{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T10:07:01Z","timestamp":1768558021575,"version":"3.49.0"},"reference-count":14,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,4,10]],"date-time":"2013-04-10T00:00:00Z","timestamp":1365552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bell-shaped vibratory angular rate gyro (abbreviated as BVG) is a new type Coriolis vibratory gyro that was inspired by Chinese traditional clocks. The resonator fuses based on a variable thickness axisymmetric multicurved surface shell. Its characteristics can directly influence the performance of BVG. The BVG structure not only has capabilities of bearing high overload, high impact and, compared with the tuning fork, vibrating beam, shell and a comb structure, but also a higher frequency to overcome the influence of the disturbance of the exterior environment than the same sized hemispherical resonator gyroscope (HRG) and the traditional cylinder vibratory gyroscope. It can be widely applied in high dynamic low precision angular rate measurement occasions. The main work is as follows: the issue mainly analyzes the structure and basic principle, and investigates the bell-shaped resonator\u2019s mathematical model. The reasonable structural parameters are obtained from finite element analysis and an intelligent platform. Using the current solid vibration gyro theory analyzes the structural characteristics and principles of BVG. The bell-shaped resonator is simplified as a paraboloid of the revolution mechanical model, which has a fixed closed end and a free opened end. It obtains the natural frequency and vibration modes based on the theory of elasticity. The structural parameters are obtained from the orthogonal method by the research on the structural parameters of the resonator analysis. It obtains the modal analysis, stress analysis and impact analysis with the chosen parameters. Finally, using the turntable experiment verifies the gyro effect of the BVG.<\/jats:p>","DOI":"10.3390\/s130404724","type":"journal-article","created":{"date-parts":[[2013,4,10]],"date-time":"2013-04-10T11:52:27Z","timestamp":1365594747000},"page":"4724-4741","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Research on Bell-Shaped Vibratory Angular Rate Gyro\u2019s Character of Resonator"],"prefix":"10.3390","volume":"13","author":[{"given":"Zhong","family":"Su","sequence":"first","affiliation":[{"name":"Institute of Intelligent Control, Beijing Information Science & Technological University,Beijing 100101, China"},{"name":"School of Automation, Beijing Institute of Technology, Beijing 100084, China"}]},{"given":"Mengyin","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Institute of Technology, Beijing 100084, China"}]},{"given":"Qing","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Intelligent Control, Beijing Information Science & Technological University,Beijing 100101, China"}]},{"given":"Ning","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Intelligent Control, Beijing Information Science & Technological University,Beijing 100101, China"},{"name":"School of Automation, Beijing Institute of Technology, Beijing 100084, China"}]},{"given":"Hong","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Intelligent Control, Beijing Information Science & Technological University,Beijing 100101, China"},{"name":"School of Automation, Beijing Institute of Technology, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2013,4,10]]},"reference":[{"key":"ref_1","unstructured":"Matveev, V.A., Basarab, M.A., and Alekin, A.V. (2009). Solid State Wave Gyro, National Defense Industry Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/62.257091","article-title":"Comparison of hemispherical resonator gyro and optical gyros","volume":"7","author":"Rybak","year":"1992","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_3","unstructured":"Shkel, A.M. (2006, January 25\u201327). Type I and Type II Micromachined Vibratory Gyroscopes. San Diego, CA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1006\/jsvi.2001.4163","article-title":"The influence of control system design on the performance of vibratory gyroscopes","volume":"255","author":"Loveday","year":"2002","journal-title":"J. Sound Vib."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.sna.2011.04.039","article-title":"Design, analysis and experiment of a novel ring vibratory gyroscope","volume":"168","author":"Tao","year":"2011","journal-title":"Sens. Actuators Phys. A"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chikovani, V.V., Okon, I.M., Barabashov, A.S., and Tewksbury, P. (2008, January 5\u20138). A Set of High Accuracy Low Cost Metallic Resonator CVG. Monterey, CA, USA.","DOI":"10.1109\/PLANS.2008.4569975"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Watson, W.S. (2010, January 4\u20136). Vibratory Gyro Skewed Pick-off and Driver Geometry. Indian Wells, CA, USA.","DOI":"10.1109\/PLANS.2010.5507130"},{"key":"ref_8","unstructured":"Kang, J.H. (1997). Three-Dimensional Vibration Analysis of Thick Shells of Revolution with Arbitrary Curvature and Variable Thickness. [Ph.D. Thesis, The Ohio State University]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1299\/jsmec.45.2","article-title":"Three-dimensional vibration analysis of paraboloidal shells","volume":"45","author":"Leissa","year":"2002","journal-title":"JSME Int. J. Ser. C-Mech Syst. Mach. Elem. Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s00707-006-0391-y","article-title":"Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory","volume":"188","author":"Kang","year":"2007","journal-title":"Acta Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1115\/1.2178358","article-title":"Three-dimensional sharp corner displacement functions for bodies of revolution","volume":"74","author":"Huang","year":"2007","journal-title":"J. Appl. Mech. Trans. ASME"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1115\/1.1406961","article-title":"Three-dimensional field equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness","volume":"68","author":"Kang","year":"2001","journal-title":"J. Appl. Mech. Trans. ASME"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.sna.2006.02.034","article-title":"Effect of polarized electric field on piezoelectric cylinder vibratory gyroscope","volume":"128","author":"Ting","year":"2006","journal-title":"Sens. Actuators Phys. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.sna.2012.03.031","article-title":"Investigation on standing wave vibration of the imperfect resonant shell for cylindrical gyro","volume":"179","author":"Xi","year":"2012","journal-title":"Sens. Actuators Phys. A"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/4\/4724\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:46:02Z","timestamp":1760219162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/4\/4724"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,10]]},"references-count":14,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,4]]}},"alternative-id":["s130404724"],"URL":"https:\/\/doi.org\/10.3390\/s130404724","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,10]]}}}