Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach
Dimitrios S. Sophianopoulos
DOI: 10.4236/wjm.2013.31005   PDF   HTML   XML   4,590 Downloads   7,906 Views   Citations


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.

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D. Sophianopoulos, "Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach," World Journal of Mechanics, Vol. 3 No. 1, 2013, pp. 62-81. doi: 10.4236/wjm.2013.31005.

Conflicts of Interest

The authors declare no conflicts of interest.


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