Geometry optimization of a Lorentz force, resonating MEMS magnetometer

Stochastic Effects on the Dynamics of a Resonant MEMS Magnetometer: A Monte Carlo Investigation

“…As already reported in [2], part of the resonating structure of the studied Lorentz force MEMS magnetometer is as shown in Figure 1. This structure senses any magnetic field aligned with the outof-plane direction ( , according to the reference frame of Figure 1); sensing is obtained thanks to the two parallel plates attached to the mid-span cross-section of the beam.…”

“…where, see [2]: (4) represent the effective mass, damping, linear and cubic stiffness, and external load terms. In Eqs.…”

“…Finally, the external load accounts for the Lorentz effect, as it results proportional to the density of the current flowing in the beam and to the external magnetic field . Relation (3), known as the Duffing equation, provides a maximum amplitude at varying circular frequency of the forcing term as a solution to [2]:…”

“…To design and predict the performance of this kind of devices, it is required to accurately model the interaction of various physical fields like the mechanical, thermal, electric and magnetic ones. In recent years, different numerical and analytical methods were proposed to better understand the underlying working principles, and increase the ability to capture the experimental evidence [1][2][3].…”

“…To model its dynamics, a coupled thermo-electro-magneto-mechanical formulation was presented in [2] and is here further discussed, along with a rather standard approach to obtain a relevant reduced-order (1 degree-of-freedom, DOF) model. We then exploit a numerical homogenization procedure to obtain the probability density function (pdf) of the Young's modulus for a representative volume of polycrystalline films.…”