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Mathematical analogy of a beam on elastic supports as a beam on elastic foundation. (English) Zbl 1130.74029
Summary: This paper presents the mathematical hypothesis that a beam on equidistant elastic supports (BOES) can be considered as a beam on an elastic foundation (BOEF) in static and free vibration problems. This modeling of BOES as BOEF is presumed to be applicable to a limited range of support stiffness, spacing and flexural rigidity of the beam. We investigate the applicability of the modeling of BOEF from the property of characteristic solutions obtained from governing equations of both BOES and BOEF. In this study, the formulation of BOES leads to governing difference equations, and the motions of BOEF are expressed by differential equations. This is because exact solutions must be employed in order to verify accurately their analogy. The characteristic solutions obtained from these two governing equations are compared to each other in order to investigate the relationship between them.
MSC:
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
74H45Vibrations (dynamical problems in solid mechanics)