Magnetic restoring forces on rocking blocks

Abstract

This study investigates the idea of adding an extra magnetic restoring force to a rocking block to improve its overall dynamic performance. The proposed concept ensues by introducing a pair of identical magnets to the rocking block. Both magnets are considered lumped on their respective volume centers and are embedded within the rocking block and the supporting base. When properly magnetized, this pair of magnets provides the rocking block with an extra magnetic restoring force which, although it takes on its maximum value when the two magnets are in contact, decreases as the distance between the two magnets increases. The proposed concept, subjected to pulse-type base excitations, reveals the inherent problem of magnetic restoring forces. From the overturning spectra of the rocking block, it is found that there are cases where the block fails (overturning) in the presence of magnets, while the same free-of-magnets block rocks safely (no overturning) when its own weight acts as the only restoring force. This interesting finding appears to be counterintuitive. Is it possible that by providing additional restoring force the block is “driven” to overturn? This study shows that when the rocking block returns toward the vertical position, the angular velocity, in the presence of magnets, is higher than the angular velocity, in the absence of them. This increase in the angular velocity is a direct outcome of the nature of the magnetic restoring forces, and it is mainly the reason that causes the overturning of the rigid block during its free vibration regime. To mitigate the shortcomings of using magnetic restoring forces, the idea of a semi-active control of the pair of magnets is introduced and explained in detail. This paper concludes with the advantages and potential disadvantages of the overall performance of rigid blocks in the presence of magnetic restoring forces.