Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers
This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the...
| الحاوية / القاعدة: | Advances in Mechanical Engineering |
|---|---|
| المؤلفون الرئيسيون: | , , |
| التنسيق: | مقال |
| اللغة: | الإنجليزية |
| منشور في: |
SAGE Publishing
2016-05-01
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| الوصول للمادة أونلاين: | https://doi.org/10.1177/1687814016646505 |
| _version_ | 1856930834767937536 |
|---|---|
| author | S Saha Ray S Sahoo S Das |
| author_facet | S Saha Ray S Sahoo S Das |
| author_sort | S Saha Ray |
| collection | DOAJ |
| container_title | Advances in Mechanical Engineering |
| description | This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots. |
| format | Article |
| id | doaj-art-00f96277482f4e8abc025e8d97c5485a |
| institution | Directory of Open Access Journals |
| issn | 1687-8140 |
| language | English |
| publishDate | 2016-05-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| spelling | doaj-art-00f96277482f4e8abc025e8d97c5485a2025-08-19T20:13:27ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402016-05-01810.1177/168781401664650510.1177_1687814016646505Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampersS Saha Ray0S Sahoo1S Das2Department of Mathematics, National Institute of Technology Rourkela, Rourkela, IndiaDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela, IndiaDepartment of Applied Mathematics, University of Calcutta, Kolkata, IndiaThis article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.https://doi.org/10.1177/1687814016646505 |
| spellingShingle | S Saha Ray S Sahoo S Das Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers |
| title | Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers |
| title_full | Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers |
| title_fullStr | Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers |
| title_full_unstemmed | Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers |
| title_short | Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers |
| title_sort | formulation and solutions of fractional continuously variable order mass spring damper systems controlled by viscoelastic and viscous viscoelastic dampers |
| url | https://doi.org/10.1177/1687814016646505 |
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