Affiliations: Department of Ocean and Mechanical Engineering,
Florida Atlantic University, Boca Raton, FL, USA | Institut Français de Mécanique
Avancée, Aubière, France
Note: [] Corresponding author: Isaac Elishakoff, Department of Ocean and
Mechanical Engineering, Florida Atlantic University, Boca Raton, FL33431-0991,
USA. Tel.: +1 561 297 2729; Fax: +1 561 297 2825; E-mail: [email protected]
Abstract: 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.
Keywords: Interval analysis, beam vibrations, rotational springs, parametrization technique
