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.

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.

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%.