The mechanical vibrations of fuel assemblies have been shown to give rise to high levels of neutron noise, triggering in some circumstances the necessity to operate nuclear reactors at a reduced power level. This work simulates and analyses the effect in the neutron field of the oscillation of one single fuel assembly without considering thermal-hydraulic feedback. The amplitude of the fuel assembly vibration ranges from 0 to 1 millimetres and this implies the use of fine meshes and accurate numerical solvers. Results show two different effects in the neutron field caused by the fuel assembly vibration. First, a global slow variation of the total neutron power due to a change in the criticality of the system. Second, an in-phase change in the neutron flux with the assembly vibration. This second effect is more important and has a strong spatial dependence. This paper shows a comparison between a time domain analysis and a frequency domain analysis of the phenomena, in order to validate the time domain solution against the frequency domain solution. Numerical results shows a really close match between these two approaches.