Suspension bridges with non-constant stiffness: bifurcation of periodic solutions

Abstract

We consider a modified version of a suspension bridge model with a spatially variable stiffness parameter to reflect the discrete nature of the placement of the bridge hangers. We study the qualitative and quantitative properties of this model and compare the cases of constant and non-constant coefficients. In particular, we show that for certain values of the stiffness parameter, the bifurcation occurs. Moreover, we can expect also the appearance of blowups, whose existence is closely connected with the so-called Fucik spectrum of the corresponding linear operator.