Theoretical, numerical, and experimental modal analysis of a single-winding gradient coil insert cylinder

The objective of this paper is to find the relatively low-frequency (200-2,000 Hz) mode shapes of a single-winding gradient coil cylinder with intermediate wall thickness. The dynamic behavior of a gradient coil cylinder plays a crucial role in determining and controlling the vibroacoustic performance of magnetic resonance imaging (MRI) scanners. Modal analyses of the gradient coil cylinder were carried out under different boundary conditions to obtain the various mode shapes. Theoretical modes, predicted by using modified Love's governing equations, and numerical modes simulated using a finite element method show close agreement with experimental modal results and reveal the mode shapes for both free-end and fixed-end boundary conditions. These results were further compared to in situ measurements of the mode shapes of the gradient coil cylinder insert during scanning in a 4 Tesla MRI. The general agreement among the analytical, numerical, and experimental mode shapes indicates that a linear combination of basic beam vibration and ring vibration patterns occupy the dynamic vibration modes in the low frequency range. The in situ vibration measurements show that the forcing function developed by the distributed Lorentz forces on the surface of the single-winding gradient coil results in predominantly beam-type bending mode patterns in the low frequency range.