Najib Kacem

Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors.

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.

Bifurcation topology tuning of a mixed behavior in nonlinear micromechanical resonators

We report the experimental observation of a four-bifurcation-point (or five possible amplitudes for a given frequency) behavior of electrostatically actuated micromechanical resonators, called the mixed (first hardening then softening) behavior. We also demonstrate both analytically and experimentally tuning the bifurcation topology of this behavior via an electrostatic mechanism. An analytical model allows for the qualitative as well as quantitative explanation of the experiments and serves as a simple tool for design of nonlinear micromechanical devices under high drive.

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.

Vibration Energy Localization from Nonlinear Quasi-Periodic Coupled Magnets

The present study investigates the modeling of the vibration energy localization from a nonlinear quasi-periodic system. The periodic system consists of n moving magnets held by n elastic structures and coupled by a nonlinear magnetic force. The quasi-periodic system has been obtained by mistuning one of the n elastic structures of the system. The mistuning of the periodic system has been achieved by changing either the linear mechanical stiffness or the mass of the elastic structures. The whole system has been modeled by forced Duffing equations for each degree of freedom. The forced Duffing equations involve the geometric nonlinearity and the mechanical damping of the elastic structures and the magnetic nonlinearity of the magnetic coupling. The governing equations, modelling the quasi-periodic system, have been solved using a numerical method combining the harmonic balance method and the asymptotic numerical method. This numerical technique allows transforming the nonlinearities present in the governing equations into purely polynomial quadratic terms. The obtained results of the stiffness and mass mistuning of the quasi-periodic system have been analyzed and discussed in depth. The obtained results showed that the mistuning and the coupling coefficients have a significant effect on the oscillation amplitude of the perturbed degree of freedom.

High Order Nonlinearities and Mixed Behavior in Micromechanical Resonators

This paper investigates the sensitivity of the third order nonlinearity cancelation 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 experimental observation of a strange attraction which can lead to a chaotic resonator.

Hysteresis Suppression in Nonlinear Mathieu M/NEMS Resonators

In order to compensate the loss of performances 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 a capacitive doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to electrical measurements of devices fabricated on 200mm SOI wafers and show a very good agreement. 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 sensors performances can be enhanced to the maximum bellow the pull-in amplitude, while keeping a linear behavior.Copyright