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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |