On the effect of local boundary condition details on the natural frequencies of simply-supported beams: Eccentric pin supports

Pinned supports, or simple supports, are boundary conditions frequently encountered in the analysis of beams, plates, and shells. Simply supported boundary conditions can be modeled as restricting the lateral motion of the structure but freely allowing rotation at the boundaries. The literature to date has treated simple supports as though they are solely pinned at the mid-plane of the structure; however, the present study investigates the effects of eccentric pinned supports on the natural frequencies of beam structures.A COMSOL finite element model is created to investigate the changes in the natural frequencies of a beam structure with respect to the through-thickness location of the pin supports. Through this study it is found that the natural frequencies are significantly influenced by pin support eccentricity. For the beams considered in this article, it is seen that moving the pin supports from the mid-plane to the bottom edge raises the first natural frequencies by over 55%, regardless of beam length.To verify the COMSOL finite element model results, a Rayleigh–Ritz approximate solution for the natural frequencies is also obtained. To capture pin eccentricity, a novel cross-sectional geometry is proposed that incorporates fictitious material through the beam thickness. This fictitious material approach is completely compatible with the existing literature pertaining to the analysis of thin beams. The natural frequencies are confirmed to be strong functions of pin eccentricity, with the Rayleigh–Ritz results matching the COMSOL results to well within 4%. From this study it can be concluded that the through-thickness location of pin supports are significant and must be specified.