Моделювання фігур Хладні на прямокутній платівці

Pavlo Ihorovych Krysenko; Maksym Olehovych Zoziuk; Oleksandr Ivanovych Yurikov; Dmytro Volodymyrovych Koroliuk; Yurii Ivanovych Yakymenko

doi:10.20535/2523-4455.mea.241698

Vol. 26 · Issue 3 · 2021 Dec 23, 2021 Microsystems and Physical Electronics

Chladni Figures Simulation on a Rectangular Plate

Pavlo Ihorovych Krysenko Corresponding Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського»,National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” [https://ror.org/00syn5v21] Ukraine

Maksym Olehovych Zoziuk Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського»,National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” [https://ror.org/00syn5v21] Ukraine

Oleksandr Ivanovych Yurikov Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» Ukraine

Dmytro Volodymyrovych Koroliuk Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського»,National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” [https://ror.org/00syn5v21] Ukraine

Yurii Ivanovych Yakymenko Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського»,National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” [https://ror.org/00syn5v21] Ukraine

Pages241698-1 - 241698-6 PublishedDec 23, 2021

PDF (Ukrainian)

VOL 26 · ISS 3 · 2021 View issue

Abstract

An analytical model for creating flat Chladni figures is presented. The equation of a standing wave in the simplest boundary conditions and the Fourier transform are used. Top view images are shown at different frequencies. The practical significance of the results obtained for the further development of the field of creating Chladni figures based on standing waves of different physical nature has been determined.

