[en] In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.

[en] Highlights: • Dynamic range improvement of electrostatically actuated circular microplates. • Pull-in instability tuning based on geometric nonlinearity and imperfections. • Predictive computational model for the nonlinear behavior of circular microplates. - Abstract: Dynamic range improvement based on geometric nonlinearity and initial deflection is demonstrated with imperfect circular microplates under electrostatic actuation. Depending on design parameters, we prove how the von Kármán nonlinearity and the plate imperfections lead to a significant delay in pull-in occurrence. These promising results open the way towards an accurate identification of static parameters of circular microplates and the development of a predictive model for the nonlinear dynamics of imperfect capacitive micromachined ultrasonic transducers.

[en] A multiphysics model of a hybrid piezoelectric–electromagnetic vibration energy harvester (VEH), including the main sources of nonlinearities, is developed. The continuum problem is derived on the basis of the extended Hamilton principle, and the modal Galerkin decomposition method is used in order to obtain a reduced-order model consisting of a nonlinear Duffing equation of motion coupled with two transduction equations. The resulting system is solved analytically using the method of multiple time scales and numerically by means of the harmonic balance method coupled with the asymptotic numerical continuation technique. Closed-form expressions for the moving magnet critical amplitude and the critical load resistance are provided in order to allow evaluation of the linear dynamic range of the proposed device. Several numerical simulations have been performed to highlight the performance of the hybrid VEH. In particular, the power density and the frequency bandwidth can be boosted, by up to 60% and 29% respectively, compared to those for a VEH with pure magnetic levitation thanks to the nonlinear elastic guidance. Moreover, the hybrid transduction permits enhancement of the power density by up to 84%. (papers)

[en] In this paper, we present a fully tunable system able to generate mode localization between a $170000$ Q-factor quartz crystal microbalance at $1\mathrm{M}\mathrm{H}\mathrm{z}$ and a digital device (field programmable gate array) simulating in real time the presence of an identical and weakly-coupled second resonator. Indeed, this method allows to precisely select each parameter value and thus to reach the optimal configuration with the maximum sensitivity to perturbations. In addition, this design gives a perfect adaptability to the geometry of the piezoelectric resonator, that allows to work with much higher frequencies and Q-factors than conventional cantilevers or tuning-forks usually selected for the design of mode-localized sensors. The experimental sensitivities reached in this work are at least two orders of magnitude higher than the ones found in the literature, which is promising for the design of a new generation of ultrasensitive sensors based on Anderson localization. (letter)

[en] This letter demonstrates the linear dynamic range enhancement of a mode-localized microelectromechanical systems sensor based on two weakly coupled cantilevers under electrostatic actuation resulting in a repulsive force. An analytical model is proposed to design the sensor, and the expression of the electrostatic force is obtained using a finite element simulation. Compared to attractive electrostatic actuation, the intensity of the resulting force is less sensitive to the change in the cantilever’s displacement, with negligible electrostatic nonlinearities. This result is confirmed by experimental measurements showing linear vibrations up to 70% of the gap, which is almost three times higher than the electrostatic critical amplitude of a similar device using attractive electrostatic force. Finally, the mass sensing capability is highlighted by depositing a few picograms of platinum on the sensor. (letter)

[en] This paper describes a comprehensive nonlinear multiphysics model based on the Euler–Bernoulli equation that remains valid up to large displacements in the case of electrostatically actuated nanocantilevers. This purely analytical model takes into account the fringing field effects which are significant for thin resonators. Analytical simulations show very good agreement with experimental electrical measurements of silicon nanodevices using wafer-scale nanostencil lithography (nSL), monolithically integrated with CMOS circuits. Close-form expressions of the critical amplitude are provided in order to compare the dynamic ranges of NEMS cantilevers and doubly clamped beams. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility of driving the cantilever beyond its critical amplitude. Consequently, the sensor performance can be enhanced by being optimally driven at very large amplitude, while maintaining linear behavior

[en] We propose a multi-modal vibration energy harvesting approach based on arrays of coupled levitated magnets. The equations of motion which include the magnetic nonlinearity and the electromagnetic damping are solved using the harmonic balance method coupled with the asymptotic numerical method. A multi-objective optimization procedure is introduced and performed using a non-dominated sorting genetic algorithm for the cases of small magnet arrays in order to select the optimal solutions in term of performances by bringing the eigenmodes close to each other in terms of frequencies and amplitudes. Thanks to the nonlinear coupling and the modal interactions even for only three coupled magnets, the proposed method enable harvesting the vibration energy in the operating frequency range of 4.6–14.5 Hz, with a bandwidth of 190% and a normalized power of $20.2\mathrm{m}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-<!--\; ???\; -->3}{\mathrm{g}}^{-<!--\; ???\; -->2}$. (paper)