{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T07:36:50Z","timestamp":1777621010598,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T00:00:00Z","timestamp":1676419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"National Science Centre, Poland","doi-asserted-by":"publisher","award":["2021\/40\/Q\/ST8\/00362"],"award-info":[{"award-number":["2021\/40\/Q\/ST8\/00362"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004281","name":"National Science Centre, Poland","doi-asserted-by":"publisher","award":["52161135106"],"award-info":[{"award-number":["52161135106"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021\/40\/Q\/ST8\/00362"],"award-info":[{"award-number":["2021\/40\/Q\/ST8\/00362"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52161135106"],"award-info":[{"award-number":["52161135106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The basic types of multi-stable energy harvesters are bistable energy harvesting systems (BEH) and tristable energy harvesting systems (TEH). The present investigations focus on the analysis of BEH and TEH systems, where the corresponding depth of the potential well and the width of their characteristics are the same. The efficiency of energy harvesting for TEH and BEH systems assuming similar potential parameters is provided. Providing such parameters allows for reliable formulation of conclusions about the efficiency in both types of systems. These energy harvesting systems are based on permanent magnets and a cantilever beam designed to obtain energy from vibrations. Starting from the bond graphs, we derived the nonlinear equations of motion. Then, we followed the bifurcations along the increasing frequency for both configurations. To identify the character of particular solutions, we estimated their corresponding phase portraits, Poincare sections, and Lyapunov exponents. The selected solutions are associated with their voltage output. The results in this numerical study clearly show that the bistable potential is more efficient for energy harvesting provided the corresponding excitation amplitude is large enough. However, the tristable potential could work better in the limits of low-level and low-frequency excitations.<\/jats:p>","DOI":"10.3390\/s23042185","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T05:12:26Z","timestamp":1676437946000},"page":"2185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Double-Versus Triple-Potential Well Energy Harvesters: Dynamics and Power Output"],"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\/0000-0002-7546-8703","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\/0000-0002-9647-8345","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\/0000-0002-4884-5403","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":[[2023,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107890","DOI":"10.1016\/j.ymssp.2021.107890","article-title":"Development and experimental validation of self-powered wireless vibration sensor node using vibration energy harvester","volume":"160","author":"Rubes","year":"2021","journal-title":"Mech. 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