The development of new types of offshore wind turbine on floating platforms requires the development of new approaches to modelling the combined platform-turbine system. In this thesis a linearised frequency-domain approach is developed which gives fast but approximate results: linearised models of the structural dynamics, hydrodynamics, aerodynamics and control system dynamics are brought together to find the overall response of the floating wind turbine to harmonic wind and wave loading.

Initially, a nonlinear flexible multibody dynamics code is developed and verified, which is then used to provide reference nonlinear simulation results. The structural dynamics of a wind turbine on a moving platform are shown to be nonlinear, but for realistic conditions the effects are small.

An approximate analysis of the second-order response of floating cylinders to hydrodynamic loads suggests slow drift motion may be relatively small for floating wind turbines, compared to other floating offshore structures.

The aerodynamic loads are linearised using both harmonic and tangent linearisation approaches; the harmonic linearisation gives improved results when stall occurs. The wake dynamics can also be included. The control system behaviour is linearised using the same method, which works well when the wind speed is far from the rated wind speed; close to the rated wind speed the nonlinearity is stronger, but further improvement should be possible.

These sub-models are combined to give a simple but complete model of a floating wind turbine, with flexible blades and a flexible tower, but neglecting the control system behaviour, wake dynamics and nonlinear hydrodynamic loads. For the OC3-Hywind turbine, the accuracy of the results is assessed by comparison to nonlinear time-domain simulations using the commercial code Bladed. Peak-peak errors of less than 5 % are achievable for many harmonic wind and wave inputs, but certain conditions lead to larger errors. The effect of including linearised control system behaviour is demonstrated for a subset of conditions. Overall, the results are promising but more work is needed for practical application.