On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder
The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power loa...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Saratov State University
2021-03-01
|
| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| Subjects: | |
| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_35-47.pdf |
| _version_ | 1818959170307620864 |
|---|---|
| author | Vatulyan, Alexandr Ovanesovitsch Nesterov, Sergei Anatolevich |
| author_facet | Vatulyan, Alexandr Ovanesovitsch Nesterov, Sergei Anatolevich |
| author_sort | Vatulyan, Alexandr Ovanesovitsch |
| collection | DOAJ |
| description | The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables. A set of canonical linear systems of differential equations of the 1st order is obtained, the solution of each of which is obtained numerically using the shooting method. The coefficient inverse problem of finding the thermomechanical characteristics of a finite length cylinder using additional information in Laplace transforms, given on the outer surface of the cylinder, is posed. The dimensionless thermomechanical characteristics of the cylinder were restored in two stages. At the first stage, the initial approximation was determined in the class of positive bounded functions. At the second stage, based on the solution of the corresponding Fredholm integral equations of the 1st kind, corrections of the reconstructed functions were found, and an iterative process of their refinement was constructed. In the course of computational experiments, it was found that monotonic characteristics are restored with good accuracy; the reconstruction procedure is resistant to input information noise. |
| first_indexed | 2024-12-20T11:37:23Z |
| format | Article |
| id | doaj.art-decf5dae978644dfbe6010a6ed4cca20 |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-20T11:37:23Z |
| publishDate | 2021-03-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-decf5dae978644dfbe6010a6ed4cca202022-12-21T19:42:05ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052021-03-01211354710.18500/1816-9791-2021-21-1-35-47On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinderVatulyan, Alexandr Ovanesovitsch0Nesterov, Sergei Anatolevich1Southern Federal University, Russia, 344006, Rostov-on-Don, B. Sadovaia str., 105Southern Federal University, Russia, 344006, Rostov-on-Don, B. Sadovaia str., 105The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables. A set of canonical linear systems of differential equations of the 1st order is obtained, the solution of each of which is obtained numerically using the shooting method. The coefficient inverse problem of finding the thermomechanical characteristics of a finite length cylinder using additional information in Laplace transforms, given on the outer surface of the cylinder, is posed. The dimensionless thermomechanical characteristics of the cylinder were restored in two stages. At the first stage, the initial approximation was determined in the class of positive bounded functions. At the second stage, based on the solution of the corresponding Fredholm integral equations of the 1st kind, corrections of the reconstructed functions were found, and an iterative process of their refinement was constructed. In the course of computational experiments, it was found that monotonic characteristics are restored with good accuracy; the reconstruction procedure is resistant to input information noise.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_35-47.pdfthermoelasticityfinite cylinderidentificationcoefficient inverse problemiterative processintegral equationshooting methodvariable separation method |
| spellingShingle | Vatulyan, Alexandr Ovanesovitsch Nesterov, Sergei Anatolevich On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика thermoelasticity finite cylinder identification coefficient inverse problem iterative process integral equation shooting method variable separation method |
| title | On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder |
| title_full | On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder |
| title_fullStr | On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder |
| title_full_unstemmed | On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder |
| title_short | On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder |
| title_sort | on the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder |
| topic | thermoelasticity finite cylinder identification coefficient inverse problem iterative process integral equation shooting method variable separation method |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_35-47.pdf |
| work_keys_str_mv | AT vatulyanalexandrovanesovitsch ontheidentificationproblemofthethermomechanicalcharacteristicsofthefinitefunctionallygradedcylinder AT nesterovsergeianatolevich ontheidentificationproblemofthethermomechanicalcharacteristicsofthefinitefunctionallygradedcylinder |