A simple theory for vibration of MRI gradient coils

Vibrations of a string can provide a model for vibrations of MRI coil assemblies. The string model for the vibrations of MRI coils is presented, and compared with experimental results. Gradient coils exhibit resonant modes because of the finite coil length, l, and the elasticity of materials that comprise the assembly. The resonance frequencies depend on l and the Young modulus, as well as on the current distribution. Under longitudinal gradient pulses, anti-symmetrical modes of surface vibration are produced due to the symmetry of current distribution. In contrast, transverse gradient pulses produce coil bending that results in symmetrical vibration modes of the coil axis. The viscosity of the assembly materials controls the width of the vibrational resonance modes. Experimental results are in agreement with this simple string model.