{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:30:05Z","timestamp":1760149805146,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Innovation and Technological Development","award":["451-03-68\/2022-14\/200156"],"award-info":[{"award-number":["451-03-68\/2022-14\/200156"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A square metal plate (Chladni plate) is excited harmonically by a vibration shaker, while the whole system is set in an anechoic chamber to stop reflections, isolate the system from sound entering from the surroundings, and deal with direct sounds only. As far as the authors are aware, such an arrangement has not been achieved so far. Vibration modes are visualized by using poppy grains scattered over the upper surface of the plate and are also recorded by a camera located above it, inserted among the acoustic wedges on the roof of the chamber, which made it possible to record the patterns and avoid unpleasant sounds associated with some of them. Four distinctive vibration modes of the plate are then originally identified using vibrational and acoustic mode identification. These responses from the plate are measured both by an accelerometer attached to the central point of the plate and by a microphone set on the same vertical line as the accelerometer but above it, measuring the direct sound. The signals from the accelerometer and the microphone are then compared in two experimental arrangements, and their forms and the frequency contents are found to be equivalent. It is shown that the existing symmetry, i.e., the exact correspondence between vibrational and acoustic responses, can be used as the identifier of the patterns formed on the plate and the associated modal frequency.<\/jats:p>","DOI":"10.3390\/sym15091748","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T21:34:12Z","timestamp":1694554452000},"page":"1748","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Chladni Plate in Anechoic Chamber: Symmetry in Vibrational and Acoustic Response"],"prefix":"10.3390","volume":"15","author":[{"given":"Ivana","family":"Kovacic","sequence":"first","affiliation":[{"name":"Faculty of Technical Sciences, Centre of Excellence for Vibro-Acoustic Systems and Signal Processing CEVAS, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1456-1135","authenticated-orcid":false,"given":"Zeljko","family":"Kanovic","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"ref_1","unstructured":"(2015). Treatise on Acoustics, Springer. 1st Comprehensive English translation of E.F.F. Chladni\u2019s Trait\u00e9 d\u2019Acoustique."},{"key":"ref_2","unstructured":"Musielak, D.E. (2015). Prime Mystery: The Life and Mathematics of Sophie Germain Paperback, Author House."},{"key":"ref_3","unstructured":"Chladni, E.F.F. (1787). Entdeckungen \u00fcber Die Theorie des Klanges, Bey Weidmannserben und Reich."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1121\/1.396430","article-title":"Parameters of violin plates and their influence on the plate modes","volume":"83","author":"Molin","year":"1988","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1121\/1.4913458","article-title":"A violin shell model: Vibrational modes and acoustics","volume":"137","author":"Gough","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.1121\/10.0003599","article-title":"Eigenfrequency optimisation of free violin plates","volume":"149","author":"Gonzalez","year":"2021","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1140\/epjst\/e2007-00148-1","article-title":"Nodal patterns in the seismic response of sedimentary valleys","volume":"145","author":"Flores","year":"2007","journal-title":"EPJ Special Top."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"026102","DOI":"10.1103\/PhysRevLett.98.026102","article-title":"Chladni figures revisited based on nanomechanics","volume":"98","author":"Dorrestijn","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"127201","DOI":"10.1103\/PhysRevLett.112.127201","article-title":"Dissipation in ultrahigh quality factor SiN membrane resonators","volume":"112","author":"Chakram","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1016\/0001-6160(88)90209-X","article-title":"On measuring the elastic and damping constants of orthotropic sheet material","volume":"36","author":"McIntyre","year":"1988","journal-title":"Acta Metall."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Sato, J., Hutchings, I.M., and Woodhouse, J. (2007, January 6\u20139). Determination of the dynamic elastic properties of paper and paperboard from the low-frequency vibration modes of rectangular plates. Proceedings of the 61st Appita Annual Conference and Exhibition, Gold Coast, Australia.","DOI":"10.2524\/jtappij.61.837"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1016\/S1359-835X(97)00056-0","article-title":"The vibration damping of laminated plates","volume":"28A","author":"Talbot","year":"1997","journal-title":"Compos. Part A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1088\/0143-0807\/34\/4\/1067","article-title":"Numerical Chladni figures","volume":"34","year":"2013","journal-title":"Eur. J. Phys."},{"key":"ref_14","unstructured":"(2022, October 07). Application Gallery, Chladni Plate. Available online: https:\/\/www.comsol.com\/model\/chladni-plate-67591."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2113","DOI":"10.1121\/1.4916704","article-title":"Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers","volume":"137","author":"Tuan","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"012022","DOI":"10.1088\/1742-6596\/582\/1\/012022","article-title":"Alternate model of Chladni figures for the circular homogenous thin plate case with open boundaries","volume":"582","year":"2015","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10844","DOI":"10.1038\/s41598-018-29244-6","article-title":"Point-driven modern Chladni figures with symmetry breaking","volume":"8","author":"Tuan","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"12764","DOI":"10.1038\/ncomms12764","article-title":"Controlling the motion of multiple objects on a Chladni plate","volume":"7","author":"Zhou","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"012301","DOI":"10.1103\/PhysRevE.82.012301","article-title":"Inversion of Chladni patterns by tuning the vibrational acceleration","volume":"82","author":"Gerner","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s100510070139","article-title":"Mixing of wave functions in rectangular microwave billiards","volume":"17","author":"Kuhl","year":"2000","journal-title":"Eur. Phys. J. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6931","DOI":"10.1103\/PhysRevB.56.6931","article-title":"Quantum scattering, resonant states, and conductance fluctuations in an open square electron billiard","volume":"56","author":"Zozoulenko","year":"1997","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"026213","DOI":"10.1103\/PhysRevE.67.026213","article-title":"Chaotic sound waves in a regular billiard","volume":"67","author":"Schaadt","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.jfluidstructs.2018.07.017","article-title":"Axisymmetric vibrations of a circular Chladni plate in air and fully submerged in water","volume":"82","author":"Escaler","year":"2018","journal-title":"J. Fluids Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"18450","DOI":"10.1103\/PhysRevLett.116.184501","article-title":"Chladni patterns in a liquid at microscale","volume":"116","author":"Vuillermet","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"184101","DOI":"10.1063\/5.0032304","article-title":"Dexterous formation of unconventional Chladni patterns using standing bulk acoustic waves","volume":"117","author":"Lei","year":"2020","journal-title":"Appl. Phys. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rzepecki, J., Chraponska, A., Budzan, S., Isaac, C.W., Mazur, K., and Pawelczyk, M. (2020). Chladni figures in modal analysis of a double-panel structure. Sensors, 20.","DOI":"10.3390\/s20154084"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Tseng, Y.C., Hsu, Y.H., Lai, Y.H., Yu, Y.T., Liang, H.C., Huang, K.F., and Chen, Y.F. (2021). Exploiting modern Chladni plates to analogously nanifest the point interaction. Appl. Sci., 11.","DOI":"10.3390\/app112110094"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1016\/j.matpr.2022.09.305","article-title":"Modal analysis of plate to analyze the effect of mass stiffeners using the Chladni plate approach","volume":"72","author":"Wani","year":"2023","journal-title":"Mater. Today Proc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1748\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:49:30Z","timestamp":1760129370000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1748"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,12]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["sym15091748"],"URL":"https:\/\/doi.org\/10.3390\/sym15091748","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,9,12]]}}}