On the existence of equilibrium states of an elastic beam on a nonlinear foundation
This paper concerns the existence and uniqueness of equilibrium states of a beam-column with hinged ends which is acted upon by axial compression and lateral forces and is in contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth-order nonlinear boundary va...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000225 |
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| _version_ | 1832560552852848640 |
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| author | M. B. M. Elgindi D. H. Y. Yen |
| author_facet | M. B. M. Elgindi D. H. Y. Yen |
| author_sort | M. B. M. Elgindi |
| collection | DOAJ |
| description | This paper concerns the existence and uniqueness of equilibrium states of a beam-column with hinged ends which is acted upon by axial compression and lateral forces and is in
contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth-order nonlinear boundary value problem in which the source of the nonlinearity comes from the
lateral constraint (the foundation). Treating the equation of equilibrium as a nonlinear eigenvalue
problem we prove the existence of a pair of eigenvalue/eigenfunction for each arbitrary prescribed
energy level. Treating the equilibrium equation as a nonlinear boundary value problem we prove
the existence and uniqueness of solution for a certain range of the acting axial compression force. |
| format | Article |
| id | doaj-art-c66bbfebfb1f417eb1d8ce154254339e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c66bbfebfb1f417eb1d8ce154254339e2025-02-03T01:27:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116119319810.1155/S0161171293000225On the existence of equilibrium states of an elastic beam on a nonlinear foundationM. B. M. Elgindi0D. H. Y. Yen1Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire 54702, WI, USADepartment of Mathematics, Michigan State University, East Lansing 48824, MI, USAThis paper concerns the existence and uniqueness of equilibrium states of a beam-column with hinged ends which is acted upon by axial compression and lateral forces and is in contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth-order nonlinear boundary value problem in which the source of the nonlinearity comes from the lateral constraint (the foundation). Treating the equation of equilibrium as a nonlinear eigenvalue problem we prove the existence of a pair of eigenvalue/eigenfunction for each arbitrary prescribed energy level. Treating the equilibrium equation as a nonlinear boundary value problem we prove the existence and uniqueness of solution for a certain range of the acting axial compression force.http://dx.doi.org/10.1155/S0161171293000225existence of equilibrium statesbeam-columnelastic beam fourth-order nonlinear boundary value problemnonlinear eigenvalue problemsvariational methods. |
| spellingShingle | M. B. M. Elgindi D. H. Y. Yen On the existence of equilibrium states of an elastic beam on a nonlinear foundation International Journal of Mathematics and Mathematical Sciences existence of equilibrium states beam-column elastic beam fourth-order nonlinear boundary value problem nonlinear eigenvalue problems variational methods. |
| title | On the existence of equilibrium states of an elastic beam on a nonlinear foundation |
| title_full | On the existence of equilibrium states of an elastic beam on a nonlinear foundation |
| title_fullStr | On the existence of equilibrium states of an elastic beam on a nonlinear foundation |
| title_full_unstemmed | On the existence of equilibrium states of an elastic beam on a nonlinear foundation |
| title_short | On the existence of equilibrium states of an elastic beam on a nonlinear foundation |
| title_sort | on the existence of equilibrium states of an elastic beam on a nonlinear foundation |
| topic | existence of equilibrium states beam-column elastic beam fourth-order nonlinear boundary value problem nonlinear eigenvalue problems variational methods. |
| url | http://dx.doi.org/10.1155/S0161171293000225 |
| work_keys_str_mv | AT mbmelgindi ontheexistenceofequilibriumstatesofanelasticbeamonanonlinearfoundation AT dhyyen ontheexistenceofequilibriumstatesofanelasticbeamonanonlinearfoundation |