Finite time blow-up in nonlinear suspension bridge models

4Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

This paper settles a conjecture by Gazzola and Pavani [10] regarding solutions to the fourth order ODE w (4) +kw"+f(w)=0 which arises in models of traveling waves in suspension bridges when k < 0. Under suitable assumptions on the nonlinearity f and initial data, we demonstrate blow-up in finite time. The case k≤. 0 was first investigated by Gazzola et al., and it is also handled here with a proof that requires less differentiability on f. Our approach is inspired by Gazzola et al. and exhibits the oscillatory mechanism underlying the finite-time blow-up. This blow-up is nonmonotone, with solutions oscillating to higher amplitudes over shrinking time intervals. In the context of bridge dynamics this phenomenon appears to be a consequence of mutually-amplifying interactions between vertical displacements and torsional oscillations.

Cite

CITATION STYLE

APA

Radu, P., Toundykov, D., & Trageser, J. (2014). Finite time blow-up in nonlinear suspension bridge models. Journal of Differential Equations, 257(11), 4030–4063. https://doi.org/10.1016/j.jde.2014.07.017

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free