Dynamic models of suspension bridges and their stabilities.

Abstract

Suspension bridges have a history of large-scale oscillations caused by wind, earthquake or traffic forces which may lead to structural failure. As a result of these oscillations and the probable resonance effects, the cables start to loosen and tighten producing a nonlinear effect. This nonlinear effect is very complex to model and only limited research has been conducted in this area. Therefore, there is a need to give a clear mathematical argument as to why suspension bridges oscillate and find the effect of nonlinearity behaviour of their cables. In order to clarify the oscillations and nonlinearity effect behaviour, this thesis presents a four dynamic Partial Differential Equations (PDE) models of suspension bridges. These models are generalized cases of those proposed by Lazer and McKenna. Further, an analytical study of the stability properties of these models under different types of dynamic loading is performed. Furthermore, for each loading situation, the results are illustrated by numerical simulation with physical interpretation.