{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T23:30:06Z","timestamp":1786577406991,"version":"build-2736575974"},"reference-count":55,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.cnsns.2026.110574","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T15:41:37Z","timestamp":1784216497000},"page":"110574","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P2","title":["Nonlinear dynamics of a double-pendulum energy harvester under low-frequency excitation: Theoretical modeling and numerical study"],"prefix":"10.1016","volume":"163","author":[{"given":"Ziyu","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fang","family":"Deng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7557-3853","authenticated-orcid":false,"given":"Hailing","family":"Fu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.cnsns.2026.110574_bib0001","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1109\/SURV.2012.110112.00192","article-title":"A survey on human activity recognition using wearable sensors","volume":"15","author":"Lara","year":"2013","journal-title":"IEEE Commun Surv Tutor"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110574_bib0002","doi-asserted-by":"crossref","DOI":"10.1016\/j.joule.2021.03.006","article-title":"Rotational energy harvesting for self-powered sensing","volume":"5","author":"Fu","year":"2021","journal-title":"Joule"},{"key":"10.1016\/j.cnsns.2026.110574_bib0003","unstructured":"Mathie M.. Monitoring and interpreting human movement patterns using a triaxial accelerometer2003."},{"issue":"9","key":"10.1016\/j.cnsns.2026.110574_bib0004","article-title":"Human-motion adaptability enhancement of wearable electromagnetic vibration energy harvesters toward self-sustained body sensor networks","volume":"5","author":"Cao","year":"2024","journal-title":"Cell Rep Phys Sci"},{"issue":"10","key":"10.1016\/j.cnsns.2026.110574_bib0005","doi-asserted-by":"crossref","first-page":"12237","DOI":"10.1109\/TPEL.2022.3164890","article-title":"Powering solutions for biomedical sensors and implants inside the human body: a comprehensive review on energy harvesting units, energy storage, and wireless power transfer techniques","volume":"37","author":"Roy","year":"2022","journal-title":"IEEE Trans Power Electron"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110574_bib0006","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1109\/COMST.2017.2731979","article-title":"A survey of wearable devices and challenges","volume":"19","author":"Seneviratne","year":"2017","journal-title":"IEEE Commun Surv Tutor"},{"key":"10.1016\/j.cnsns.2026.110574_bib0007","series-title":"Wearable monitoring systems","first-page":"27","article-title":"Energy harvesting for self-powered wearable devices","author":"Leonov","year":"2010"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0008","article-title":"Design and optimization of a low power pressure sensor for wireless biomedical applications","volume":"2015","author":"Sosa","year":"2015","journal-title":"J Sens"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0009","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1109\/JSSC.2011.2170633","article-title":"A 3-\u03bcw CMOS glucose sensor for wireless contact-lens tear glucose monitoring","volume":"47","author":"Liao","year":"2012","journal-title":"IEEE J Solid State Circuits"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110574_bib0010","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MIM.2009.4811133","article-title":"Energy management in wireless sensor networks with energy-hungry sensors","volume":"12","author":"Alippi","year":"2009","journal-title":"IEEE Instrum Meas Mag"},{"key":"10.1016\/j.cnsns.2026.110574_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.nanoen.2025.111317","article-title":"Mimosa-inspired tribo-electromagnetic nanogenerator for adaptive wind energy harvesting and intelligent wind monitoring","volume":"143","author":"Liao","year":"2025","journal-title":"Nano Energy"},{"key":"10.1016\/j.cnsns.2026.110574_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijmecsci.2024.109523","article-title":"Jellyfish-inspired bistable piezoelectric-triboelectric hybrid generator for low-frequency vibration energy harvesting","volume":"279","author":"Cui","year":"2024","journal-title":"Int J Mech Sci"},{"key":"10.1016\/j.cnsns.2026.110574_bib0013","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2024.111854","article-title":"Bio-inspired vibration isolator with triboelectric nanogenerator for self-powered monitoring","volume":"223","author":"Yang","year":"2025","journal-title":"Mech Syst Signal Process"},{"issue":"21","key":"10.1016\/j.cnsns.2026.110574_bib0014","doi-asserted-by":"crossref","first-page":"18665","DOI":"10.1007\/s11071-024-10040-z","article-title":"Pendulum-based hybrid system for multidirectional energy harvesting","volume":"112","author":"Costa","year":"2024","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110574_bib0015","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1016\/j.apm.2023.03.027","article-title":"Exploring nonlinear degradation benefit of bio-inspired oscillator for engineering applications","volume":"119","author":"Yang","year":"2023","journal-title":"Appl Math Model"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110574_bib0016","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1177\/1045389X20905989","article-title":"Review of nonlinear vibration energy harvesting: duffing, bistability, parametric, stochastic and others","volume":"31","author":"Jia","year":"2020","journal-title":"J Intell Mater Syst Struct"},{"key":"10.1016\/j.cnsns.2026.110574_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2025.112730","article-title":"A multidirectional broadband pendulum piezoelectric vibration energy harvester utilizing magnetic potential well","volume":"232","author":"Yu","year":"2025","journal-title":"Mech Syst Signal Process"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0018","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s11071-021-06611-z","article-title":"Energy harvesting in a