{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T20:37:04Z","timestamp":1767904624787,"version":"3.49.0"},"reference-count":51,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T00:00:00Z","timestamp":1689897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Centre, Poland","award":["2021\/40\/Q\/ST8\/00362"],"award-info":[{"award-number":["2021\/40\/Q\/ST8\/00362"]}]},{"name":"National Science Centre, Poland","award":["52161135106"],"award-info":[{"award-number":["52161135106"]}]},{"name":"National Natural Science Foundation of China","award":["2021\/40\/Q\/ST8\/00362"],"award-info":[{"award-number":["2021\/40\/Q\/ST8\/00362"]}]},{"name":"National Natural Science Foundation of China","award":["52161135106"],"award-info":[{"award-number":["52161135106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we compare three energy harvesting systems in which we introduce additional bumpers whose mathematical model is mapped with a non-linear characteristic based on the hyperbolic sine Fibonacci function. For the analysis, we construct non-linear two-well, three-well and four-well systems with a cantilever beam and permanent magnets. In order to compare the effectiveness of the systems, we assume comparable distances between local minima of external wells and the maximum heights of potential barriers. Based on the derived dimensionless models of the systems, we perform simulations of non-linear dynamics in a wide spectrum of frequencies to search for chaotic and periodic motion zones of the systems. We present the issue of the occurrence of transient chaos in the analyzed systems. In the second part of this work, we determine and compare the effectiveness of the tested structures depending on the characteristics of the bumpers and an external excitation whose dynamics are described by the harmonic function, and find the best solutions from the point view of energy harvesting. The most effective impact of the use of bumpers can be observed when dealing with systems described by potential with deep external wells. In addition, the use of the Fibonacci hyperbolic sine is a simple and effective numerical tool for mapping non-linear properties of such motion limiters in energy harvesting systems.<\/jats:p>","DOI":"10.3390\/s23146593","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T03:03:25Z","timestamp":1690167805000},"page":"6593","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Energy Harvesting System Whose Potential Is Mapped with the Modified Fibonacci Function"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2249-4059","authenticated-orcid":false,"given":"Jerzy","family":"Margielewicz","sequence":"first","affiliation":[{"name":"Faculty of Transport and Aviation Engineering, Silesian University of Technology, Krasi\u0144skiego 8, 40-019 Katowice, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2968-1626","authenticated-orcid":false,"given":"Damian","family":"G\u0105ska","sequence":"additional","affiliation":[{"name":"Faculty of Transport and Aviation Engineering, Silesian University of Technology, Krasi\u0144skiego 8, 40-019 Katowice, Poland"}]},{"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, Nadbystrzycka 36, 20-618 Lublin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7546-8703","authenticated-orcid":false,"given":"Jacek","family":"Caban","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4884-5403","authenticated-orcid":false,"given":"Agnieszka","family":"Dudziak","sequence":"additional","affiliation":[{"name":"Faculty of Production Engineering, University of Life Sciences in Lublin, G\u0142\u0119boka 28, 20-612 Lublin, Poland"}]},{"given":"Xiaoqing","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4034-193X","authenticated-orcid":false,"given":"Shengxi","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116886","DOI":"10.1016\/j.jsv.2022.116886","article-title":"Multistable vibration energy harvesters: Principle, progress, and perspectives","volume":"528","author":"Zhou","year":"2022","journal-title":"J. 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