On the existence of equilibrium states of an elastic beam on a nonlinear foundation

M. B. M. Elgindi and D. H. Y. Yen

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-6

Abstract:

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:390576

DOI: 10.1155/S0161171293000225

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