{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T04:59:13Z","timestamp":1785473953387,"version":"3.56.0"},"reference-count":72,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"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":"crossref","award":["52375110"],"award-info":[{"award-number":["52375110"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12372055"],"award-info":[{"award-number":["12372055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["52375110"],"award-info":[{"award-number":["52375110"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["12372055"],"award-info":[{"award-number":["12372055"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Multistable energy harvesters have attracted considerable attention due to their shallow potential wells, which facilitate low-energy inter-well oscillations. Although bistable or tristable configurations can be realized using combined magnets or springs, two critical challenges remain: (i) the difficulty in obtaining a higher number of stable equilibrium points and (ii) the inability to arbitrarily prescribe the coordinates of these equilibrium points. To address these issues, this paper proposes a piezoelectric cantilever beam-based multistable energy harvester that allows programmable specification of both the number and the positions of equilibrium points. As demonstrations, a tristable and a pentastable energy harvester with user-defined equilibrium coordinates are designed, and their energy harvesting performances are systematically investigated. Simulation and experimental results show that under an excitation acceleration of 0.1 g, both harvesters can only perform intra-well motion, exhibiting softening nonlinearity. When the excitation acceleration increases to 0.2 g, the pentastable harvester successfully overcomes the maximum potential barrier to achieve inter-well oscillation, displaying hardening nonlinearity and significantly broadening the operational bandwidth, while the tristable harvester remains confined to intra-well motion. At an excitation acceleration of 0.4 g, both harvesters can achieve inter-well oscillation, but the pentastable harvester possesses a wider operational bandwidth and a lower starting frequency for energy harvesting. The proposed method enables the design of multistable vibration energy harvesters without increasing structural complexity with the number of equilibrium points, which is of great significance for optimizing multistable vibration energy harvesters.<\/jats:p>","DOI":"10.3390\/s26154812","type":"journal-article","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T08:16:52Z","timestamp":1785313012000},"page":"4812","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Design of a Multistable Cantilever Piezoelectric Vibration Energy Harvester with Nonlinear Force Customization"],"prefix":"10.3390","volume":"26","author":[{"given":"Erfang","family":"Luo","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Shanghai Minhang Polytechnic, Shanghai 201111, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fazhi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Shanghai Minhang Polytechnic, Shanghai 201111, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaolei","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Shanghai Minhang Polytechnic, Shanghai 201111, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoqing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Shanghai Minhang Polytechnic, Shanghai 201111, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhushi","family":"Rao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donglin","family":"Zou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120388","DOI":"10.1016\/j.measurement.2026.120388","article-title":"Two piezoelectric simply supported beams with T-mass collision for broadband vibration energy harvesting","volume":"266","author":"Wang","year":"2026","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"524785","DOI":"10.1007\/s10409-025-24785-x","article-title":"Transient responses of a nonlinear main structure coupled with two-degree-of-freedom nonlinear energy sink and piezoelectric energy harvester","volume":"42","author":"Nie","year":"2026","journal-title":"Acta Mech. 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