{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:36Z","timestamp":1760144016248,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"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":["12302016"],"award-info":[{"award-number":["12302016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bifurcation topology transfer phenomena in the presence of mode localization are investigated using double-ended fixed electrostatically coupled tuning fork resonators. An analytical model is proposed for the coupled tuning fork resonators, and the effects of feedthrough capacitance on the structure are also analyzed and eliminated by means of data post-processing. Then, an open-loop experimental platform is established, when the system is in balance state, the quality factor is obtained under test as Q = 9858, and comparison of the experiment with numerical simulation results is in good agreement. Finally, with the voltage increases, the two resonators gradually exhibit nonlinear characteristics. It is worth noting that when one of the coupled resonators exhibits nonlinear vibration behavior, even though the vibration amplitude of the other resonator is lower than the critical amplitude, it still exhibits nonlinear behavior, and the results confirm the existence of the bifurcation topology transfer phenomenon in coupled resonators\u2019 mode localization phenomenon.<\/jats:p>","DOI":"10.3390\/s24051563","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T10:37:36Z","timestamp":1709116656000},"page":"1563","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Experimental Investigation of Mode Localization\u2019s Bifurcation Topology Transfer in Electrostatically Coupled Tuning Fork Resonators"],"prefix":"10.3390","volume":"24","author":[{"given":"Ming","family":"Lyu","sequence":"first","affiliation":[{"name":"Institute of Transportation, Inner Mongolia University, Hohhot 010021, China"},{"name":"Inner Mongolia Engineering Research Center for Intelligent Transportation Equipment, Hohhot 010021, China"}]},{"given":"Xiang","family":"Zhi","sequence":"additional","affiliation":[{"name":"Institute of Transportation, Inner Mongolia University, Hohhot 010021, China"},{"name":"Inner Mongolia Engineering Research Center for Intelligent Transportation Equipment, Hohhot 010021, China"}]},{"given":"Na","family":"Yan","sequence":"additional","affiliation":[{"name":"Institute of Transportation, Inner Mongolia University, Hohhot 010021, China"},{"name":"Inner Mongolia Engineering Research Center for Intelligent Transportation Equipment, Hohhot 010021, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6305-806X","authenticated-orcid":false,"given":"Rongjian","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Guo, M.L., Fang, J.W., Chen, J.F., Li, B.L., Chen, H., Zhou, Q., Wang, Y., Song, H.Z., Arutyunov, K.Y., and Guo, G.C. (2023). Mode Coupling in Electromechanical Systems: Recent Advances and Applications. Adv. Electron. Mater., 9.","DOI":"10.1002\/aelm.202201305"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Asadi, K., Yu, J., and Cho, H. (2018). Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: Intermodal coupling, internal resonance and synchronization. Philos. Trans. A Math. Phys. Eng. Sci., 376.","DOI":"10.1098\/rsta.2017.0141"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Xia, C., Wang, D.F., Ono, T., Itoh, T., and Maeda, R. (2020). A mass multi-warning scheme based on one-to-three internal resonance. Mech. Syst. Sig. Process., 142.","DOI":"10.1016\/j.ymssp.2020.106784"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rabenimanana, T., Walter, V., Kacem, N., Le Moal, P., Bourbon, G., and Lardi\u00e8s, J. (2020). Functionalization of electrostatic nonlinearities to overcome mode aliasing limitations in the sensitivity of mass microsensors based on energy localization. Appl. Phys. Lett., 117.","DOI":"10.1063\/5.0007446"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rabenimanana, T.H., Walter, V., Kacem, N., Le Moal, P., Bourbon, G., and Lardies, J. (2021). Enhancing the linear dynamic range of a mode-localized MEMS mass sensor with repulsive electrostatic actuation. Smart Mater. Struct., 30.","DOI":"10.1088\/1361-665X\/ac075b"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Lyu, M., Zhao, J., Kacem, N., Tang, B., Liu, P., Song, J., Zhong, H., and Huang, Y. (2021). Design and modeling of a MEMS accelerometer based on coupled mode-localized nonlinear resonators under electrostatic actuation. Commun. Nonlinear Sci. Numer. Simul., 