TITLE:
Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach
AUTHORS:
Dimitrios S. Sophianopoulos
KEYWORDS:
Mechanical Models; Nonlinear Stability; Distinct Critical Points; Bifurcation Theory; Singularities
JOURNAL NAME:
World Journal of Mechanics,
Vol.3 No.1,
February
19,
2013
ABSTRACT: 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.