Stabilisation of nonlinear beams

Abstract

In this thesis we develop large amplitude models for the planar motion of beams under the influence of certain feedback boundary conditions. These are generalisations of the standard linear models, but the geometric construction gives rise to nonlinearities in the equations of motion. Finite element methods are applied to calculate approximate solutions of the equations while Galerkin approximations are used to generate weak solutions. Existence of classical solutions for both the nonlinear Rayleigh and Euler-Bernoulli beam models is proved and it is shown that these solutions are uniformly exponentially stable.