Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity
The interaction of parametric oscillations and self-oscillations under nonlinear parametric excitation and delay in elasticity is considered. To solve the differential equations of the system motion, the direct linearization method was used and equations for non-stationary and stationary modes of os...
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| Format: | Article |
| Language: | English |
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Peter the Great St.Petersburg Polytechnic University
2024-12-01
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| Series: | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
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| Online Access: | https://physmath.spbstu.ru/article/2024.77.04/ |
| _version_ | 1826865959591215104 |
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| author | Alifov Alishir |
| author_facet | Alifov Alishir |
| author_sort | Alifov Alishir |
| collection | DOAJ |
| description | The interaction of parametric oscillations and self-oscillations under nonlinear parametric excitation and delay in elasticity is considered. To solve the differential equations of the system motion, the direct linearization method was used and equations for non-stationary and stationary modes of oscillations were derived. Using the Routh–Hurwitz criteria, stability conditions for stationary regimes were obtained. To find out the effect of nonlinear parametric excitation on the dynamics of mixed autoparametric oscillations, relevant calculations were carried out and a comparison was made of the results obtained in the presence and absence of delay. According to calculated data, in the presence of a delay, a change in amplitude values occurs, accompanied by a shift in the amplitude curves in the amplitude-frequency area, as well as their narrowing or broadening, compared to no lag. The presence of lag also affects the stability of oscillations. |
| first_indexed | 2025-02-16T21:50:36Z |
| format | Article |
| id | doaj.art-3281059f7a964e808dd11b012f5edd84 |
| institution | Directory Open Access Journal |
| issn | 2405-7223 |
| language | English |
| last_indexed | 2025-02-16T21:50:36Z |
| publishDate | 2024-12-01 |
| publisher | Peter the Great St.Petersburg Polytechnic University |
| record_format | Article |
| series | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| spelling | doaj.art-3281059f7a964e808dd11b012f5edd842025-01-16T13:35:28ZengPeter the Great St.Petersburg Polytechnic UniversitySt. Petersburg Polytechnical University Journal: Physics and Mathematics2405-72232024-12-0117410.18721/JPM.1740420714726Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticityAlifov Alishir0https://orcid.org/0000-0003-2327-068XMechanical Engineering Research Institute of the Russian Academy of SciencesThe interaction of parametric oscillations and self-oscillations under nonlinear parametric excitation and delay in elasticity is considered. To solve the differential equations of the system motion, the direct linearization method was used and equations for non-stationary and stationary modes of oscillations were derived. Using the Routh–Hurwitz criteria, stability conditions for stationary regimes were obtained. To find out the effect of nonlinear parametric excitation on the dynamics of mixed autoparametric oscillations, relevant calculations were carried out and a comparison was made of the results obtained in the presence and absence of delay. According to calculated data, in the presence of a delay, a change in amplitude values occurs, accompanied by a shift in the amplitude curves in the amplitude-frequency area, as well as their narrowing or broadening, compared to no lag. The presence of lag also affects the stability of oscillations.https://physmath.spbstu.ru/article/2024.77.04/self-oscillationsparametric oscillationsinteractionnonlinearitydelayelasticitymethod of direct linearization |
| spellingShingle | Alifov Alishir Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity St. Petersburg Polytechnical University Journal: Physics and Mathematics self-oscillations parametric oscillations interaction nonlinearity delay elasticity method of direct linearization |
| title | Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity |
| title_full | Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity |
| title_fullStr | Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity |
| title_full_unstemmed | Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity |
| title_short | Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity |
| title_sort | parametric and self excited oscillations under nonlinear parametric action and lag in elasticity |
| topic | self-oscillations parametric oscillations interaction nonlinearity delay elasticity method of direct linearization |
| url | https://physmath.spbstu.ru/article/2024.77.04/ |
| work_keys_str_mv | AT alifovalishir parametricandselfexcitedoscillationsundernonlinearparametricactionandlaginelasticity |