Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions
Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were exp...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2015-12-01
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| Series: | International Journal of Applied Mechanics and Engineering |
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| Online Access: | https://www.ijame-poland.com/Green-s-Function-In-Free-Axisymmetric-Vibration-Analysis-Of-Annular-Thin-Plates-With,167167,0,2.html |
| _version_ | 1797750758114852864 |
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| author | K.K. Żur |
| author_facet | K.K. Żur |
| author_sort | K.K. Żur |
| collection | DOAJ |
| description | Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature. |
| first_indexed | 2024-03-12T16:38:34Z |
| format | Article |
| id | doaj.art-7466be7f85cd48b3b735814b556ad6f0 |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:38:34Z |
| publishDate | 2015-12-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-7466be7f85cd48b3b735814b556ad6f02023-08-08T14:47:05ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032015-12-0120493995110.1515/ijame-2015-0060167167Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary ConditionsK.K. Żur0Faculty of Management, Bialystok University of Technology, 2 Ojca Stefana Tarasiuka St., 16-001 Kleosin, POLANDFree vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.https://www.ijame-poland.com/Green-s-Function-In-Free-Axisymmetric-Vibration-Analysis-Of-Annular-Thin-Plates-With,167167,0,2.htmlannular platesgreen’s functionsingularities |
| spellingShingle | K.K. Żur Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions International Journal of Applied Mechanics and Engineering annular plates green’s function singularities |
| title | Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions |
| title_full | Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions |
| title_fullStr | Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions |
| title_full_unstemmed | Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions |
| title_short | Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions |
| title_sort | green s function in free axisymmetric vibration analysis of annular thin plates with different boundary conditions |
| topic | annular plates green’s function singularities |
| url | https://www.ijame-poland.com/Green-s-Function-In-Free-Axisymmetric-Vibration-Analysis-Of-Annular-Thin-Plates-With,167167,0,2.html |
| work_keys_str_mv | AT kkzur greensfunctioninfreeaxisymmetricvibrationanalysisofannularthinplateswithdifferentboundaryconditions |