Keywords

#Chladni figures #Metasurfaces #Numerical simulation #Mathematical model

References

[1]. M. I. Hossaina, N. Yumnam, W. Qarony, A. Salleo, V. Wagner, D. Knipp, Y.H. Tsang, “Non-resonant metal-oxide metasurfaces for efficient perovskite solar cells,” Solar Energy, vol. 198, pp. 570–577, March 2020. DOI: 10.1016/j.solener.2020.01.082
[2]. Z. Liu, H. Zhong, H. Zhang, Z. Huang, G. Liu, X. Liu, G. Fu, C. Tang, “Silicon multi-resonant metasurface for full-spectrum perfect solar energy absorption,” Solar Energy, vol. 199, pp. 360–365, March 2020. DOI: 10.1016/j.solener.2020.02.053
[3]. M.S. Islam, J. Sultana, M. Biabanifard, Z. Vafapour, M.J. Nine, A. Dinovitser, C.M.B. Cordeiro, B.W.-H. Ng, D. Abbott, “Tunable localized surface plasmon graphene metasurface for multiband superabsorption and terahertz sensing,” Carbon, vol. 158, pp. 559 – 567, March 2020. DOI: 10.1016/j.carbon.2019.11.026
[4]. M. Faraday, “On a Peculiar Class of Acoustical Figures; and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces,” Philosophical Transactions of the Royal Society of London, vol. 121, pp. 299–340, 1831. DOI: 10.1098/rspl.1830.0024
Timoshenko, S. and Woinowsky-Krieger, S., Theory of plates and shells, McGraw-Hill New York, 1959.
M.Zozyuk, D.Koroliouk, V.Moskaliuk, A.Yurikov and Yu.Yakymenko. Creation of quasiperiodic surfaces under the action of vibrating dielectric matrices, ELNANO-2020, pp. 224 - 229, 2019. DOI: 10.1109/ELNANO50318.2020.9088821
Mikhailov I. G., Soloviev V. A., Syrnikov Yu. P. Fundamentals of molecular acoustics. Nauka, M., 1964.
Isakovich M.A. General acoustics. Nauka, M., 1973.
M. O. Zozyuk, A. I. Yurikov, D. V. Koroliouk, Yu. I. Yakymenko. The Principle of Creating Quasiperiodic Surfaces under the Action of a Vibrating Dielectric Matrix, MicrosystElectronAcoust, 2020, vol. 25, no. 1, 5-10. DOI: 10.20535/2523-4455.mea.202632
Babych B., Borisova O., Machulianskyi O., Yakimenko Y., Rodionov M., Koroliouk D., Yakymenko Yu. Applications of Metal-dielectric nanocomposite structures in information systems. Comm. In ELNANO – IEEE 38th Conference on Electronics and Nanotechnology, 2018, pp. 96-100. DOI: 10.1109/ELNANO.2018.8477509
D. Koroliouk, Classification of binary deterministic statistical experiments with persistent regression, Cybernetics and System Analysis, Springer NY, 2015, vol. 51, No. 4, 644-649. DOI: 10.1007/s10559-015-9755-4
D. Koroliouk, D. Koroliouk, Adapted statistical experiments. Journal of Mathematical Sciences, Springer NY, Vol. 220, No. 5, February 2017, 615-623. DOI: 10.1007/s10958-016-3204-4
D. Koroliouk, “Two component binary statistical experiments with persistent linear regression”, Theory of Probability and Mathematical Statistics, 2015, v.90, pp.103- 114. DOI: 10.1090/tpms/952
[14]. Koroliouk D., “Stationary statistical experiments and the optimal estimator for a predictable component” Journal of Mathematical Sciences, 2016, 214(2), pp.220-228. DOI: 10.1007/s10958-016-2770-9
Koroliouk, D.V., Koroliuk, V.S., Rosato, N., Equilibrium Processes in Biomedical Data Analysis: The Wright–Fisher Model. Cybernetics and Systems Analysis, 2014, 50(6), pp.890-897. DOI: 10.1007/s10559-014-9680-y
Koroliouk, D., Statistical experiments in a balanced Markov random environment. Cybernetics and Systems Analysis, 2015, vol. 51, No. 5, pp.766-771. DOI: 10.1007/s10559-015-9769-y
Koroliouk D., The problem of discrete Markov diffusion leaving an interval. Cybernetics and Systems Analysis, 2016, vol. 52, No. 4, pp.571-576. DOI: 10.1007/s10559-016-9859-5
D. Koroliouk Dynamics of Statistical Experiments, ISTE-WILEY, London, 2020, 224 p. ISBN: 978-1-786-30598-5
D. Koroliouk, I. Samoilenko. Random evolutionary systems: asymptotic properties and large deviations. ISTE-WILEY, London, 2021, 350 p. ISBN: 978-1-119-85125-7
M. D. Waller. Chladni Figures. G. Bell, London, 1961.
H. R. Schwarz. Methode der ﬁniten Elemente. B. G. Teubner, Stuttgart, Germany, 1991. ISBN: 9783519223498
T. Driscoll. Eigenmodes of isospectral drums. SIAM Review, vol. 39, No. 1, pp. 1–17, 1997. URL: https://tobydriscoll.net/publication/driscoll-eigenmodes-isospectral-drums-1997-a/driscoll-eigenmodes-isospectral-drums-1997-a.pdf
Mark Kac. Can one hear the shape of a drum? The American Mathematical Monthly, vol. 73, No. 4, pp. 1–23, 1966. DOI: 10.2307/2313748
D.Koroliouk, M.Zozyuk, Yu.I.Yakymenko. The principle of creating quasiperiodic surfaces under the action of vibrating dielectric matrix, 2020, arXiv:2005.11053 [physics.app-ph].

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[1] [1]. M. I. Hossaina, N. Yumnam, W. Qarony, A. Salleo, V. Wagner, D. Knipp, Y.H. Tsang, “Non-resonant metal-oxide metasurfaces for efficient perovskite solar cells,” Solar Energy, vol. 198, pp. 570–577, March 2020. DOI: 10.1016/j.solener.2020.01.082

[2] [2]. Z. Liu, H. Zhong, H. Zhang, Z. Huang, G. Liu, X. Liu, G. Fu, C. Tang, “Silicon multi-resonant metasurface for full-spectrum perfect solar energy absorption,” Solar Energy, vol. 199, pp. 360–365, March 2020. DOI: 10.1016/j.solener.2020.02.053

[3] [3]. M.S. Islam, J. Sultana, M. Biabanifard, Z. Vafapour, M.J. Nine, A. Dinovitser, C.M.B. Cordeiro, B.W.-H. Ng, D. Abbott, “Tunable localized surface plasmon graphene metasurface for multiband superabsorption and terahertz sensing,” Carbon, vol. 158, pp. 559 – 567, March 2020. DOI: 10.1016/j.carbon.2019.11.026

[4] [4]. M. Faraday, “On a Peculiar Class of Acoustical Figures; and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces,” Philosophical Transactions of the Royal Society of London, vol. 121, pp. 299–340, 1831. DOI: 10.1098/rspl.1830.0024

[5] Timoshenko, S. and Woinowsky-Krieger, S., Theory of plates and shells, McGraw-Hill New York, 1959.