nonlinear energy sink absorber using delayed resonators","volume":"105","author":"Karama","year":"2021","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110574_bib0019","doi-asserted-by":"crossref","first-page":"3119","DOI":"10.1007\/s11071-024-10392-6","article-title":"Dual-source energy harvester for collecting both flow-induced and multi-directional vibratory energies","volume":"113","author":"Chen","year":"2024","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110574_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2024.108520","article-title":"Prediction of the flutter envelope and parametric analysis of a flutter-based aeroelastic piezoelectric energy harvester","volume":"142","author":"Hao","year":"2025","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110574_bib0021","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2024.108354","article-title":"Modeling and theoretical analysis of a stochastic novel vibro-impact galloping energy harvester with a u-shaped base","volume":"140","author":"Deng","year":"2025","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110574_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2024.108433","article-title":"A new analysis framework for solving multiple frequencies and solutions of nonlinear piezoelectric energy harvesters","volume":"140","author":"Yang","year":"2025","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0023","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/S0921-4526(00)00804-8","article-title":"Analytic conditions for targeted energy transfer between nonlinear oscillators or discrete breathers","volume":"296","author":"Aubry","year":"2001","journal-title":"Phys B Condens Matter"},{"issue":"8","key":"10.1016\/j.cnsns.2026.110574_bib0024","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1016\/j.cnsns.2013.12.018","article-title":"Frequency\u2013energy plots of steady-state solutions for forced and damped systems, and vibration isolation by nonlinear mode localization","volume":"19","author":"Kurt","year":"2014","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110574_bib0025","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/S0020-7462(01)00137-8","article-title":"Dual mode vibration isolation based on non-linear mode localization","volume":"38","author":"Jiang","year":"2003","journal-title":"Int J Non Linear Mech"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0026","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1023\/A:1012994430793","article-title":"The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables","volume":"25","author":"Manevitch","year":"2001","journal-title":"Nonlinear Dyn"},{"issue":"1-2","key":"10.1016\/j.cnsns.2026.110574_bib0027","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1177\/107754603030742","article-title":"Shock isolation through the use of nonlinear energy sinks","volume":"9","author":"Vakakis","year":"2003","journal-title":"J Vib Control"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0028","first-page":"1","article-title":"Ultra-low frequency energy harvesting using bi-stability and rotary-translational motion in a magnet-tethered oscillator","author":"Fu","year":"2020","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110574_bib0029","article-title":"An electromagnetic rotational energy harvester using sprung eccentric rotor, driven by pseudo-walking motion","author":"Halim","year":"2018","journal-title":"Appl Energy Barking Then Oxf"},{"key":"10.1016\/j.cnsns.2026.110574_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2022.107027","article-title":"Bifurcation analysis and nonlinear dynamics of a rolling magnet multistable electromagnetic energy harvester","volume":"118","author":"Wang","year":"2023","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"8","key":"10.1016\/j.cnsns.2026.110574_bib0031","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1177\/1045389X12441510","article-title":"Natural frequency self-tuning energy harvester using a circular halbach array magnetic disk","volume":"23","author":"Wang","year":"2012","journal-title":"J Intell Mater Syst Struct"},{"issue":"8-1","key":"10.1016\/j.cnsns.2026.110574_bib0032","article-title":"High-power density inertial energy harvester without additional proof mass for wearables","author":"Cai","year":"2021","journal-title":"IEEE Internet Things J"},{"key":"10.1016\/j.cnsns.2026.110574_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2020.107251","article-title":"Enhanced electromagnetic wrist-worn energy harvester using repulsive magnetic spring","volume":"150","author":"Cai","year":"2021","journal-title":"Mech Syst Signal Process"},{"issue":"23","key":"10.1016\/j.cnsns.2026.110574_bib0034","doi-asserted-by":"crossref","DOI":"10.1002\/aenm.202000886","article-title":"Robust triboelectric nanogenerator achieved by centrifugal force induced automatic working mode transition","volume":"10","author":"Chen","year":"2020","journal-title":"Adv Energy Mater"},{"key":"10.1016\/j.cnsns.2026.110574_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.enconman.2019.112166","article-title":"Magnetic coupling and flextensional amplification mechanisms for high-robustness ambient wind energy harvesting","volume":"201","author":"Zhao","year":"2019","journal-title":"Energy Convers Manag"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110574_bib0036","doi-asserted-by":"crossref","DOI":"10.1063\/1.5140060","article-title":"Exploiting the advantages of the centrifugal softening effect in rotational impact energy harvesting","volume":"116","author":"Fang","year":"2020","journal-title":"Appl Phys Lett"},{"key":"10.1016\/j.cnsns.2026.110574_bib0037","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.sna.2013.10.003","article-title":"A piezoelectric frequency up-converting energy harvester with rotating proof mass for human body applications","volume":"206","author":"Andrew","year":"2014","journal-title":"Sens Actuators Phys"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0038","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TMECH.2024.3413086","article-title":"Toward