Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations
The paper discusses the impact of the von Kármán type geometric nonlinearity introduced to a mathematical model of beam vibrations on the amplitude-frequency characteristics of the signal for the proposed mathematical models of beam vibrations. An attempt is made to separate vibrations of continuous...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/3038179 |
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| author | A. V. Krysko Jan Awrejcewicz Irina V. Papkova Olga Szymanowska V. A. Krysko |
| author_facet | A. V. Krysko Jan Awrejcewicz Irina V. Papkova Olga Szymanowska V. A. Krysko |
| author_sort | A. V. Krysko |
| collection | DOAJ |
| description | The paper discusses the impact of the von Kármán type geometric nonlinearity introduced to a mathematical model of beam vibrations on the amplitude-frequency characteristics of the signal for the proposed mathematical models of beam vibrations. An attempt is made to separate vibrations of continuous mechanical systems subjected to a harmonic load from noise induced by the nonlinearity of the system by employing the principal component analysis (PCA). Straight beams lying on Winkler foundations are analysed. Differential equations are obtained based on the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Levinson-Reddy hypotheses. Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA). |
| format | Article |
| id | doaj-art-5730a2271b16446c8b2520baa13e8e24 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-5730a2271b16446c8b2520baa13e8e242025-02-03T01:01:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/30381793038179Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam VibrationsA. V. Krysko0Jan Awrejcewicz1Irina V. Papkova2Olga Szymanowska3V. A. Krysko4Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politeknicheskaya Str., Saratov 41054, RussiaDepartment of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, PolandDepartment of Mathematics and Modelling, Saratov State Technical University, 77 Politeknicheskaya Str., Saratov 41054, RussiaDepartment of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, PolandDepartment of Mathematics and Modelling, Saratov State Technical University, 77 Politeknicheskaya Str., Saratov 41054, RussiaThe paper discusses the impact of the von Kármán type geometric nonlinearity introduced to a mathematical model of beam vibrations on the amplitude-frequency characteristics of the signal for the proposed mathematical models of beam vibrations. An attempt is made to separate vibrations of continuous mechanical systems subjected to a harmonic load from noise induced by the nonlinearity of the system by employing the principal component analysis (PCA). Straight beams lying on Winkler foundations are analysed. Differential equations are obtained based on the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Levinson-Reddy hypotheses. Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA).http://dx.doi.org/10.1155/2017/3038179 |
| spellingShingle | A. V. Krysko Jan Awrejcewicz Irina V. Papkova Olga Szymanowska V. A. Krysko Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations Advances in Mathematical Physics |
| title | Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations |
| title_full | Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations |
| title_fullStr | Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations |
| title_full_unstemmed | Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations |
| title_short | Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations |
| title_sort | principal component analysis in the nonlinear dynamics of beams purification of the signal from noise induced by the nonlinearity of beam vibrations |
| url | http://dx.doi.org/10.1155/2017/3038179 |
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