{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T07:30:37Z","timestamp":1788334237041,"version":"build-2803163510"},"reference-count":29,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T00:00:00Z","timestamp":1635465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Founds of China","award":["No.51974228"],"award-info":[{"award-number":["No.51974228"]}]},{"name":"the National Green Manufacturing System Integration Project","award":["No.2017-327"],"award-info":[{"award-number":["No.2017-327"]}]},{"name":"Natural Science Foundation of Shaanxi Province-Coal Joint Fund Project","award":["No. 2021JLM-03"],"award-info":[{"award-number":["No. 2021JLM-03"]}]},{"name":"Key R&amp;D project in Shaanxi","award":["Grant No.2018ZDCXL-GY-06-04"],"award-info":[{"award-number":["Grant No.2018ZDCXL-GY-06-04"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes a parameter identification method for the multiparameter identification study of the linear\u2013arch composite beam piezoelectric energy harvester. According to the voltage response characteristics of the system under short-circuit conditions, the mechanical equation is solved by transient excitation, combined with the backbone curve theory and logarithmic attenuation method, to obtain the system\u2019s linear damping, linear stiffness, and nonlinear stiffness. According to the voltage response characteristics of the system under open-circuit conditions, combined with the electrical equations, the system electromechanical coupling coefficient and equivalent capacitance coefficient are obtained; numerical simulation results show that the identification parameters have good accuracy. Finally, an experimental platform was built for verification, and the results show that the method has high accuracy and practicability.<\/jats:p>","DOI":"10.3390\/s21217213","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T22:24:22Z","timestamp":1635805462000},"page":"7213","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Method for Parameter Identification of Composite Beam Piezoelectric Energy Harvester"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5216-1362","authenticated-orcid":false,"given":"Xuhui","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Shaanxi Key Laboratory of Mine Electromechanical Equipment Intelligent Monitoring, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luyang","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyu","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongmei","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Shaanxi Key Laboratory of Mine Electromechanical Equipment Intelligent Monitoring, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9891-0568","authenticated-orcid":false,"given":"Hongwei","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"},{"name":"Shaanxi Key Laboratory of Mine Electromechanical Equipment Intelligent Monitoring, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fulin","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1016\/j.apenergy.2018.09.082","article-title":"A piezoelectric spring pendulum oscillator used for multi-directional and ultra-low frequency vibration energy harvesting","volume":"231","author":"Wu","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1016\/j.joule.2018.03.011","article-title":"High-Performance Piezoelectric Energy Harvesters and Their Applications","volume":"2","author":"Yang","year":"2018","journal-title":"Joule"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.ijengsci.2018.02.003","article-title":"Ambient vibration energy harvesters: A review on nonlinear techniques for performance enhancement","volume":"127","author":"Tran","year":"2018","journal-title":"Int. J. Eng. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3899","DOI":"10.1109\/TIE.2017.2762640","article-title":"A Comprehensive Analysis and Modeling of the Self-Powered Synchronous Switching Harvesting Circuit With Electronic Breakers","volume":"65","author":"Liu","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1177\/1045389X14544138","article-title":"Strain-based piezoelectric energy harvesting for wireless sensor systems in a tire","volume":"26","author":"Lee","year":"2015","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1109\/TMECH.2015.2459014","article-title":"Toward Harvesting Vibration Energy from Multiple Directions by a Nonlinear Compressive-Mode Piezoelectric Transducer","volume":"21","author":"Yang","year":"2015","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"095019","DOI":"10.1088\/0964-1726\/22\/9\/095019","article-title":"Piezoelectric energy harvesting from traffic-induced bridge vibrations","volume":"22","author":"Peigney","year":"2013","journal-title":"Smart Mater. Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.sna.2018.06.022","article-title":"A multiple energy-harvester combination for pattern-recognizable power-free wireless sensing to vibration event","volume":"279","author":"He","year":"2018","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.physb.2012.10.029","article-title":"Broadband characteristics of vibration energy harvesting using one-dimensional phononic piezoelectric cantilever beams","volume":"410","author":"Chen","year":"2013","journal-title":"Phys. B Condens. Matter"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, X.H., Yang, W.J., Zuo, M., Tan, H., Fan, H., Mao, Q., and Wan, X. (2018). An Arc-shaped Piezoelectric Bistable Vibration Energy Harvester: Modeling and Experiments. Sensors, 18.","DOI":"10.3390\/s18124472"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"012038","DOI":"10.1088\/1757-899X\/531\/1\/012038","article-title":"Dynamics analysis of multi-field coupled piezoelectric energy harvester under random exci-tation","volume":"Volume 531","author":"Zhang","year":"2019","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.ymssp.2018.05.029","article-title":"Modeling of a horizontal asymmetric U-shaped vibration-based piezoelectric energy harvester (U-VPEH)","volume":"114","author":"Sun","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"173903","DOI":"10.1063\/1.4919532","article-title":"Influence of potential well depth on nonlinear tristable energy harvesting","volume":"106","author":"Cao","year":"2015","journal-title":"Appl. Phys. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ymssp.2016.03.015","article-title":"Nonlinear vibrating system identification via Hilbert decomposition","volume":"84","author":"Feldman","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1177\/1077546318777414","article-title":"Nonlinear jump based parameter estimation for both stiffness and damping nonlinearities","volume":"25","author":"Lu","year":"2018","journal-title":"J. Vib. Control."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.cnsns.2017.12.010","article-title":"Nonlinear dynamics of a circular piezoelectric plate for vibratory energy har-vesting","volume":"59","author":"Yuan","year":"2018","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.piutam.2017.08.031","article-title":"Harmonic Balance in the Dynamic Analysis of Circular Composite Plate Harvester","volume":"22","author":"Chen","year":"2017","journal-title":"Procedia IUTAM"},{"key":"ref_18","first-page":"73","article-title":"Restoring force surface method and Hilbert transform one for nonlinear system identification","volume":"38","author":"Chen","year":"2019","journal-title":"J. Vib. Shock."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.apenergy.2014.07.077","article-title":"Broadband tristable energy harvester: Modeling and experiment verification","volume":"133","author":"Zhou","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2495","DOI":"10.1007\/s11071-017-3815-4","article-title":"Nonlinear characteristic of a circular composite plate energy harvester: Experiments and simula-tions","volume":"90","author":"Yuan","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"074903","DOI":"10.1063\/1.3486519","article-title":"Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experi-mental identification","volume":"108","author":"Stanton","year":"2010","journal-title":"J. Appl. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1016\/j.ymssp.2018.10.042","article-title":"Modelling and parameter identification of electromechanical systems for energy harvesting and sensing","volume":"121","author":"Kefal","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1088\/0964-1726\/16\/2\/010","article-title":"Identification of electromechanical modal parameters of linear piezoelectric structures","volume":"16","author":"Porfiri","year":"2007","journal-title":"Smart Mater. Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1177\/1045389X12457253","article-title":"Identification of electromechanical parameters in piezoelectric shunt damping and loss factor prediction","volume":"24","author":"Delpero","year":"2012","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_25","first-page":"102460U","article-title":"Parameter identification from frequency response of MEMS energy harvesters Smart Sensors, Actuators, and MEMS VIII","volume":"10246","author":"Truong","year":"2017","journal-title":"Int. Soc. Opt. Photonics"},{"key":"ref_26","first-page":"87","article-title":"Theoretical modeling and experimental study of a new bistable piezoelectric vibration energy harvesting system","volume":"32","author":"Zhang","year":"2019","journal-title":"J. Vib. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Erturk, A., and Inman, D.J. (2011). Piezoelectric Energy Harvesting, John Wiley & Sons.","DOI":"10.1002\/9781119991151"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, X.H., Zuo, M., Yang, W.J., and Wan, X. (2020). A Tri-Stable Piezoelectric Vibration Energy Harvester for Composite Shape Beam: Nonlinear Modeling and Analysis. Sensors, 20.","DOI":"10.3390\/s20051370"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kovacic, I., and Brennan, M.J. (2011). The Duffing Equation: Nonlinear Oscillators and Their Behaviour, Wiley.","DOI":"10.1002\/9780470977859"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/21\/7213\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:23:07Z","timestamp":1760167387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/21\/7213"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,29]]},"references-count":29,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21217213"],"URL":"https:\/\/doi.org\/10.3390\/s21217213","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,29]]}}}