{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:47:26Z","timestamp":1740149246030,"version":"3.37.3"},"reference-count":22,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,9,7]],"date-time":"2016-09-07T00:00:00Z","timestamp":1473206400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Defense Preliminary Research Project"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"This paper presents analytical models, as well as numerical and experimental verification of intrinsic dissipation due to thermoelastic loss in tuning-fork resonator. The thermoelastic analytical governing equations are created for resonator vibrating at drive-mode and sense-mode, and thermoelastic vibration field quantities are deduced. Moreover, the theoretical values are verified that coincided well with finite element analysis (FEM) simulation results. Also, the comparison of vibration field quantities is made to investigate the effect of different conditions on resonator thermoelastic vibration behavior. The significant parameters of thermoelastic damping and quality factor are subsequently deduced to analyze the energy dissipation situation in the vibration process. Meanwhile, the corresponding conclusions from other studies are used to verify our theoretical model and numerical results. By comparing with the experimental quality factor, the numerical values are validated. The combination of the theoretical expressions, numerical results and experimental data leads to an important insight into the achievable quality factor value of tuning-fork resonator, namely, that the thermoelastic damping is the main loss mechanism in the micro-comb finger structure and the quality factor varies under different vibration modes. The results demonstrate that the critical geometry dimensions of tuning-fork resonator can be well designed with the assistance of this study.<\/jats:p>","DOI":"10.3390\/s16091445","type":"journal-article","created":{"date-parts":[[2016,9,7]],"date-time":"2016-09-07T13:59:46Z","timestamp":1473256786000},"page":"1445","source":"Crossref","is-referenced-by-count":2,"title":["Study of Intrinsic Dissipation Due to Thermoelastic Coupling in Gyroscope Resonators"],"prefix":"10.3390","volume":"16","author":[{"given":"Changlong","family":"Li","sequence":"first","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Shiqiao","family":"Gao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Shaohua","family":"Niu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Haipeng","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.sna.2012.05.014","article-title":"Novel piezoresistive high-g accelerometer geometry with very high sensitivity-bandwidth product","volume":"182","author":"Kuells","year":"2012","journal-title":"Sens. Actuators A Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10146","DOI":"10.3390\/s150510146","article-title":"A new MEMS gyroscope used for single-channel damping","volume":"15","author":"Zhang","year":"2015","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19633","DOI":"10.3390\/s150819633","article-title":"Study on Pyroelectric Harvesters with Various Geometry","volume":"15","author":"Siao","year":"2015","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1016\/j.jsv.2008.12.005","article-title":"A thermal-energy method for calculating thermoelastic damping in micromechanical resonators","volume":"322","author":"Hao","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1103\/PhysRev.52.230","article-title":"Internal friction in solids. I. Theory of internal friction in reeds","volume":"52","author":"Zener","year":"1937","journal-title":"Phys. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1103\/PhysRev.53.90","article-title":"Internal friction in solids II. General theory of thermoelastic internal friction","volume":"53","author":"Zener","year":"1938","journal-title":"Phys. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5600","DOI":"10.1103\/PhysRevB.61.5600","article-title":"Thermoelastic damping in micro-and nanomechanicalsystems","volume":"61","author":"Lifshitz","year":"2000","journal-title":"Phys. Rev. B"},{"key":"ref_8","first-page":"54","article-title":"Study of thermoelastic damping in capacitive micro-beam resonators using hyperbolic heat conduction model","volume":"108","author":"Rezazadeh","year":"2009","journal-title":"Sens. Transducers J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.mechrescom.2014.08.006","article-title":"Thermoelastic damping of micro resonators operating in the longitudinal vibration mode: In comparison with the case of flexural vibration","volume":"62","author":"Jiao","year":"2014","journal-title":"Mech. Res. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/S0093-6413(03)00061-2","article-title":"Thermoelastic coupling effect on a micro-machined beam resonator","volume":"30","author":"Guo","year":"2003","journal-title":"Mech. Res. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kausinis, S., Yee, K., and Barauskas, R. (2012). Estimation of thermo-elastic damping of vibrations in micro-electro-mechanical systems resonators: Finite element modeling. J. Micro\/Nanolith. MEMS MOEMS, 11.","DOI":"10.1117\/1.JMM.11.3.033005"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.ijmecsci.2013.04.013","article-title":"A finite element analysis of thermoelastic damping in vented MEMS beam resonators","volume":"74","author":"Guo","year":"2013","journal-title":"Int. J. Mech. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1115\/1.4001506","article-title":"Finite Element Analysis of Thermoelastic Damping in Contour-Mode Vibrations of Micro and Nanoscale Ring, Disk, and Elliptical Plate Resonators","volume":"132","author":"Yi","year":"2010","journal-title":"J. Vib. Acoust."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1109\/JMEMS.2006.883573","article-title":"Engineering MEMS resonators with low thermoelastic damping","volume":"15","author":"Duwel","year":"2006","journal-title":"Microelectromech. Syst. J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Nayfeh, A.H., and Younis, M.I. (2004). Modeling and simulations of thermoelastic damping in microplates. J. Micromech. Microeng., 14.","DOI":"10.1088\/0960-1317\/14\/12\/016"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"De, S.K., and Aluru, N.R. (2006). Theory of thermoelastic damping in electrostatically actuated microstructures. Phys. Rev. B, 74.","DOI":"10.1103\/PhysRevB.74.144305"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"167","DOI":"10.15632\/jtam-pl.53.1.167","article-title":"Thermoelastic problem of an axially moving microbeam subjected to an external transverse excitation","volume":"53","author":"Abouelregal","year":"2015","journal-title":"J. Theor. Appl. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"10009","DOI":"10.1016\/j.amc.2012.03.029","article-title":"Thermo-elastic behavior of thin sandwich panel made of piezoelectric layers","volume":"218","author":"Bassiouny","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1618","DOI":"10.1177\/1077546314543810","article-title":"On the flexural vibrations of generalized thermo-elasto-diffusive thin cantilever beam","volume":"22","author":"Sharma","year":"2016","journal-title":"J. Vib. Control"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tzou, D.Y. (2014). Macro-to Microscale Heat Transfer: The Lagging Behavior, John Wiley & Sons.","DOI":"10.1002\/9781118818275"},{"key":"ref_21","unstructured":"Landau, L.D., and Lifshitz, E.M. (1959). Course of Theoretical Physics Vol. 7: Theory and Elasticity, Pergamon Press."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.sna.2009.03.003","article-title":"Numerical models and experimental investigation of energy loss mechanisms in SOI-based tuning-fork gyroscopes","volume":"152","author":"Xu","year":"2009","journal-title":"Sens. Actuators A Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/9\/1445\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T01:41:21Z","timestamp":1717638081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/9\/1445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,7]]},"references-count":22,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2016,9]]}},"alternative-id":["s16091445"],"URL":"https:\/\/doi.org\/10.3390\/s16091445","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,9,7]]}}}