Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever
The paper deals with free small vibrations of a micro-cantilever near the deformed static position incorporating the electrostatic and intermolecular forces acting from the fixed electrode. First, the initial static deviation of the cantilever due to the external forces is determined using the appro...
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| Format: | Article |
| Language: | Belarusian |
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Belarusian State University
2024-11-01
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| Series: | Журнал Белорусского государственного университета: Математика, информатика |
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| Online Access: | https://journals.bsu.by/index.php/mathematics/article/view/6609 |
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| _version_ | 1850275755943002112 |
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| author | Геннадий Иванович Михасев Вячеслав Владимирович Мисник Марина Георгиевна Ботогова |
| author_facet | Геннадий Иванович Михасев Вячеслав Владимирович Мисник Марина Георгиевна Ботогова |
| author_sort | Геннадий Иванович Михасев |
| collection | DOAJ |
| description | The paper deals with free small vibrations of a micro-cantilever near the deformed static position incorporating the electrostatic and intermolecular forces acting from the fixed electrode. First, the initial static deviation of the cantilever due to the external forces is determined using the approach based on the approximation of the resultant lateral forces by the linear or parabolic functions of the axial coordinate, the initial deflection being evaluated under the values of voltage and intermolecular forces less than the critical ones. To study free small vibrations of the initially deformed cantilever, we linearise the nonlinear differential equation in the neighbourhood of the deformed static position. The derived governing equation with variable coefficients is solved using both the asymptotic approach and the Runge – Kutta method. The effect of the applied voltage and the intermolecular forces, including the van der Waals and Casimir ones, is analysed. |
| format | Article |
| id | doaj-art-96bdd47ef8e449cf9d6fae707782c927 |
| institution | OA Journals |
| issn | 2520-6508 2617-3956 |
| language | Belarusian |
| publishDate | 2024-11-01 |
| publisher | Belarusian State University |
| record_format | Article |
| series | Журнал Белорусского государственного университета: Математика, информатика |
| spelling | doaj-art-96bdd47ef8e449cf9d6fae707782c9272025-08-20T01:50:37ZbelBelarusian State UniversityЖурнал Белорусского государственного университета: Математика, информатика2520-65082617-39562024-11-01362726609Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantileverГеннадий Иванович Михасев0Вячеслав Владимирович Мисник1Марина Георгиевна Ботогова2Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, ChinaPeleng, 25 Makajonka Street, Minsk 220114, BelarusBelarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, BelarusThe paper deals with free small vibrations of a micro-cantilever near the deformed static position incorporating the electrostatic and intermolecular forces acting from the fixed electrode. First, the initial static deviation of the cantilever due to the external forces is determined using the approach based on the approximation of the resultant lateral forces by the linear or parabolic functions of the axial coordinate, the initial deflection being evaluated under the values of voltage and intermolecular forces less than the critical ones. To study free small vibrations of the initially deformed cantilever, we linearise the nonlinear differential equation in the neighbourhood of the deformed static position. The derived governing equation with variable coefficients is solved using both the asymptotic approach and the Runge – Kutta method. The effect of the applied voltage and the intermolecular forces, including the van der Waals and Casimir ones, is analysed.https://journals.bsu.by/index.php/mathematics/article/view/6609micro-cantileverelectrostatic forcesintermolecular forcesfree small vibrations |
| spellingShingle | Геннадий Иванович Михасев Вячеслав Владимирович Мисник Марина Георгиевна Ботогова Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever Журнал Белорусского государственного университета: Математика, информатика micro-cantilever electrostatic forces intermolecular forces free small vibrations |
| title | Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever |
| title_full | Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever |
| title_fullStr | Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever |
| title_full_unstemmed | Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever |
| title_short | Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever |
| title_sort | effect of electrostatic and intermolecular forces on free small vibrations of a micro cantilever |
| topic | micro-cantilever electrostatic forces intermolecular forces free small vibrations |
| url | https://journals.bsu.by/index.php/mathematics/article/view/6609 |
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