroborate the establishment of energetic orbits for energy harvesting.<\/jats:p>","DOI":"10.3390\/axioms11120667","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T03:00:13Z","timestamp":1669345213000},"page":"667","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Fractional Dynamical Behavior of an Elastic Magneto Piezo Oscillator Including Non-Ideal Motor Excitation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7314-0723","authenticated-orcid":false,"given":"Mauricio A.","family":"Ribeiro","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Technology\u2014Parana, Ponta Grossa 84017-220, Paran\u00e1, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9796-3609","authenticated-orcid":false,"given":"Jose M.","family":"Balthazar","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Technology\u2014Parana, Ponta Grossa 84017-220, Paran\u00e1, Brazil"},{"name":"Faculty of Mechanical Engineering, S\u00e3o Paulo State University, Bauru 17033-360, S\u00e3o Paulo, Brazil"}]},{"given":"Wagner B.","family":"Lenz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Technology\u2014Parana, Ponta Grossa 84017-220, Paran\u00e1, Brazil"}]},{"given":"Jorge L. P.","family":"Felix","sequence":"additional","affiliation":[{"name":"Department of Environmental Engineering and Sanitary, Universidade Federal da Fronteira Sul. Cerro Largo, S\u00e3o Pedro 89802-112, Rio Grande do Sul, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9647-8345","authenticated-orcid":false,"given":"Grzegorz","family":"Litak","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Lublin University of Technology, 20-618 Lublin, Poland"}]},{"given":"Angelo M.","family":"Tusset","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Technology\u2014Parana, Ponta Grossa 84017-220, Paran\u00e1, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,24]]},"reference":[{"key":"ref_1","unstructured":"Awrejcewicz, J., Ka\u017amierczak, M., Mrozowski, J., and Olejnik, P. 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