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This paper describes that eigen frequencies for two dimensional beam structures under gravity. Because the beam structures were consisted of extremely thin flexible components, the shapes of the structures were changed due to their self-weight. And both ends of the beam structures were assumed to be clamped, To analyze these phenomena, discrete equations using finite element in consideration with geometrical nonlinearity were derived as cubic simultaneous nonlinear differential equations. First, large static deformations of the structures due to gravity were calculated using the proposed FEM. Next, linear natural frequencies for the deformed structures were investigated. The calculated results for straight beams and shallow arches using the FEM were consistent with the theoretical results carried by authors previously. Further, the influences of self-weight on eigen frequencies of the structure which was comprised of three straight beams were clarified.

Eigen Frequencies of Two-Dimensional Beam Structures Subjected to Large Static Deformations due to Gravity (FEM Analysis with Geometric Nonlinearity)