Vibration modes of the brushless DC motor

The objective of this project is to determine in an analytical way the modes of vibration of the stator of a brushless DC motor. The knowledge of these modes is important. Once the vibration modes are determined we can avoid their excitation and thus reduce the noise emitted by the motor and its stress. This task is already performed by the use of finite element methods but they have the disadvantage of hiding the relations between the geometry of the stator and the vibration frequencies. In the first part the geometrical assumptions will be presented as well as the description of the deformations. Then the demonstration of the equation describing the vibration will be presented particularly for curved beams. The model of the thick beam or Timoshenko beam theory has been chosen. Contrary to the Euler-Bernoulli model, this model takes into account the effect of rotary inertia and shear deformation. The chapter 3 will present additional relation that will be used in chapter 4 dedicated to the resolution of the vibration modes and the determination of the vibration frequencies. The chapter 5 will brie y conclude on a few results.