Sébastien Baguet

Stability control of nonlinear micromechanical resonators under simultaneous primary and superharmonic resonances

Fast effects of a slow excitation on the main resonance of a nonlinear micromechanical resonator are analytically and experimentally investigated. We show, in particular, how the bifurcation topology of an undesirable unstable behavior is modified when the resonator is simultaneously actuated at its primary and superharmonic resonances. A stabilization mechanism is proposed and demonstrated by increasing the superharmonic excitation.

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.

Pull-In Retarding in Nonlinear Nanoelectromechanical Resonators Under Superharmonic Excitation

In 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.

Steady-state dynamic behavior of an on-board rotor under combined base motions.

In the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to rotary inertia, gyroscopic inertia, and shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor’s rigid base. The use of Lagrange’s equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.

Dynamic analysis of a harmonically excited on-board rotor-bearing system

The aim of this paper is to investigate the dynamic behavior of an on-board rotor mounted on elastic bearings in the presence of rigid support movements. The proposed on-board rotor model is based on the Timoshenko beam finite elements. It takes into account the six deterministic translations and rotations of its rigid support and the geometric asymmetry of shaft and/or rigid disks. Thus the obtained linear equations of motion of the rotating rotor in bending contain time-varying parametric terms which can lead to lateral dynamic instability. The influence of rotational or translational motions of the support is analyzed by means of orbits of the rotor, responses in the time domain and fast Fourier transforms (FFTs).

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

A 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.

Real time sensing in the non linear regime of nems resonators

This paper reports the proof of concept of a nonlinear detection scheme for Nanoelectromechanical (NEMS) resonators for sensing applications. This set-up increases the dynamic range of a resonant sensor by operating it at amplitudes beyond its limit of linearity. Unlike other works in non-linear sensing, this method allows the tracking of the resonance frequency in real time, while being suitable for multi-mode operation and hence, single-particle detection for example.

Parametric Analysis of the Nonlinear Behavior of Rotating Structures

In nonlinear rotordynamics, techniques can take advantage of the periodic steady state behavior to predict quickly and accurately the mass unbalance response to a series of parameters, especially with the presence of certain nonlinearities which leads to nonlinear dynamics and complicated responses. The method proposed here calculates the response curve by combining Harmonic Balance Method, Alternating Frequency-Time method and continuation. The singular points where a stability change often arises are detected with the sign change of the Jacobian determinant and then located through a penalty method that increases the solving equation system by a completing constraint. Tracking these points, which provides an efficient way to analyze parametrically the nonlinear behavior of a system, can be fulfilled, once again, by the continuation technique.Copyright

Bifurcation Analysis of a Non-linear On-Board Rotor-Bearing System

The non-linear dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings and subject to rigid base excitations is investigated in this work. The proposed finite element rotor model takes into account the geometric asymmetry of shaft and/or rigid disk and considers six types of base deterministic motions (rotations and translations) and non-linear fluid film forces obtained from the Reynolds equation. The equations of motion contain time-varying parametric coefficients because of the geometric asymmetry of the rotor and the base rotations. In the case when sinusoidal excitations of the rotor base lead to periodic (harmonic and sub-harmonic) responses, an optimized shooting algorithm based on the non-linear Newmark time integration scheme is employed to solve the equations of motion. The non-linear phenomena observed in the on-board rotor-bearing system, such as period-doubling motion and chaos, are characterized by means of bifurcation diagrams, rotor orbits and Poincare maps.

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

In 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).Copyright