Magnetostatic Spring Softening and Stiffening in Magneto-Mechanical Resonator Systems

Integrating magnets into resonant mechanical systems allows for intriguing capabilities, such as the ability to tune the mechanical resonance frequency or induce coupling between resonators without any physical contact. Here, we present analytical models as well as the experimental study of an integrated magneto-mechanical system. Using a point dipole approximation, we explore the magneto-static spring effect, which can either soften or stiffen a spring depending on dipole orientation and spatial position of the magnets. We use translational and rotational resonance as commonly encountered demonstrative cases and, experimentally, demonstrate both the spring softening and stiffening effects.