{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T13:49:17Z","timestamp":1768744157383,"version":"3.49.0"},"reference-count":75,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,9]],"date-time":"2018-05-09T00:00:00Z","timestamp":1525824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51575426"],"award-info":[{"award-number":["51575426"]}],"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":["51421004"],"award-info":[{"award-number":["51421004"]}],"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":["11602223"],"award-info":[{"award-number":["11602223"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff\u2019s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.<\/jats:p>","DOI":"10.3390\/s18051492","type":"journal-article","created":{"date-parts":[[2018,5,10]],"date-time":"2018-05-10T03:48:27Z","timestamp":1525924107000},"page":"1492","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis"],"prefix":"10.3390","volume":"18","author":[{"given":"Shengxi","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Yan","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering &amp; Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6195-1334","authenticated-orcid":false,"given":"Daniel J.","family":"Inman","sequence":"additional","affiliation":[{"name":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1088\/0964-1726\/13\/5\/018","article-title":"A piezoelectric vibration based generator for wireless electronics","volume":"13","author":"Roundy","year":"2004","journal-title":"Smart Mater. 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