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

Investigation on the Dynamics of an On-Board Rotor-Bearing System

International audienceIn ship and aircraft turbine rotors, the rotating mass unbalance and the different movements of the rotor base are among the main causes of vibrations in bending. The goal of this paper is to investigate the dynamic behavior of an on-board rotor under rigid base excitations. The modeling takes into consideration six types of base deterministic motions (rotations and translations) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are computed. The finite element method is used in the rotor modeling by employing the Timoshenko beam theory. The proposed on-board rotor model takes into account the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk. The Lagrange's equations are applied to establish the differential equations of the rotor in bending with respect to the rigid base which represents a noninertial reference frame. The linear equations of motion display periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the base rotational motions. In the proposed applications, the rotor mounted on rigid/elastic bearings is excited by a rotating mass unbalance associated with sinusoidal vibrations of the rigid base. The dynamic behavior of the rotor is analyzed by means of orbits of the rotor as well as fast Fourier transforms (FFTs)

Prediction of the non-linear dynamic behavior of on-board rotors under extreme solicitations

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Effect of support sinusoidal motions on the vibration of an on-board rotor-bearing system

International audienceIn generator and pump rotors installed in power plants, the rotating mass unbalance and the different motions of the rotor support are among the main sources of flexural vibrations. This work aims to observe the dynamic behavior of an on-board rotor subject to rigid support movements. The modeling takes into account six types of support deterministic motions (rotational and translational motions) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are calculated. The finite element method is applied using the Timoshenko beam theory. The proposed on-board rotor model considers the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk of the rotor. By computing the Rayleigh damping coefficients, the effect of rotor internal damping is included in the study. The Lagrange's equations are used to obtain the differential equations of the rotor in bending relative to the rigid support which forms a noninertial reference frame. The equations of motion exhibit periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the support rotations. In the presented applications, the rotor mounted on rigid/elastic linear bearings is excited by a rotating mass unbalance combined with sinusoidal oscillations of the rigid support. The dynamic behavior of the rotor is analyzed by means of rotor orbits and fast Fourier transforms (FFTs)

Steady-state response of a rotor excited by combined rotational and translational base motions

International audienceIn the transportation domain, the on-board rotor in bending is subjected not only to rotating mass unbalance but also to support movements. The equations of motion in bending of the rotating rotor take into account the geometric asymmetry of disks and/or shaft and consider six types of deterministic support motions. The application of Lagrange's equations using the finite element method based on the theory of Timoshenko leads to the equations of motion which highlight periodic parametric terms due to the asymmetry of the rotor and time-varying parametric terms due to the rotational base excitations. When the rotor base is subjected to combined rotation and sinusoidal translation, analytical solutions are derived and analyzed by means of Campbell diagrams and steady-state responses

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

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

Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics

International audienceA frequency-domain approach for direct parametric analysis of limit points of nonlinear dynamical systems is presented in this paper. Instead of computing responses curves for several values of a given system parameter, the direct tracking of limit points is performed. The whole numerical procedure is based on the Harmonic Balance Method and can be decomposed in three distinct steps. Firstly, a response curve is calculated by HBM combined with a continuation technique until a limit point is detected. Then this starting limit point is used to initialize the direct tracking of limit points which is based on the combination of a so-called extended system and a continuation technique. With only one computation, a complete branch of limit points is obtained, which provides the stability boundary with respect to system parameters such as nonlinearity or excitation level. Several numerical examples demonstrate the capabilities and the performance of the proposed method

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

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