On one solution of the vibration problem of mechanical systems with moving boundaries
An analytical method of solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional-difference equa...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2024-04-01
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| Series: | Вестник Самарского университета: Естественнонаучная серия |
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| Online Access: | https://journals.ssau.ru/est/article/viewFile/27354/10536 |
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| author | Vladislav L. Litvinov Kristina V. Litvinova |
| author_facet | Vladislav L. Litvinov Kristina V. Litvinova |
| author_sort | Vladislav L. Litvinov |
| collection | DOAJ |
| description | An analytical method of solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional-difference equations, which can be solved using direct and inverse methods. An inverse method is described that makes it possible to approximate quite diverse laws of boundary motion by laws obtained from solving the inverse problem. New particular solutions are obtained for a fairly wide range of laws of boundary motion. A direct asymptotic method for the approximate solution of a functional equation is considered. An estimate of the errors of the approximate method was made depending on the speed of the boundary movement. |
| format | Article |
| id | doaj-art-328eb4e5d2ca4a648c27a2e7f12de14b |
| institution | OA Journals |
| issn | 2541-7525 2712-8954 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Вестник Самарского университета: Естественнонаучная серия |
| spelling | doaj-art-328eb4e5d2ca4a648c27a2e7f12de14b2025-08-20T01:54:07ZengSamara National Research UniversityВестник Самарского университета: Естественнонаучная серия2541-75252712-89542024-04-01301404910.18287/2541-7525-2024-30-1-40-498800On one solution of the vibration problem of mechanical systems with moving boundariesVladislav L. Litvinov0https://orcid.org/0000-0002-6108-803XKristina V. Litvinova1https://orcid.org/0000-0002-1711-9273Samara State Technical UniversityMoscow State UniversityAn analytical method of solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional-difference equations, which can be solved using direct and inverse methods. An inverse method is described that makes it possible to approximate quite diverse laws of boundary motion by laws obtained from solving the inverse problem. New particular solutions are obtained for a fairly wide range of laws of boundary motion. A direct asymptotic method for the approximate solution of a functional equation is considered. An estimate of the errors of the approximate method was made depending on the speed of the boundary movement.https://journals.ssau.ru/est/article/viewFile/27354/10536wave equationboundary value problemsoscillations of systems with moving boundarieschange of variableslaws of boundary motionfunctional equations |
| spellingShingle | Vladislav L. Litvinov Kristina V. Litvinova On one solution of the vibration problem of mechanical systems with moving boundaries Вестник Самарского университета: Естественнонаучная серия wave equation boundary value problems oscillations of systems with moving boundaries change of variables laws of boundary motion functional equations |
| title | On one solution of the vibration problem of mechanical systems with moving boundaries |
| title_full | On one solution of the vibration problem of mechanical systems with moving boundaries |
| title_fullStr | On one solution of the vibration problem of mechanical systems with moving boundaries |
| title_full_unstemmed | On one solution of the vibration problem of mechanical systems with moving boundaries |
| title_short | On one solution of the vibration problem of mechanical systems with moving boundaries |
| title_sort | on one solution of the vibration problem of mechanical systems with moving boundaries |
| topic | wave equation boundary value problems oscillations of systems with moving boundaries change of variables laws of boundary motion functional equations |
| url | https://journals.ssau.ru/est/article/viewFile/27354/10536 |
| work_keys_str_mv | AT vladislavllitvinov ononesolutionofthevibrationproblemofmechanicalsystemswithmovingboundaries AT kristinavlitvinova ononesolutionofthevibrationproblemofmechanicalsystemswithmovingboundaries |