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Shock and Vibration
Volume 20 (2013), Issue 1, Pages 143-156

Remedy to Overestimation of Classical Interval Analysis: Analysis of Beams with Uncertain Boundary Conditions

Isaac Elishakoff1 and Clément Soret2

1Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL, USA
2Institut Français de Mécanique Avancée, Aubière, France

Received 21 July 2011; Revised 13 December 2011

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study investigates both the static and dynamic behaviors for the uniform beam supported at its ends by rotational supports. The stiffness coefficients of these supports are treated as interval variables. It is first demonstrated on the static problem that the classical interval analysis may lead to overestimation of the response. The paper introduces a remedy for this "ill" of the classical interval analysis. The artificial interval parameter is introduced and the extrema of the static displacements and natural frequencies are determined. Finally, the hybrid case of uncertain boundary conditions and uncertain mass density is treated with attendant interesting results.