Parametric linear vibration response studies for longitudinal whole-body gradient coils: Theoretical predictions based on an exact linear elastodynamic model
Magnetic Resonance Imaging
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Passive reduction of gradient coil (GC) cylinder vibration depends critically on a thorough knowledge of how all pertinent physical parameters affect the vibration response. In this paper, we employ a recently introduced linear elastodynamic Z-coil model to study how the displacement response of a whole-body GC cylinder (subject to exclusive excitation of its Z-coil windings) is affected by independent regularized variations in its: (i) length; (ii) radial thickness; (iii) mass density; (iv) Poisson ratio; and (v) Young modulus (stiffness). The results exhibit a rich variety of behaviors at different excitation frequencies, and in the parameter ranges of interest, the displacement response is found to be particularly sensitive to variations in cylinder geometry and mass density. The results also show that, with the exception of the stiffness, there are no optimal ranges of regularized values of the considered parameters that will reduce the displacement (and hence the vibration) of a GC cylinder at all frequencies of interest. For typical GC cylinder geometries and densities, and under the condition that only the Z-coil windings are excited, the model predicts that increasing the cylinder stiffness above 100 GPa will reduce vibration at all frequencies below 2000 Hz.