Search results for "Transcritical bifurcation"

On Bifurcation Analysis of Implicitly Given Functionals in the Theory of Elastic Stability

2015

In this paper, we analyze the stability and bifurcation of elastic systems using a general scheme developed for problems with implicitly given functionals. An asymptotic property for the behaviour of the natural frequency curves in the small vicinity of each bifurcation point is obtained for the considered class of systems. Two examples are given. First is the stability analysis of an axially moving elastic panel, with no external applied tension, performing transverse vibrations. The second is the free vibration problem of a stationary compressed panel. The approach is applicable to a class of problems in mechanics, for example in elasticity, aeroelasticity and axially moving materials (su…