Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions
Abstract Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approa...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-02-01
|
| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-52860-4 |
| _version_ | 1797274880090046464 |
|---|---|
| author | János Lelkes Bendegúz Dezső Bak Tamás Kalmár-Nagy |
| author_facet | János Lelkes Bendegúz Dezső Bak Tamás Kalmár-Nagy |
| author_sort | János Lelkes |
| collection | DOAJ |
| description | Abstract Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approach for solving the equations describing the longitudinal vibration of functionally graded rods with viscous and elastic boundary conditions is proposed. The characteristic equation of the system is derived for the solution of the undamped case for the constant stiffness rod. Then, a homotopy method is applied to compute the eigenvalues and mode shapes of graded rods for viscoelastic boundary conditions. The changes of the eigenvalues and mode shapes as function of the damping parameters are investigated. The optimal damping of the system is computed. It is shown that the qualitative behavior depends on the relation between the actual damping and the optimal damping of the system. The energy density distribution of graded rods is also discussed. An energy measure, the mean scaled energy density distribution is introduced to characterize the energy distribution along the rod in the asymptotic time limit. The significance of such a measure is that it reveals how the energy tends to distribute along the rod. It is shown that the energy distribution can be manipulated by changing the damping parameters. Qualitative changes depending on the relation between the actual damping and the optimal damping are highlighted. |
| first_indexed | 2024-03-07T15:05:29Z |
| format | Article |
| id | doaj.art-9b2aa930f46e488b9ebfb6589fc30641 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-07T15:05:29Z |
| publishDate | 2024-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-9b2aa930f46e488b9ebfb6589fc306412024-03-05T18:55:40ZengNature PortfolioScientific Reports2045-23222024-02-0114111610.1038/s41598-024-52860-4Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditionsJános Lelkes0Bendegúz Dezső Bak1Tamás Kalmár-Nagy2Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and EconomicsDepartment of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and EconomicsDepartment of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and EconomicsAbstract Functionally graded materials have broad engineering applications including mechanical engineering, electronics, chemistry, and biomedical engineering. One notable advantage of such materials is that their stiffness distribution can be optimized to avoid stress concentration. A novel approach for solving the equations describing the longitudinal vibration of functionally graded rods with viscous and elastic boundary conditions is proposed. The characteristic equation of the system is derived for the solution of the undamped case for the constant stiffness rod. Then, a homotopy method is applied to compute the eigenvalues and mode shapes of graded rods for viscoelastic boundary conditions. The changes of the eigenvalues and mode shapes as function of the damping parameters are investigated. The optimal damping of the system is computed. It is shown that the qualitative behavior depends on the relation between the actual damping and the optimal damping of the system. The energy density distribution of graded rods is also discussed. An energy measure, the mean scaled energy density distribution is introduced to characterize the energy distribution along the rod in the asymptotic time limit. The significance of such a measure is that it reveals how the energy tends to distribute along the rod. It is shown that the energy distribution can be manipulated by changing the damping parameters. Qualitative changes depending on the relation between the actual damping and the optimal damping are highlighted.https://doi.org/10.1038/s41598-024-52860-4 |
| spellingShingle | János Lelkes Bendegúz Dezső Bak Tamás Kalmár-Nagy Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions Scientific Reports |
| title | Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions |
| title_full | Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions |
| title_fullStr | Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions |
| title_full_unstemmed | Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions |
| title_short | Vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions |
| title_sort | vibrations and energy distribution in inhomogeneous rods with elastic and viscous boundary conditions |
| url | https://doi.org/10.1038/s41598-024-52860-4 |
| work_keys_str_mv | AT janoslelkes vibrationsandenergydistributionininhomogeneousrodswithelasticandviscousboundaryconditions AT bendeguzdezsobak vibrationsandenergydistributionininhomogeneousrodswithelasticandviscousboundaryconditions AT tamaskalmarnagy vibrationsandenergydistributionininhomogeneousrodswithelasticandviscousboundaryconditions |