The present embodiments relate to a method for reducing mechanical vibrations in a magnetic resonance imaging system that includes a gradient system having a gradient coil body and an electrically conductive shroud that at least partly encloses the gradient coil body. The method includes determining a mechanical natural vibration mode of the gradient coil body in the magnetic resonance imaging system, and determining excitation force components for the natural vibration mode. The method also includes determining electrically conductive areas of the gradient system, which during operation of the magnetic resonance imaging system, generate a Lorentz force component that contributes to the excitation force components. The method further includes modifying the determined electrically conductive areas such that a minimal number of the Lorentz force components coincide with the excitation force components.