Méthode Asymptotique Numérique adaptative pour la dynamique transitoire non-linéaire

National audienceCet article décrit le couplage de la Méthode Asymptotique Numérique (MAN) avec un schéma d’intégration temporelle permettant la dissipation numérique des hautes fréquences tout en conservant les moments linéaires et angulaires. Différentes stratégies sont présentées afin d’optimiser l’efficacité de la méthode proposée, dont l’adaptation de l’ordre des séries de la MAN à chaque pas de temps. L’algorithme obtenu est appliqué à des structures minces fortement non linéaires discrétisées par éléments finis

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

Direct computation of paths of limit points using the Asymptotic Numerical Method

International audienceThis paper is concerned with parameter dependent problems for structural instability. The aim is the direct determination of the so called fold curve connecting the limit points of the equilibrium path for a structure subjected to a variable imperfection. This is traditionally achieved by adding a well-chosen constraint equation requiring the criticality of the equilibrium. The crucial feature of the paper lies in the numerical resolution of the obtained augmented system. Indeed, it is solved using the Asymptotic Numerical Method (A.N.M.) which is well-known for its robustness. The theoretical framework upon which the A.N.M. and the extended system are based are presented. From a numerical point of view, it leads to an efficient treatment which takes the singularity of the tangent stiffness matrix into account. Emphasis is given on two specific types of geometrical imperfections. Eventually, the numerical isolation of an initial starting limit point is discussed

Influence of the Nonlinear Dynamic Behavior of Journal Bearings on Gear-Bearing Assemblies

International audienceJournal bearings cannot be considered as passive elements in gear-bearing assemblies, and the lubricant is recognized as playing an important role in the interactions between the shafts and the bearings. In order to take this influence into account, bearings are usually modeled by means of eight dynamic coefficients, i.e., asymmetric stiffness and damping matrices. In this paper, a nonlinear approach is proposed enabling the behavior of a gear-shaft-bearing assembly to be analyzed. A discrete finite element model is used for the shafts, and a specific gear element is introduced which accounts for non-linear time-varying mesh stiffness as well as tooth shape deviations. The meshing forces are internal system forces whereas the effects of the bearings on the shafts are taken to be external. A combination of the Newmark time integration scheme and the Newton-Raphson algorithm is used to simultaneously solve the contact problem for the gear, and the Reynolds equations for the bearings. The resulting algorithm is applied to a single stage geared system with two shafts, four bearings, a pinion and a gear while taking mass unbalance, eccentricity and meshing excitations into account. Several examples are presented which demonstrate the influence of bearing nonlinearity and the efficiency of the proposed model and numerical procedure

Buckling of Imperfect Elastic Shells using the Asymptotic Numerical Method

International audienceThis paper is concerned with stability behaviour and imperfection sensitivity of elastic shells. The aim is to determine the reduction of the critical buckling load as a function of the imperfection amplitude. For this purpose, the direct calculation of the so-called fold line connecting all the limit points of the equilibrium branches of the imperfect structures is performed. An augmented system demanding the criticality of the equilibrium is used. In order to solve the augmented system, the Asymptotic Numerical Method is used as an alternative to Newton-like incremental-iterative procedures. It results in a very robust and efficient path-following algorithm that takes the singularity of the tangent stiffness matrix into account. Two specific types of imperfections are detailed and several numerical examples are discussed

From MEMS to NEMS: Modelling and characterization of the non linear dynamics of resonators, a way to enhance the dynamic range

International audienceThe resonant sensing technique is highly sensitive, has the potential for large dynamic range, good linearity, low noiseand potentially low power. The detection principle is based on frequency change that is induced by rigidity changes in theresonator. In order to compensate the loss of performances when scaling sensors down to NEMS, it proves convenient to find physical conditions in order to maximise the signal variations and to push the limits of the linear behavior. To do so, a comprehensive model including the main sources of nonlinearities is needed. In the present paper, a process, characterization methods and above all an original analytical model are presented.Le mode de détection fréquentielle a pour avantages d'être extrêmement sensible, a le potentiel d'avoir une large gamme dynamique, peu sensible au bruit, une large gamme de linéarité et une faible consommation électrique. Le principe de détection est basé sur le changement de la fréquence de résonance induit par une modification de la raideur du résonateur. Afin de compenser la détérioration des performances lorsqu'on réduit les tailles des résonateurs des MEMS au NEMS, il s'avère important de trouver des conditions physiques permettant de maximiser le signal de détection et pousser les limites du comportement linéaire. Pour cela, un modèle complet qui prend en compte toutes les sources principales des non-linéarités est nécessaire. Dans ce papier, un modèle analytique sur la dynamique non linéaire de micro et nanorésonateurs ainsi qu'une validation expérimentale sont présentés

Nonlinear dynamics of nanoelectromechanical cantilevers based on nanowire piezoresistive detection

International audienceThe nonlinear dynamics of in-plane nanoelectromechanical cantilevers based on silicon nanowire piezoresistive detection is investigated using a comprehensive analytical model that remains valid up to large displacements in the case of electrostatic actuation. This multiphysics model takes into account geometric, inertial and electrostatic nonlinearities as well as the fringing field effects which are significant for thin resonators. The bistability as well as multistability limits are considered in order to provide close-form expressions of the critical amplitudes. Third order nonlinearity cancellation is analytically inspected and set via an optimal DC drive voltage which permits the actuation of the NEMS beyond its critical amplitude. It may result on a large enhancement of the sensor performances by driving optimally the nanocantilever at very large amplitude, while suppressing the hysteresis

Sensitive detection of nonlinear nanomechanical motion using capacitive signal down-mixing for resonant NEMS-based sensors

International audienceNanoelectromechanical systems (NEMS) are emerging as strong candidates for a host of important applications in semiconductor-based technology and fundamental science. At this level of miniaturization, the electric characterization of capacitive NEMS is a challenge. In fact, the high-frequency signals are normally cut off due to the limited bandwidth of the readout circuitry dominated by stray capacitance between the large amplifier and the high impedance tunneling junction. In order to overcome such limitations, some methods have been suggested: using several amplifier stages, inserting an LC resonator, or the scanning tunneling microscopy down-mixing readout technique. Nevertheless, these methods are efficient only at oscillations below the critical amplitude due to nonlinearities which induce noise mixing. In the present paper, a new characterization technique for resonant NEMS based on capacitive down-mixing has been developed and applied to M&NEMS accelerometers. The considered method is highly sensitive and permits a simple tuning of the signal to nonlinearity ratio

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

International audienc

Nonlinear techniques for wide-bandwidth resonant energy harvesting

International audienceEnergy harvesting from motion is presently receiving great worldwide attention as a means to power autonomous systems. Conventional linear vibration energy harvesters are usually designed to be resonantly tuned to the ambient dominant frequency. They have a narrow operating bandwidth that limits their application in real-world environments where the ambient vibrations have their energy distributed over a wide spectrum of frequencies, with significant predominance of low frequency components and frequency tuning is not always possible due to geometrical/dynamical constraints