Mixed forms of free oscillations of a rectangular CFCF-plate
Mixed (symmetrically/antisymmetric) forms of natural oscillations of a thin rectangular plate of constant thickness, in which two parallel sides are rigidly pinched, and the other two are free (CFCF plate, C — clamped, F — free), are studied. When all the conditions of the boundary value problem ar...
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| Format: | Article |
| Language: | English |
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Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University)
2023-04-01
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| Series: | Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki |
| Subjects: | |
| Online Access: | https://ntv.ifmo.ru/file/article/21918.pdf |
| _version_ | 1797845399046717440 |
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| author | Mikhail V. Sukhoterin Elena I. Rasputina Natalya F. Pizhurina |
| author_facet | Mikhail V. Sukhoterin Elena I. Rasputina Natalya F. Pizhurina |
| author_sort | Mikhail V. Sukhoterin |
| collection | DOAJ |
| description | Mixed (symmetrically/antisymmetric) forms of natural oscillations of a thin rectangular plate of constant thickness, in which two parallel sides are rigidly pinched, and the other two are free (CFCF plate, C — clamped, F — free), are
studied. When all the conditions of the boundary value problem are satisfied, a resolving infinite homogeneous system of linear algebraic equations with respect to unknown coefficients of the series is obtained using two hyperbolotrigonometric series of the coordinate deflection function. Even functions on one coordinate and odd functions on
another coordinate were used to obtain symmetric-antisymmetric waveforms. As a parameter, the resulting system contains the relative frequency of free oscillations. Nontrivial solutions of the reduced system were found by the method of successive approximations in combination with a search of the frequency parameter. Numerical results are obtained for the spectrum of the first six mixed (symmetric/antisymmetric — S-A and A-S) forms of free oscillations of a thin square CFCF plate of constant thickness. The natural frequencies were compared with the results of other authors and with known experimental values. The influence on the accuracy of the results of the number of members held in rows
(the size of the reduced system) and the number of iterations is investigated. 3-D images of the found waveforms are presented. The results obtained can be used in the design of various sensors and sensors using the resonance phenomenon. |
| first_indexed | 2024-04-09T17:38:25Z |
| format | Article |
| id | doaj.art-50d6f69f709749ea8295d1c9f75b5b0b |
| institution | Directory Open Access Journal |
| issn | 2226-1494 2500-0373 |
| language | English |
| last_indexed | 2024-04-09T17:38:25Z |
| publishDate | 2023-04-01 |
| publisher | Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University) |
| record_format | Article |
| series | Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki |
| spelling | doaj.art-50d6f69f709749ea8295d1c9f75b5b0b2023-04-17T10:18:18ZengSaint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University)Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki2226-14942500-03732023-04-0123241342110.17586/2226-1494-2023-23-2-413-421Mixed forms of free oscillations of a rectangular CFCF-plateMikhail V. Sukhoterin0https://orcid.org/0000-0002-8295-7089Elena I. Rasputina1https://orcid.org/0000-0002-7155-2641Natalya F. Pizhurina2https://orcid.org/0000-0002-4687-2280D.Sc., Associate Professor, Head of Department, Admiral Makarov State University of Maritime and Inland Shipping, Saint-Petersburg, 198035, Russian Federation, sc 16496923700PhD (Physics & Mathematics), Associate Professor, Admiral Makarov State University of Maritime and Inland Shipping, Saint-Petersburg, 198035, Russian Federation, sc 57204360630PhD, Associate Professor, Professor, Admiral Makarov State University of Maritime and Inland Shipping, Saint- Petersburg, 198035, Russian Federation, sc 57213917458Mixed (symmetrically/antisymmetric) forms of natural oscillations of a thin rectangular plate of constant thickness, in which two parallel sides are rigidly pinched, and the other two are free (CFCF plate, C — clamped, F — free), are studied. When all the conditions of the boundary value problem are satisfied, a resolving infinite homogeneous system of linear algebraic equations with respect to unknown coefficients of the series is obtained using two hyperbolotrigonometric series of the coordinate deflection function. Even functions on one coordinate and odd functions on another coordinate were used to obtain symmetric-antisymmetric waveforms. As a parameter, the resulting system contains the relative frequency of free oscillations. Nontrivial solutions of the reduced system were found by the method of successive approximations in combination with a search of the frequency parameter. Numerical results are obtained for the spectrum of the first six mixed (symmetric/antisymmetric — S-A and A-S) forms of free oscillations of a thin square CFCF plate of constant thickness. The natural frequencies were compared with the results of other authors and with known experimental values. The influence on the accuracy of the results of the number of members held in rows (the size of the reduced system) and the number of iterations is investigated. 3-D images of the found waveforms are presented. The results obtained can be used in the design of various sensors and sensors using the resonance phenomenon.https://ntv.ifmo.ru/file/article/21918.pdfrectangular cfcf platemixed oscillation formsnatural frequencieshyperbolic-trigonometric series |
| spellingShingle | Mikhail V. Sukhoterin Elena I. Rasputina Natalya F. Pizhurina Mixed forms of free oscillations of a rectangular CFCF-plate Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki rectangular cfcf plate mixed oscillation forms natural frequencies hyperbolic-trigonometric series |
| title | Mixed forms of free oscillations of a rectangular CFCF-plate |
| title_full | Mixed forms of free oscillations of a rectangular CFCF-plate |
| title_fullStr | Mixed forms of free oscillations of a rectangular CFCF-plate |
| title_full_unstemmed | Mixed forms of free oscillations of a rectangular CFCF-plate |
| title_short | Mixed forms of free oscillations of a rectangular CFCF-plate |
| title_sort | mixed forms of free oscillations of a rectangular cfcf plate |
| topic | rectangular cfcf plate mixed oscillation forms natural frequencies hyperbolic-trigonometric series |
| url | https://ntv.ifmo.ru/file/article/21918.pdf |
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