International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 193-198
doi:10.1155/S0161171293000225
On the existence of equilibrium states of an elastic beam on a nonlinear foundation
M.B.M. Elgindi1
and D.H.Y. Yen2
1Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire 54702, WI, USA
2Department of Mathematics, Michigan State University, East Lansing 48824, MI, USA
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.