Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure
In this paper, a new type of one-degree-of-freedom pure nonlinear oscillator with a time variable degree of nonlinearity is introduced. Namely, the degree of the nonlinearity in the restitution force is not a constant but a ‘slow time’ variable function. The mathematical model is a second-order nonl...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3958 |
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| author | L. Cveticanin M. Zukovic |
| author_facet | L. Cveticanin M. Zukovic |
| author_sort | L. Cveticanin |
| collection | DOAJ |
| description | In this paper, a new type of one-degree-of-freedom pure nonlinear oscillator with a time variable degree of nonlinearity is introduced. Namely, the degree of the nonlinearity in the restitution force is not a constant but a ‘slow time’ variable function. The mathematical model is a second-order nonlinear differential equation with time-variable parameters. An approximate solving procedure based on the method of time-variable amplitude, frequency and phase is developed. It is found that the vibration properties depend on initial conditions and the degree of time-variable function. The theoretical results are tested on almost linear, cubic and high-degree nonlinear oscillators. According to theoretical considerations, the process of aging in fiber-reinforced polymer composite structure is investigated. It is found that the amplitude and the frequency of vibration of the reinforced polymer structure decrease over time. The result is in good agreement with already published experimental data. The additional conclusion of the research is that the oscillator model suggested in the paper is suitable for the prediction of mechanic properties of the polymer structure in aging and also in similar destructive processes. |
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| format | Article |
| id | doaj.art-957853d8e68d4335b8b2d23f192a6ff6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:30:11Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-957853d8e68d4335b8b2d23f192a6ff62023-11-19T11:49:57ZengMDPI AGMathematics2227-73902023-09-011118395810.3390/math11183958Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite StructureL. Cveticanin0M. Zukovic1Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, SerbiaFaculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, SerbiaIn this paper, a new type of one-degree-of-freedom pure nonlinear oscillator with a time variable degree of nonlinearity is introduced. Namely, the degree of the nonlinearity in the restitution force is not a constant but a ‘slow time’ variable function. The mathematical model is a second-order nonlinear differential equation with time-variable parameters. An approximate solving procedure based on the method of time-variable amplitude, frequency and phase is developed. It is found that the vibration properties depend on initial conditions and the degree of time-variable function. The theoretical results are tested on almost linear, cubic and high-degree nonlinear oscillators. According to theoretical considerations, the process of aging in fiber-reinforced polymer composite structure is investigated. It is found that the amplitude and the frequency of vibration of the reinforced polymer structure decrease over time. The result is in good agreement with already published experimental data. The additional conclusion of the research is that the oscillator model suggested in the paper is suitable for the prediction of mechanic properties of the polymer structure in aging and also in similar destructive processes.https://www.mdpi.com/2227-7390/11/18/3958aging in fiber-reinforced polymer compositeanalytic solving procedureAteb functionnonlinear oscillatortime-variable nonlinearitymarine industry |
| spellingShingle | L. Cveticanin M. Zukovic Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure Mathematics aging in fiber-reinforced polymer composite analytic solving procedure Ateb function nonlinear oscillator time-variable nonlinearity marine industry |
| title | Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure |
| title_full | Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure |
| title_fullStr | Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure |
| title_full_unstemmed | Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure |
| title_short | Oscillator with Time-Variable Degree of Nonlinearity: Theory and Application in Aging of Polymer Composite Structure |
| title_sort | oscillator with time variable degree of nonlinearity theory and application in aging of polymer composite structure |
| topic | aging in fiber-reinforced polymer composite analytic solving procedure Ateb function nonlinear oscillator time-variable nonlinearity marine industry |
| url | https://www.mdpi.com/2227-7390/11/18/3958 |
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