In their paper 1, the authors investigate the vibration damping of a beam by means of a permanent magnet whose axis is perpendicular to the vibration direction. They acknowledge the fact that only the radial magnetic field will participate in the damping, while the axial magnetic field has no effect.
They then propose an improved concept consisting of two magnets positioned on opposite sides of the beam, rather than a single magnet: “It is realized that when two similar magnetic poles are placed close to each other, the magnetic flux of each magnet is compressed in the poling direction, causing the intensity in the radial direction to be enhanced as shown in Fig. 2” (p. 295). This calls for the following comments:
Magnetic fields add vectorially. It is then misleading to say that using two opposite magnets will result in a ”compressed” magnetic field: what happens is that the two axial magnetic fields cancel each other, while the two radial fields add to each other. Two identical magnets produce a radial magnetic field exactly twice as high (no more, no less) as the one produced by a single magnet (this is apparent in Fig. 11).
It is true that the performances of the two magnets are impressive. This is because, as clearly explained in the paper, the damping force due to the eddy currents is proportional to the square of the radial magnetic field intensity (Eq. (14)). This means that doubling the intensity of the radial magnetic field will result in a structural damping four times higher. A single magnet produces a damping ratio of about 0.25–0.35 (Fig. 13); two magnets will produce a damping ratio greater than 1, i.e., overcritical damping.
As a conclusion, we found that the term “improved concept” is inappropriate: doubling the amount of magnetic material will do no more than double the useful (radial) magnetic field. A single magnet with a magnetization constant twice as high would produce the same result.