Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach

• 作者: Dimitrios S. Sophianopoulos
• 来源期刊: 力学国际期刊(英文)
• 学科: 数学
• 关键词: Mechanical Models Nonlinear Stability DISTINCT Critical POINTS BIFURCATION Theory SINGULARITIES
• 年，卷（期）: 2013,（1）
• 页码范围: 62-81
• 页数: 20页
• 分类号: O1

摘要

The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pioneer as well as in more recent literature to exhibit all kinds of distinct critical points. Its response is thoroughly discussed, the effect of all parameters involved is extensively examined, including imperfection sensitivity, and the results obtained lead to the important conclusion that the model is possibly associated with the butterfly singularity, a fact which will be validated by the contents of a companion paper, based on catastrophe theory.