Complex dynamics and multistability in nonlinear resonant nanosystems beyond the duffing critical amplitude

International audienceAnalytical multi-physics models which include main sources of nonlinearities for nanoresonators electrostatically actuated are developed in order to assess complex dynamics in nanosystems beyond the Duffing critical amplitude. In particular, multistability is investigated for doubly clamped beams and cantilevers. The bifurcation topology of a particular multistable behavior (up to five amplitudes for a given frequency) is parametrically identified and experimentally validated

Internal resonances in nonlinear nanocantilever arrays under electrostatic actuation

International audienceThe nonlinear dynamics of nanoelectromechanical cantilever arrays is investigated using a comprehensive analytical multiphysics model that takes into account geometric and electrostatic nonlinearities. In particular, the internal resonances between the different cantilevers are analyzed using a multi-modal Galerkin discretization coupled with a perturbation technique. Such systems offer a perfect mechanical synchronization, interesting nonlinear behaviors and exchange of energy between their different components which makes them potential candidates for multi-mass sensing applications

Overcoming limitations of nanomechanical resonators with simultaneous resonances

Dynamic stabilization by simultaneous primary and superharmonic resonances for high order nonlinearity cancellation is demonstrated with an electrostatically-actuated, piezoresistively-transduced nanomechanical resonator. We prove experimentally how the combination of both the third-order nonlinearity cancellation and simultaneous resonances can be used to linearly drive a nanocantilever up to very large amplitudes compared to fundamental limits like pull-in occurrence, opening the way towards resonators with high frequency stability for high-performance sensing or time reference

Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors

International audienceLarge-amplitude non-linear vibrations of micro- and nano-electromechanical resonant sensors around their primary resonance are investigated. A comprehensive multiphysics model based on the Galerkin decomposition method coupled with the averaging method is developed in the case of electrostatically actuated clamped-clamped resonators. The model is purely analytical and includes the main sources of non-linearities as well as fringing field effects. The influence of the higher modes and the validation of the model is demonstrated with respect to the shooting method as well as the harmonic balance coupled with the asymptotic numerical method. This model allows designers to investigate the sensitivity variation of resonant sensors in the non-linear regime with respect to the electrostatic forcing

Pull-In Retarding in Nonlinear Nanoelectromechanical Resonators Under Superharmonic Excitation

International audienceIn order to compensate for the loss of performance when scaling resonant sensors down to NEMS, a complete analytical model, including all main sources of nonlinearities, is presented as a predictive tool for the dynamic behavior of clamped-clamped nanoresonators electrostatically actuated. The nonlinear dynamics of such NEMS under superharmonic resonance of an order half their fundamental natural frequencies is investigated. It is shown that the critical amplitude has the same dependence on the quality factor Q and the thickness h as the case of the primary resonance. Finally, a way to retard the pull-in by decreasing the AC voltage is proposed in order to enhance the performance of NEMS resonators

Nonlinear phenomena in nanomechanical resonators: mechanical behaviors and physical limitations

International audienceIn order to overcome the loss of performances issue when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to large displacements and hence high nonlinearities. A comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities in the case of a capacitive doubly clamped beam is presented. This purely analytical model captures all the nonlinear phenomena present in NEMS resonators electrostatically actuated including bistability, multistability which can lead to several physical limitations such as noise mixing, frequency stability deterioration as well as dynamic pull-in. Moreover, close-form expressions of the critical amplitudes and pull-in domain initiation amplitude are provided which can potentially serve for NEMS designers as quick design rules

Capteurs résonants M/NEMS et phénomènes non linéaires

Accessible via http://www.bruit.fr/flipbook/AT57/index.html#/10/Les capteurs résonants de type M/NEMS jouent et joueront un rôle essentiel dans les nouvelles technologies. Cependant leur comportement est souvent fortement non linéaire ce qui est préjudiciable à la précision de la mesure exigée. Les résonateurs M/NEMS analysés ont des comportements complexes combinant raidissements, assouplissements, instabilités latérales car régis par des larges déflexions, des excitations paramétriques, des couplages géométrique et électrique. Ces comportements nécessitent une conception soigneuse qui doit s'appuyer sur des modèles les plus simples possibles mais tout en gardant leur pertinence pour modéliser au mieux les différents phénomènes physiques en jeu

