### 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.

Original language | English |
---|---|

Pages (from-to) | 193-198 |

Number of pages | 6 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |

### Fingerprint

### Keywords

- beam-column
- elastic beam
- Existence of equilibrium states
- fourth-order nonlinear boundary value problem
- nonlinear eigenvalue problems
- variational methods

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**On the Existence of Equilibrium States of an Elastic Beam on a Nonlinear Foundation.** / Elgindi, Mohamed; Yen, D. H.Y.

Research output: Contribution to journal › Article

*International Journal of Mathematics and Mathematical Sciences*, vol. 16, no. 1, pp. 193-198. https://doi.org/10.1155/S0161171293000225

}

TY - JOUR

T1 - On the Existence of Equilibrium States of an Elastic Beam on a Nonlinear Foundation

AU - Elgindi, Mohamed

AU - Yen, D. H.Y.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

KW - beam-column

KW - elastic beam

KW - Existence of equilibrium states

KW - fourth-order nonlinear boundary value problem

KW - nonlinear eigenvalue problems

KW - variational methods

UR - http://www.scopus.com/inward/record.url?scp=84969005166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969005166&partnerID=8YFLogxK

U2 - 10.1155/S0161171293000225

DO - 10.1155/S0161171293000225

M3 - Article

VL - 16

SP - 193

EP - 198

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

IS - 1

ER -