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

Abstract

Eigen frequencies for two dimensional beam structures are investigated under initial axial displacements. When the beam structures are consisted of extremely thin flexible components, the shapes of the structures are changed due to the initial axial displacement. And then, their eigen frequencies are affected by the axial displacements. To analyze these phenomena, discrete equations using finite elements with consideration of geometrical nonlinearity are derived as cubic simultaneous nonlinear differential equations. First, large static deformations of the structures due to initial axial displacement are calculated using the proposed FEM. Linear natural frequencies for the deformed structures are investigated secondly. In the numerical analysis, both ends of the beam structures are clamped. The calculated results for straight beams with initial compressive displacement using the FEM are consistent with the theoretical results carried out by the authors previously. Further, the influences of initial axial displacement on eigen frequencies of the plane structure which is comprised of five straight beams are clarified.