103.","DOI":"10.1016\/j.cnsns.2021.105960"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wang, C., Chen, F., Wang, Y., Sadeghpour, S., Wang, C., Baijot, M., Esteves, R., Zhao, C., Bai, J., and Liu, H. (2020). Micromachined Accelerometers with Sub-\u00b5g\/\u221aHz Noise Floor: A Review. Sensors, 20.","DOI":"10.3390\/s20144054"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Thiruvenkatanathan, P., Yan, J., and Seshia, A.A. (2010, January 1\u20134). Ultrasensitive Mode-Localized Micromechanical Electrometer. Proceedings of the Frequency Control Symposium(FCS), Newport Beach, CA, USA.","DOI":"10.1109\/FREQ.2010.5556368"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.ijmecsci.2016.11.030","article-title":"Investigation of modal interactions and their effects on the nonlinear dynamics of a periodic coupled pendulums chain","volume":"127","author":"Bitar","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.ijnonlinmec.2018.12.008","article-title":"Nonlinear dynamics and parameter identification of electrostatically coupled resonators","volume":"110","author":"Li","year":"2019","journal-title":"Int. J. Non Linear Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s11071-022-07227-7","article-title":"Dynamical analysis and chaos control of MEMS resonators by using the analog circuit","volume":"108","author":"Luo","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, X., Yang, Q., Huan, R., Shi, Z., Zhu, W., Jiang, Z., Deng, Z., and Wei, X. (2022). Frequency comb in 1:3 internal resonance of coupled micromechanical resonators. Appl. Phys. Lett., 120.","DOI":"10.1063\/5.0091237"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"14739","DOI":"10.1109\/JSEN.2021.3072416","article-title":"Oscillatory Airflow Sensing Employing MEMS Weakly Coupled Resonators","volume":"21","author":"Guo","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Guo, X., Yang, B., Li, C., and Liang, Z. (2021). Enhancing output linearity of weakly coupled resonators by simple algebraic operations. Sens. Actuators A, 325.","DOI":"10.1016\/j.sna.2021.112696"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4325","DOI":"10.1109\/JSEN.2020.3032470","article-title":"A Micromechanical Mode-Localized Voltmeter","volume":"21","author":"Hao","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yang, J., Kang, H., and Chang, H. (2018, January 21\u201325). A micro resonant electrometer with 9-electron charge resolution in room temperature. Proceedings of the 2018 IEEE Micro Electro Mechanical Systems (MEMS), Belfast, UK.","DOI":"10.1109\/MEMSYS.2018.8346484"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, H., Zhang, Z., Zu, L., Hao, Y., and Chang, H. (2022). Micromechanical mode-localized electric current sensor. Microsyst. Nanoeng., 8.","DOI":"10.1038\/s41378-022-00375-1"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6081","DOI":"10.1109\/JSEN.2015.2453401","article-title":"Influences of the Feedthrough Capacitance on the Frequency Synchronization of the Weakly Coupled Resonators","volume":"15","author":"Zhang","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bitar, D., Kacem, N., and Bouhaddi, N. (2017, January 6\u20139). Multistability and Bifurcation Topology in Electrostatically Coupled Nanobeams Under Parametric Resonance. Proceedings of the ASME 2017 International Design Engineering Technical Conferences & Computers & Information in Engineering Conference, Cleveland, OH, USA.","DOI":"10.1115\/DETC2017-67588"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Belhaq, M., Souayeh, S., and Kacem, N. (2014, January 19\u201321). Bifurcation topology transfer in nonlinear nanocantilever arrays subject to parametric and internal resonances. Proceedings of the International Conference on Structural Nonlinear Dynamics & Diagnosis, EDP Sciences, Agadir, Morocco.","DOI":"10.1051\/matecconf\/20141604004"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kacem, N., Hentz, S., Pinto, D., Reig, B., and Nguyen, V. (2009). Nonlinear dynamics of nanomechanical beam resonators: Improving the performance of NEMS-based sensors. Nanotechnology, 20.","DOI":"10.1088\/0957-4484\/20\/27\/275501"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1563\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:06:38Z","timestamp":1760105198000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1563"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,28]]},"references-count":21,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24051563"],"URL":"https:\/\/doi.org\/10.3390\/s24051563","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,2,28]]}}}