Eddy current shielding by a Faraday cage is an effective way to shield alternating-current magnetic fields in scientific instrumentation. In a strong static magnetic field, however, the eddy current in the conductive shield is subject to the Lorentz force, which causes the shield to vibrate. In addition to mechanical issues (e.g., acoustic noise), such vibration induces motional eddy current in the shield that can dominate the original, electromagnetic eddy current to undermine the conductor's shielding capability. In this work, we investigate a method to control motional eddy current by making cut-out patterns in the conductor that follow the electromagnetic eddy current image. This effectively limits the surface current of the plate to a single mode and prevents the proliferation of uncontrolled motion-induced surface currents that disrupts eddy current shielding. After developing a comprehensive theory of magneto-mechanical interaction in a conductive plate, the proposed method was tested on a flat-geometry testbed experiment inside a 3 T magnetic resonance imaging (MRI) magnet. It was found that the magnetic field generated by the motional eddy current was much more localized in space and frequency for a patterned-copper shield compared to a solid copper. The magnetic field of the patterned shield could be accurately predicted from the impedance measurement in the magnet. Implications of our results for improved shielding of gradient fields in high-field MRI are discussed.