Non linear dynamics of Mathieu resonators for resonant gyroscope applications

A complete model describing the non linear dynamics of Mathieu resonators is presented in order to study the stability of resonant MEM gyroscopes

Mixed behavior identification in nonlinear nanomechanical resonators

International audienceThe small size of NEMS resonators combined with their physical attributes make NEMS quite attractive and suitable for a wide range of technological applications such as ultrasensitive force and mass sensing, narrow band filtering, and time keeping. However, at this size regime, nonlinearities occur sooner which reduce the NEMS dynamic range [1]. Consequently, a nonlinear multiphysics model is needed as a tool of performances optimization in resonant sensors for MEMS and NEMS designers. To this end, the nonlinear behavior of resonators remains yet to be explored, and numerous models have been presented. Some models are purely analytical [2, 3] but they include coarse assumptions concerning nonlinearities. Other models [4, 5] are more complicated and use numerical simulations which make them less interesting for MEMS designers. In the present paper, a compact and analytical model including the main sources of nonlinearities (mechanical and electrostatic) is presented and validated thanks to the fabrication of a resonant accelerometer and the characterization of its sensing element, an electrostatically doubly clamped beam. A perturbation technique, the averaging method [6], has been used to obtain two first-order-nonlinear-ordinary-differential equations which describe the amplitude and phase modulation of the response and allows the computation of its stability. This analytical approach proves to be a powerful and quick tool for the sensor design, enabling the description of the competition between the hardening and the softening behavior (Figure 1), and thus the capture of all possible dynamic behaviors, particularly, the mixed behavior characterized by four bifurcation points. Furthermore, the model may be used as a tool to enhance the dynamic range of the resonator, i.e. its detectability. On the way from MEMS to NEMS, a "small" MEMS resonant accelerometer [1] shown in Figure 2a has been fabricated. The sensor structure has not been designed to display high inertial performances, but rather is a way to validate process [7], characterization and model choices. In order to electrically characterize its sensitive part (the resonator described in Figure 2b), the device was placed in a vacuum chamber (down to 1 mTorr), and the 2-port electrical measurements were performed at room temperature using a low noise lock-in amplifier (Signal Recovery 7280). The drive voltage is V ac = 0.5V and the beam is polarized with V dc = 10V. This ensures a mixed behavior as shown in Figure 3. The quality factor obtained with this polarization voltage and in a linear regime is 4000. The critical amplitude [7] is then A c = 53nm, i.e. V c = 25µV. The peak obtained is then far beyond A c , up to 75% of the gap. The mixed behavior is fully identified with its four bifurcation points using a sweep up frequency to capture the points P and 2 as well as a sweep down frequency for points 1 and 3. Moreover, we experimentally track the point P (mixed behavior initiation point) while varying the drive and the bias voltage and we show that this bifurcation point is fixed by the design parameters. Then, the mixed behavior can be retarded and avoided by designing resonators for which the P point amplitude is close to the gap. Further measurements are under work to validate the dynamic range enhancement based on the compensation of the nonlinearities shown by the model

High Order Nonlinearities and Mixed Behavior in Micromechanical Resonators

International audienceThis paper investigates the sensitivity of the third order nonlinearity cancellation to the mixed (hardening and softening) behavior in electrostatically actuated micromechanical resonators under primary resonance at large amplitudes compared to the gap. We demonstrate the dominance of the mixed behavior due to the quintic nonlinearities, beyond the critical amplitude when the third order mechanical and electrostatic nonlinearities are balanced. We also report the experimentalobservation of a strange attraction which can lead to a chaotic resonator