Stability of certain models of suspension bridges.

Abstract

In this thesis the problem of stability and analysis of distributed dynamical systems with applications to engineering is considered. A methodology has been developed for rigorous modelling of suspension bridges. It was shown that the complete dynamics of the system could be described by a coupled system of hyperbolic partial differential equations. Two models (A) and (B) have been developed. These models are generalized cases of those proposed by Lazer and McKenna and that suggested by Jacober-McKenna, which includes aerodynamic forces as developed by Maurice Roseau. Stability of the system has been proved using Lyapunov's approach under different types of dynamic loading. Further the model (B) has been extended to its stochastic counter parts. Stability of suspension bridge in the presence of distributed white noise has been investigated. Also, for each loading situation, the results are illustrated by numerical simulation with physical interpretation. And finally a dynamic model of suspension bridge based on Kirchhoff plate model as road way has been presented.