high-performance wrist-worn energy harvester via hybrid approach","volume":"30","author":"Cai","year":"2024","journal-title":"IEEE ASME Trans Mechatron"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110574_bib0039","doi-asserted-by":"crossref","DOI":"10.1088\/1361-665X\/ab1598","article-title":"Design of a disk-swing driven piezoelectric energy harvester for slow rotary system application","volume":"28","author":"Nezami","year":"2019","journal-title":"Smart Mater Struct"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110574_bib0040","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1109\/TMECH.2012.2205266","article-title":"A piezoelectric energy harvester for rotary motion applications: design and experiments","volume":"18","author":"Khameneifar","year":"2013","journal-title":"IEEE ASME Trans Mechatron"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0041","doi-asserted-by":"crossref","first-page":"011005.1","DOI":"10.1115\/1.4002789","article-title":"Modeling and analysis of a piezoelectric energy scavenger for rotary motion applications","volume":"133","author":"Khameneifar","year":"2011","journal-title":"J Vib Acoust"},{"key":"10.1016\/j.cnsns.2026.110574_bib0042","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.sna.2016.02.004","article-title":"An vibration energy harvester with broadband and frequency-doubling characteristics based on rotary pendulums","volume":"241","author":"Dai","year":"2016","journal-title":"Sens Actuators a: Phys"},{"key":"10.1016\/j.cnsns.2026.110574_bib0043","doi-asserted-by":"crossref","DOI":"10.1016\/j.enconman.2021.114465","article-title":"Interplay between internal resonance and nonlinear magnetic interaction for multi-directional energy harvesting","volume":"244","author":"Bao","year":"2021","journal-title":"Energy Convers Manag"},{"key":"10.1016\/j.cnsns.2026.110574_bib0044","doi-asserted-by":"crossref","DOI":"10.1016\/j.enconman.2022.116155","article-title":"Piezoelectric energy harvester featuring a magnetic chaotic pendulum","volume":"269","author":"Chen","year":"2022","journal-title":"Energy Convers Manag"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110574_bib0045","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1016\/S0960-0779(04)00430-8","article-title":"Rotating orbits of a parametrically-excited pendulum","volume":"23","author":"Xu","year":"2005","journal-title":"Chaos Solit Fractals"},{"key":"10.1016\/j.cnsns.2026.110574_bib0046","doi-asserted-by":"crossref","DOI":"10.15632\/jtam-pl.54.3.717","article-title":"Rotating orbits of pendulum in stochastic excitation","author":"Teh","year":"2016","journal-title":"J Theor Appl Mech"},{"key":"10.1016\/j.cnsns.2026.110574_bib0047","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.ymssp.2019.01.037","article-title":"Energy harvesting from chaos in base excited double pendulum","volume":"124","author":"Kumar","year":"2019","journal-title":"Mech Syst Signal Process"},{"key":"10.1016\/j.cnsns.2026.110574_bib0048","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2022.109415","article-title":"Pendulum-based embedded energy harvester for rotating systems","volume":"180","author":"Zaouali","year":"2022","journal-title":"Mech Syst Signal Process"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0049","first-page":"8","article-title":"Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry","volume":"59","author":"Camacho","year":"2013","journal-title":"Rev Mex Fis Publ Ensen Hist Filos Soc Mex Fis"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110574_bib0050","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1007\/s11071-020-05697-1","article-title":"Is it really chaos? the complexity of transient dynamics of double pendula","volume":"102","author":"Dudkowski","year":"2020","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.110574_bib0051","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.115694","article-title":"A novel global perspective: characterizing the fractal basins of attraction and the level of chaos in a double pendulum","volume":"189","author":"Qin","year":"2024","journal-title":"Chaos Solit Fractals"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110574_bib0052","doi-asserted-by":"crossref","DOI":"10.1155\/2014\/892793","article-title":"Bifurcations of oscillatory and rotational solutions of double pendulum with parametric vertical excitation","volume":"2014","author":"Marszal","year":"2014","journal-title":"Math Probl Eng"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110574_bib0053","doi-asserted-by":"crossref","DOI":"10.1063\/1.5098962","article-title":"Macro fiber composite-based energy harvester for human knee","volume":"115","author":"Gao","year":"2019","journal-title":"Appl Phys Lett"},{"key":"10.1016\/j.cnsns.2026.110574_bib0054","doi-asserted-by":"crossref","DOI":"10.1016\/j.sna.2021.112650","article-title":"Double helix triboelectric nanogenerator for self-powered weight sensors","volume":"323","author":"Fu","year":"2021","journal-title":"Sens Actuators A Phys"},{"key":"10.1016\/j.cnsns.2026.110574_bib0055","doi-asserted-by":"crossref","DOI":"10.1016\/j.ijmecsci.2024.109029","article-title":"Low-frequency human motion energy scavenging with wearable tumbler-inspired electromagnetic energy harvesters","volume":"268","author":"Pan","year":"2024","journal-title":"Int J Mech Sci"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426009287?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426009287?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T23:25:30Z","timestamp":1786577130000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426009287"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":55,"alternative-id":["S1007570426009287"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110574","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Nonlinear dynamics of a double-pendulum energy harvester under low-frequency excitation: Theoretical modeling and numerical study","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110574","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110574"}}