细长弹性杆在轴压下的二次分叉

SECONDARY BIFURCATIONS OF A SLENDER ELASTIC BAR UNDER AXIAL COMPRESSION

基于[1]的弹性曲杆的平衡方程,本文研究了矩形横截面细长杆在轴压下的后屈曲行为。设横截面的边长比为 1:2δ,使用 Poincare-Keller 的打靶法并引进坐标的伸缩变换,研究了δ在 δ_0=1 附近的情形。当δ≠1 时,发现了杆平衡态的二次分叉。我们也给出了原始后屈曲解支及二次分支的渐近表示并分析了各个解支的稳定性。

Based on the equilibrium equation of an elastic curved bar in [1] , the post-buckling behavior of a slender bar with rectangular cross-section under axial compression is studied. Let the ratio of the lengths of the sides of the cross-section be 1:26. By using Poin-care-Keller's shooting method and introducing rescaling functions, we investigate the case in which 6 is in a neighborhood of δ0= 1. The secondary bifurcations of the equilibrium state of the bar are found whenδ≠1; we also give the asymptotic unfoldings of the primary branchesand secondary branches, and make analysis on the stability of each branch.Based on the equilibrium equation of an elastic curved bar in [1] , the post-buckling behavior of a slender bar with rectangular cross-section under axial compression is studied. Let the ratio of the lengths of the sides of the cross-section be 1:26. By using Poin-care-Keller's shooting method and introducing rescaling functions, we investigate the case in which 6 is in a neighborhood of δ0= 1. The secondary bifurcations of the equilibrium state of the bar are found whenδ≠1; we also give the asymptotic unfoldings of the primary branchesand secondary branches, and make analysis on the stability of each branch.