[6] M.Zozyuk, D.Koroliouk, V.Moskaliuk, A.Yurikov and Yu.Yakymenko. Creation of quasiperiodic surfaces under the action of vibrating dielectric matrices, ELNANO-2020, pp. 224 - 229, 2019. DOI: 10.1109/ELNANO50318.2020.9088821

[7] Mikhailov I. G., Soloviev V. A., Syrnikov Yu. P. Fundamentals of molecular acoustics. Nauka, M., 1964.

[8] Isakovich M.A. General acoustics. Nauka, M., 1973.

[9] M. O. Zozyuk, A. I. Yurikov, D. V. Koroliouk, Yu. I. Yakymenko. The Principle of Creating Quasiperiodic Surfaces under the Action of a Vibrating Dielectric Matrix, MicrosystElectronAcoust, 2020, vol. 25, no. 1, 5-10. DOI: 10.20535/2523-4455.mea.202632

[10] Babych B., Borisova O., Machulianskyi O., Yakimenko Y., Rodionov M., Koroliouk D., Yakymenko Yu. Applications of Metal-dielectric nanocomposite structures in information systems. Comm. In ELNANO – IEEE 38th Conference on Electronics and Nanotechnology, 2018, pp. 96-100. DOI: 10.1109/ELNANO.2018.8477509

[11] D. Koroliouk, Classification of binary deterministic statistical experiments with persistent regression, Cybernetics and System Analysis, Springer NY, 2015, vol. 51, No. 4, 644-649. DOI: 10.1007/s10559-015-9755-4

[12] D. Koroliouk, D. Koroliouk, Adapted statistical experiments. Journal of Mathematical Sciences, Springer NY, Vol. 220, No. 5, February 2017, 615-623. DOI: 10.1007/s10958-016-3204-4

[13] D. Koroliouk, “Two component binary statistical experiments with persistent linear regression”, Theory of Probability and Mathematical Statistics, 2015, v.90, pp.103- 114. DOI: 10.1090/tpms/952

[14] [14]. Koroliouk D., “Stationary statistical experiments and the optimal estimator for a predictable component” Journal of Mathematical Sciences, 2016, 214(2), pp.220-228. DOI: 10.1007/s10958-016-2770-9

[15] Koroliouk, D.V., Koroliuk, V.S., Rosato, N., Equilibrium Processes in Biomedical Data Analysis: The Wright–Fisher Model. Cybernetics and Systems Analysis, 2014, 50(6), pp.890-897. DOI: 10.1007/s10559-014-9680-y

[16] Koroliouk, D., Statistical experiments in a balanced Markov random environment. Cybernetics and Systems Analysis, 2015, vol. 51, No. 5, pp.766-771. DOI: 10.1007/s10559-015-9769-y

[17] Koroliouk D., The problem of discrete Markov diffusion leaving an interval. Cybernetics and Systems Analysis, 2016, vol. 52, No. 4, pp.571-576. DOI: 10.1007/s10559-016-9859-5

[18] D. Koroliouk Dynamics of Statistical Experiments, ISTE-WILEY, London, 2020, 224 p. ISBN: 978-1-786-30598-5

[19] D. Koroliouk, I. Samoilenko. Random evolutionary systems: asymptotic properties and large deviations. ISTE-WILEY, London, 2021, 350 p. ISBN: 978-1-119-85125-7

[20] M. D. Waller. Chladni Figures. G. Bell, London, 1961.

[21] H. R. Schwarz. Methode der ﬁniten Elemente. B. G. Teubner, Stuttgart, Germany, 1991. ISBN: 9783519223498

[22] T. Driscoll. Eigenmodes of isospectral drums. SIAM Review, vol. 39, No. 1, pp. 1–17, 1997. URL: https://tobydriscoll.net/publication/driscoll-eigenmodes-isospectral-drums-1997-a/driscoll-eigenmodes-isospectral-drums-1997-a.pdf

[23] Mark Kac. Can one hear the shape of a drum? The American Mathematical Monthly, vol. 73, No. 4, pp. 1–23, 1966. DOI: 10.2307/2313748

[24] D.Koroliouk, M.Zozyuk, Yu.I.Yakymenko. The principle of creating quasiperiodic surfaces under the action of vibrating dielectric matrix, 2020, arXiv:2005.11053 [physics.app-ph].

Chladni Figures Simulation on a Rectangular Plate

Abstract

Keywords

References

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