区分変断面を有する座屈後はりの非線形振動解析

抄録

In this study, a new analytical procedure on nonlinear vibrations of a post-buckled stepped beam. The beam is divided into a few segments to express the geometry of the stepped beam. The deflection of the beam is expanded with the mode shape function that is expressed with the product of truncated power series and trigonometric functions. Taking the axial displacements, the deflections, slopes, bending moments and shearing forces at the nodes of the segments as unknown variables, nonlinear coupled ordinary differential equations are derived with the Galerkin procedure. Different from the previous analysis, the axial displacements at the both ends of the segments are expressed in terms of deflection, which makes it possible to consider nonlinear coupling between lateral and axial deformation of a stepped beam. These numerical results on nonlinear vibrations are compared with the experimental results.